strategies for teaching problem solving in mathematics

High Impact Tutoring Built By Math Experts

Personalized standards-aligned one-on-one math tutoring for schools and districts

Free ready-to-use math resources

Hundreds of free math resources created by experienced math teachers to save time, build engagement and accelerate growth

20 Effective Math Strategies To Approach Problem-Solving 

Katie Keeton

Math strategies for problem-solving help students use a range of approaches to solve many different types of problems. It involves identifying the problem and carrying out a plan of action to find the answer to mathematical problems.  

Problem-solving skills are essential to math in the general classroom and real-life. They require logical reasoning and critical thinking skills. Students must be equipped with strategies to help them find solutions to problems.

This article explores mathematical problem solving strategies, logical reasoning and critical thinking skills to help learners with solving math word problems independently in real-life situations. 

What are problem-solving strategies?

Problem-solving strategies in math are methods students can use to figure out solutions to math problems. Some problem-solving strategies: 

• Draw a model
• Use different approaches
• Check the inverse to make sure the answer is correct

Students need to have a toolkit of math problem-solving strategies at their disposal to provide different ways to approach math problems. This makes it easier to find solutions and understand math better. 

Strategies can help guide students to the solution when it is difficult ot know when to start.

The ultimate guide to problem solving techniques

Download these ready-to-go problem solving techniques that every student should know. Includes printable tasks for students including challenges, short explanations for teachers with questioning prompts.

20 Math Strategies For Problem-Solving

Different problem-solving math strategies are required for different parts of the problem. It is unlikely that students will use the same strategy to understand and solve the problem. 

Here are 20 strategies to help students develop their problem-solving skills. 

Strategies to understand the problem

Strategies that help students understand the problem before solving it helps ensure they understand: 

• The context
• What the key information is
• How to form a plan to solve it

Following these steps leads students to the correct solution and makes the math word problem easier .

Here are five strategies to help students understand the content of the problem and identify key information. 

1. Read the problem aloud

Read a word problem aloud to help understand it. Hearing the words engages auditory processing. This can make it easier to process and comprehend the context of the situation.

2. Highlight keywords 

When keywords are highlighted in a word problem, it helps the student focus on the essential information needed to solve it. Some important keywords help determine which operation is needed.  For example, if the word problem asks how many are left, the problem likely requires subtraction.  Ensure students highlight the keywords carefully and do not highlight every number or keyword. There is likely irrelevant information in the word problem.

3. Summarize the information

Read the problem aloud, highlight the key information and then summarize the information. Students can do this in their heads or write down a quick summary.  Summaries should include only the important information and be in simple terms that help contextualize the problem.

4. Determine the unknown

A common problem that students have when solving a word problem is misunderstanding what they are solving. Determine what the unknown information is before finding the answer.  Often, a word problem contains a question where you can find the unknown information you need to solve. For example, in the question ‘How many apples are left?’ students need to find the number of apples left over.

5. Make a plan

Once students understand the context of the word problem, have dentified the important information and determined the unknown, they can make a plan to solve it.  The plan will depend on the type of problem. Some problems involve more than one step to solve them as some require more than one answer.  Encourage students to make a list of each step they need to take to solve the problem before getting started.

Strategies for solving the problem 

1. draw a model or diagram.

Students may find it useful to draw a model, picture, diagram, or other visual aid to help with the problem solving process.  It can help to visualize the problem to understand the relationships between the numbers in the problem. In turn, this helps students see the solution.

Similarly, you could draw a model to represent the objects in the problem:

2. Act it out

This particular strategy is applicable at any grade level but is especially helpful in math investigation in elementary school . It involves a physical demonstration or students acting out the problem using movements, concrete resources and math manipulatives .  When students act out a problem, they can visualize and contectualize the word problem in another way and secure an understanding of the math concepts.  The examples below show how 1st-grade students could “act out” an addition and subtraction problem:

3. Work backwards

Working backwards is a popular problem-solving strategy. It involves starting with a possible solution and deciding what steps to take to arrive at that solution.  This strategy can be particularly helpful when students solve math word problems involving multiple steps. They can start at the end and think carefully about each step taken as opposed to jumping to the end of the problem and missing steps in between.

For example,

To solve this problem working backwards, start with the final condition, which is Sam’s grandmother’s age (71) and work backwards to find Sam’s age. Subtract 20 from the grandmother’s age, which is 71.  Then, divide the result by 3 to get Sam’s age. 71 – 20 = 51 51 ÷ 3 = 17 Sam is 17 years old.

4. Write a number sentence

When faced with a word problem, encourage students to write a number sentence based on the information. This helps translate the information in the word problem into a math equation or expression, which is more easily solved.  It is important to fully understand the context of the word problem and what students need to solve before writing an equation to represent it.

5. Use a formula

Specific formulas help solve many math problems. For example, if a problem asks students to find the area of a rug, they would use the area formula (area = length × width) to solve.   Make sure students know the important mathematical formulas they will need in tests and real-life. It can help to display these around the classroom or, for those who need more support, on students’ desks.

Strategies for checking the solution 

Once the problem is solved using an appropriate strategy, it is equally important to check the solution to ensure it is correct and makes sense. 

There are many strategies to check the solution. The strategy for a specific problem is dependent on the problem type and math content involved.

Here are five strategies to help students check their solutions. 

1. Use the Inverse Operation

For simpler problems, a quick and easy problem solving strategy is to use the inverse operation. For example, if the operation to solve a word problem is 56 ÷ 8 = 7 students can check the answer is correct by multiplying 8 × 7. As good practice, encourage students to use the inverse operation routinely to check their work. 

2. Estimate to check for reasonableness

Once students reach an answer, they can use estimation or rounding to see if the answer is reasonable.  Round each number in the equation to a number that’s close and easy to work with, usually a multiple of ten.  For example, if the question was 216 ÷ 18 and the quotient was 12, students might round 216 to 200 and round 18 to 20. Then use mental math to solve 200 ÷ 20, which is 10.  When the estimate is clear the two numbers are close. This means your answer is reasonable. 

3. Plug-In Method

This method is particularly useful for algebraic equations. Specifically when working with variables.  To use the plug-in method, students solve the problem as asked and arrive at an answer. They can then plug the answer into the original equation to see if it works. If it does, the answer is correct.

If students use the equation 20m+80=300 to solve this problem and find that m = 11, they can plug that value back into the equation to see if it is correct. 20m + 80 = 300 20 (11) + 80 = 300 220 + 80 = 300 300 = 300 ✓

4. Peer Review

Peer review is a great tool to use at any grade level as it promotes critical thinking and collaboration between students. The reviewers can look at the problem from a different view as they check to see if the problem was solved correctly.   Problem solvers receive immediate feedback and the opportunity to discuss their thinking with their peers. This strategy is effective with mixed-ability partners or similar-ability partners. In mixed-ability groups, the partner with stronger skills provides guidance and support to the partner with weaker skills, while reinforcing their own understanding of the content and communication skills.  If partners have comparable ability levels and problem-solving skills, they may find that they approach problems differently or have unique insights to offer each other about the problem-solving process.

5. Use a Calculator

A calculator can be introduced at any grade level but may be best for older students who already have a foundational understanding of basic math operations. Provide students with a calculator to allow them to check their solutions independently, accurately, and quickly. Since calculators are so readily available on smartphones and tablets, they allow students to develop practical skills that apply to real-world situations.  

Step-by-step problem-solving processes for your classroom

In his book, How to Solve It , published in 1945, mathematician George Polya introduced a 4-step process to solve problems. 

Polya’s 4 steps include:

• Understand the problem
• Devise a plan
• Carry out the plan

Today, in the style of George Polya, many problem-solving strategies use various acronyms and steps to help students recall. 

Many teachers create posters and anchor charts of their chosen process to display in their classrooms. They can be implemented in any elementary, middle school or high school classroom. 

Here are 5 problem-solving strategies to introduce to students and use in the classroom.

How Third Space Learning improves problem-solving 

Resources .

Third Space Learning offers a free resource library is filled with hundreds of high-quality resources. A team of experienced math experts carefully created each resource to develop students mental arithmetic, problem solving and critical thinking. 

Explore the range of problem solving resources for 2nd to 8th grade students. 

One-on-one tutoring 

Third Space Learning offers one-on-one math tutoring to help students improve their math skills. Highly qualified tutors deliver high-quality lessons aligned to state standards. 

Former teachers and math experts write all of Third Space Learning’s tutoring lessons. Expertly designed lessons follow a “my turn, follow me, your turn” pedagogy to help students move from guided instruction and problem-solving to independent practice. 

Throughout each lesson, tutors ask higher-level thinking questions to promote critical thinking and ensure students are developing a deep understanding of the content and problem-solving skills.

Problem-solving

Educators can use many different strategies to teach problem-solving and help students develop and carry out a plan when solving math problems. Incorporate these math strategies into any math program and use them with a variety of math concepts, from whole numbers and fractions to algebra. 

Teaching students how to choose and implement problem-solving strategies helps them develop mathematical reasoning skills and critical thinking they can apply to real-life problem-solving.

READ MORE :

• 8 Common Core math examples
• Tier 3 Interventions: A School Leaders Guide
• Tier 2 Interventions: A School Leaders Guide
• Tier 1 Interventions: A School Leaders Guide

There are many different strategies for problem-solving; Here are 5 problem-solving strategies: • draw a model  • act it out  • work backwards  • write a number sentence • use a formula

Here are 10 strategies for problem-solving: • Read the problem aloud • Highlight keywords • Summarize the information • Determine the unknown • Make a plan • Draw a model  • Act it out  • Work backwards  • Write a number sentence • Use a formula

1. Understand the problem 2. Devise a plan 3. Carry out the plan 4. Look back

Some strategies you can use to solve challenging math problems are: breaking the problem into smaller parts, using diagrams or models, applying logical reasoning, and trying different approaches.

Related articles

Why Student Centered Learning Is Important: A Guide For Educators

13 Effective Learning Strategies: A Guide to Using them in your Math Classroom

Differentiated Instruction: 9 Differentiated Curriculum And Instruction Strategies For Teachers 

5 Math Mastery Strategies To Incorporate Into Your 4th and 5th Grade Classrooms

Ultimate Guide to Metacognition [FREE]

Looking for a summary on metacognition in relation to math teaching and learning?

Check out this guide featuring practical examples, tips and strategies to successfully embed metacognition across your school to accelerate math growth.

Privacy Overview

Teaching Problem Solving in Math

• Freebies , Math , Planning

Every year my students can be fantastic at math…until they start to see math with words. For some reason, once math gets translated into reading, even my best readers start to panic. There is just something about word problems, or problem-solving, that causes children to think they don’t know how to complete them.

Every year in math, I start off by teaching my students problem-solving skills and strategies. Every year they moan and groan that they know them. Every year – paragraph one above. It was a vicious cycle. I needed something new.

I put together a problem-solving unit that would focus a bit more on strategies and steps in hopes that that would create problem-solving stars.

The Problem Solving Strategies

First, I wanted to make sure my students all learned the different strategies to solve problems, such as guess-and-check, using visuals (draw a picture, act it out, and modeling it), working backward, and organizational methods (tables, charts, and lists). In the past, I had used worksheet pages that would introduce one and provide the students with plenty of problems practicing that one strategy. I did like that because students could focus more on practicing the strategy itself, but I also wanted students to know when to use it, too, so I made sure they had both to practice.

I provided students with plenty of practice of the strategies, such as in this guess-and-check game.

There’s also this visuals strategy wheel practice.

I also provided them with paper dolls and a variety of clothing to create an organized list to determine just how many outfits their “friend” would have.

Then, as I said above, we practiced in a variety of ways to make sure we knew exactly when to use them. I really wanted to make sure they had this down!

Anyway, after I knew they had down the various strategies and when to use them, then we went into the actual problem-solving steps.

The Problem Solving Steps

I wanted students to understand that when they see a story problem, it isn’t scary. Really, it’s just the equation written out in words in a real-life situation. Then, I provided them with the “keys to success.”

S tep 1 – Understand the Problem.   To help students understand the problem, I provided them with sample problems, and together we did five important things:

• read the problem carefully
• restated the problem in our own words
• crossed out unimportant information
• circled any important information
• stated the goal or question to be solved

We did this over and over with example problems.

Once I felt the students had it down, we practiced it in a game of problem-solving relay. Students raced one another to see how quickly they could get down to the nitty-gritty of the word problems. We weren’t solving the problems – yet.

Then, we were on to Step 2 – Make a Plan . We talked about how this was where we were going to choose which strategy we were going to use. We also discussed how this was where we were going to figure out what operation to use. I taught the students Sheila Melton’s operation concept map.

We talked about how if you know the total and know if it is equal or not, that will determine what operation you are doing. So, we took an example problem, such as:

Sheldon wants to make a cupcake for each of his 28 classmates. He can make 7 cupcakes with one box of cupcake mix. How many boxes will he need to buy?

We started off by asking ourselves, “Do we know the total?” We know there are a total of 28 classmates. So, yes, we are separating. Then, we ask, “Is it equal?” Yes, he wants to make a cupcake for EACH of his classmates. So, we are dividing: 28 divided by 7 = 4. He will need to buy 4 boxes. (I actually went ahead and solved it here – which is the next step, too.)

Step 3 – Solving the problem . We talked about how solving the problem involves the following:

• taking our time
• working the problem out
• showing all our work
• estimating the answer
• using thinking strategies

We talked specifically about thinking strategies. Just like in reading, there are thinking strategies in math. I wanted students to be aware that sometimes when we are working on a problem, a particular strategy may not be working, and we may need to switch strategies. We also discussed that sometimes we may need to rethink the problem, to think of related content, or to even start over. We discussed these thinking strategies:

• switch strategies or try a different one
• rethink the problem
• think of related content
• decide if you need to make changes
• check your work
• but most important…don’t give up!

To make sure they were getting in practice utilizing these thinking strategies, I gave each group chart paper with a letter from a fellow “student” (not a real student), and they had to give advice on how to help them solve their problem using the thinking strategies above.

Finally, Step 4 – Check It.   This is the step that students often miss. I wanted to emphasize just how important it is! I went over it with them, discussing that when they check their problems, they should always look for these things:

• compare your answer to your estimate
• check for reasonableness
• check your calculations
• add the units
• restate the question in the answer
• explain how you solved the problem

Then, I gave students practice cards. I provided them with example cards of “students” who had completed their assignments already, and I wanted them to be the teacher. They needed to check the work and make sure it was completed correctly. If it wasn’t, then they needed to tell what they missed and correct it.

To demonstrate their understanding of the entire unit, we completed an adorable lap book (my first time ever putting together one or even creating one – I was surprised how well it turned out, actually). It was a great way to put everything we discussed in there.

Once we were all done, students were officially Problem Solving S.T.A.R.S. I just reminded students frequently of this acronym.

Stop – Don’t rush with any solution; just take your time and look everything over.

Think – Take your time to think about the problem and solution.

Act  – Act on a strategy and try it out.

Review – Look it over and see if you got all the parts.

Wow, you are a true trooper sticking it out in this lengthy post! To sum up the majority of what I have written here, I have some problem-solving bookmarks FREE to help you remember and to help your students!

You can grab these problem-solving bookmarks for FREE by clicking here .

You can do any of these ideas without having to purchase anything. However, if you are looking to save some time and energy, then they are all found in my Math Workshop Problem Solving Unit . The unit is for grade three, but it  may work for other grade levels. The practice problems are all for the early third-grade level.

• freebie , Math Workshop , Problem Solving

FIND IT NOW!

Check me out on tpt.

CHECK THESE OUT

5th Grade Math Workshop Growing Bundle- 9 Units

Three Types of Rocks and Minerals with Rock Cycle Circle Book

Want to save time?

COPYRIGHT © 2016-2024. The Owl Teacher | Privacy page | Disclosure Page | Shipping | Returns/Refunds

BOGO on EVERYTHING!

Want to create or adapt books like this? Learn more about how Pressbooks supports open publishing practices.

5 Teaching Mathematics Through Problem Solving

Janet Stramel

In his book “How to Solve It,” George Pólya (1945) said, “One of the most important tasks of the teacher is to help his students. This task is not quite easy; it demands time, practice, devotion, and sound principles. The student should acquire as much experience of independent work as possible. But if he is left alone with his problem without any help, he may make no progress at all. If the teacher helps too much, nothing is left to the student. The teacher should help, but not too much and not too little, so that the student shall have a reasonable share of the work.” (page 1)

What is a problem  in mathematics? A problem is “any task or activity for which the students have no prescribed or memorized rules or methods, nor is there a perception by students that there is a specific ‘correct’ solution method” (Hiebert, et. al., 1997). Problem solving in mathematics is one of the most important topics to teach; learning to problem solve helps students develop a sense of solving real-life problems and apply mathematics to real world situations. It is also used for a deeper understanding of mathematical concepts. Learning “math facts” is not enough; students must also learn how to use these facts to develop their thinking skills.

According to NCTM (2010), the term “problem solving” refers to mathematical tasks that have the potential to provide intellectual challenges for enhancing students’ mathematical understanding and development. When you first hear “problem solving,” what do you think about? Story problems or word problems? Story problems may be limited to and not “problematic” enough. For example, you may ask students to find the area of a rectangle, given the length and width. This type of problem is an exercise in computation and can be completed mindlessly without understanding the concept of area. Worthwhile problems  includes problems that are truly problematic and have the potential to provide contexts for students’ mathematical development.

There are three ways to solve problems: teaching for problem solving, teaching about problem solving, and teaching through problem solving.

Teaching for problem solving begins with learning a skill. For example, students are learning how to multiply a two-digit number by a one-digit number, and the story problems you select are multiplication problems. Be sure when you are teaching for problem solving, you select or develop tasks that can promote the development of mathematical understanding.

Teaching about problem solving begins with suggested strategies to solve a problem. For example, “draw a picture,” “make a table,” etc. You may see posters in teachers’ classrooms of the “Problem Solving Method” such as: 1) Read the problem, 2) Devise a plan, 3) Solve the problem, and 4) Check your work. There is little or no evidence that students’ problem-solving abilities are improved when teaching about problem solving. Students will see a word problem as a separate endeavor and focus on the steps to follow rather than the mathematics. In addition, students will tend to use trial and error instead of focusing on sense making.

Teaching through problem solving  focuses students’ attention on ideas and sense making and develops mathematical practices. Teaching through problem solving also develops a student’s confidence and builds on their strengths. It allows for collaboration among students and engages students in their own learning.

Consider the following worthwhile-problem criteria developed by Lappan and Phillips (1998):

• The problem has important, useful mathematics embedded in it.
• The problem requires high-level thinking and problem solving.
• The problem contributes to the conceptual development of students.
• The problem creates an opportunity for the teacher to assess what his or her students are learning and where they are experiencing difficulty.
• The problem can be approached by students in multiple ways using different solution strategies.
• The problem has various solutions or allows different decisions or positions to be taken and defended.
• The problem encourages student engagement and discourse.
• The problem connects to other important mathematical ideas.
• The problem promotes the skillful use of mathematics.
• The problem provides an opportunity to practice important skills.

Of course, not every problem will include all of the above. Sometimes, you will choose a problem because your students need an opportunity to practice a certain skill.

Key features of a good mathematics problem includes:

• It must begin where the students are mathematically.
• The feature of the problem must be the mathematics that students are to learn.
• It must require justifications and explanations for both answers and methods of solving.

Problem solving is not a  neat and orderly process. Think about needlework. On the front side, it is neat and perfect and pretty.

But look at the b ack.

It is messy and full of knots and loops. Problem solving in mathematics is also like this and we need to help our students be “messy” with problem solving; they need to go through those knots and loops and learn how to solve problems with the teacher’s guidance.

When you teach through problem solving , your students are focused on ideas and sense-making and they develop confidence in mathematics!

Mathematics Tasks and Activities that Promote Teaching through Problem Solving

Choosing the Right Task

Selecting activities and/or tasks is the most significant decision teachers make that will affect students’ learning. Consider the following questions:

• Teachers must do the activity first. What is problematic about the activity? What will you need to do BEFORE the activity and AFTER the activity? Additionally, think how your students would do the activity.
• What mathematical ideas will the activity develop? Are there connections to other related mathematics topics, or other content areas?
• Can the activity accomplish your learning objective/goals?

Low Floor High Ceiling Tasks

By definition, a “ low floor/high ceiling task ” is a mathematical activity where everyone in the group can begin and then work on at their own level of engagement. Low Floor High Ceiling Tasks are activities that everyone can begin and work on based on their own level, and have many possibilities for students to do more challenging mathematics. One gauge of knowing whether an activity is a Low Floor High Ceiling Task is when the work on the problems becomes more important than the answer itself, and leads to rich mathematical discourse [Hover: ways of representing, thinking, talking, agreeing, and disagreeing; the way ideas are exchanged and what the ideas entail; and as being shaped by the tasks in which students engage as well as by the nature of the learning environment].

The strengths of using Low Floor High Ceiling Tasks:

• Allows students to show what they can do, not what they can’t.
• Provides differentiation to all students.
• Promotes a positive classroom environment.
• Advances a growth mindset in students
• Aligns with the Standards for Mathematical Practice

Examples of some Low Floor High Ceiling Tasks can be found at the following sites:

• YouCubed – under grades choose Low Floor High Ceiling
• NRICH Creating a Low Threshold High Ceiling Classroom
• Inside Mathematics Problems of the Month

Math in 3-Acts

Math in 3-Acts was developed by Dan Meyer to spark an interest in and engage students in thought-provoking mathematical inquiry. Math in 3-Acts is a whole-group mathematics task consisting of three distinct parts:

Act One is about noticing and wondering. The teacher shares with students an image, video, or other situation that is engaging and perplexing. Students then generate questions about the situation.

In Act Two , the teacher offers some information for the students to use as they find the solutions to the problem.

Act Three is the “reveal.” Students share their thinking as well as their solutions.

“Math in 3 Acts” is a fun way to engage your students, there is a low entry point that gives students confidence, there are multiple paths to a solution, and it encourages students to work in groups to solve the problem. Some examples of Math in 3-Acts can be found at the following websites:

• Dan Meyer’s Three-Act Math Tasks
• Graham Fletcher3-Act Tasks ]
• Math in 3-Acts: Real World Math Problems to Make Math Contextual, Visual and Concrete

Number Talks

Number talks are brief, 5-15 minute discussions that focus on student solutions for a mental math computation problem. Students share their different mental math processes aloud while the teacher records their thinking visually on a chart or board. In addition, students learn from each other’s strategies as they question, critique, or build on the strategies that are shared.. To use a “number talk,” you would include the following steps:

• The teacher presents a problem for students to solve mentally.
• Provide adequate “ wait time .”
• The teacher calls on a students and asks, “What were you thinking?” and “Explain your thinking.”
• For each student who volunteers to share their strategy, write their thinking on the board. Make sure to accurately record their thinking; do not correct their responses.
• Invite students to question each other about their strategies, compare and contrast the strategies, and ask for clarification about strategies that are confusing.

“Number Talks” can be used as an introduction, a warm up to a lesson, or an extension. Some examples of Number Talks can be found at the following websites:

• Inside Mathematics Number Talks
• Number Talks Build Numerical Reasoning

Saying “This is Easy”

“This is easy.” Three little words that can have a big impact on students. What may be “easy” for one person, may be more “difficult” for someone else. And saying “this is easy” defeats the purpose of a growth mindset classroom, where students are comfortable making mistakes.

When the teacher says, “this is easy,” students may think,

• “Everyone else understands and I don’t. I can’t do this!”
• Students may just give up and surrender the mathematics to their classmates.
• Students may shut down.

Instead, you and your students could say the following:

• “I think I can do this.”
• “I have an idea I want to try.”
• “I’ve seen this kind of problem before.”

Tracy Zager wrote a short article, “This is easy”: The Little Phrase That Causes Big Problems” that can give you more information. Read Tracy Zager’s article here.

Using “Worksheets”

Do you want your students to memorize concepts, or do you want them to understand and apply the mathematics for different situations?

What is a “worksheet” in mathematics? It is a paper and pencil assignment when no other materials are used. A worksheet does not allow your students to use hands-on materials/manipulatives [Hover: physical objects that are used as teaching tools to engage students in the hands-on learning of mathematics]; and worksheets are many times “naked number” with no context. And a worksheet should not be used to enhance a hands-on activity.

Students need time to explore and manipulate materials in order to learn the mathematics concept. Worksheets are just a test of rote memory. Students need to develop those higher-order thinking skills, and worksheets will not allow them to do that.

One productive belief from the NCTM publication, Principles to Action (2014), states, “Students at all grade levels can benefit from the use of physical and virtual manipulative materials to provide visual models of a range of mathematical ideas.”

You may need an “activity sheet,” a “graphic organizer,” etc. as you plan your mathematics activities/lessons, but be sure to include hands-on manipulatives. Using manipulatives can

• Provide your students a bridge between the concrete and abstract
• Serve as models that support students’ thinking
• Provide another representation
• Support student engagement
• Give students ownership of their own learning.

Adapted from “ The Top 5 Reasons for Using Manipulatives in the Classroom ”.

any task or activity for which the students have no prescribed or memorized rules or methods, nor is there a perception by students that there is a specific ‘correct’ solution method

should be intriguing and contain a level of challenge that invites speculation and hard work, and directs students to investigate important mathematical ideas and ways of thinking toward the learning

involves teaching a skill so that a student can later solve a story problem

when we teach students how to problem solve

teaching mathematics content through real contexts, problems, situations, and models

a mathematical activity where everyone in the group can begin and then work on at their own level of engagement

20 seconds to 2 minutes for students to make sense of questions

Mathematics Methods for Early Childhood Copyright © 2021 by Janet Stramel is licensed under a Creative Commons Attribution 4.0 International License , except where otherwise noted.

Share This Book

• Grades 6-12
• School Leaders

Have you entered to win this adorable math giveaway? ✨

Every product is independently selected by (obsessive) editors. Things you buy through our links may earn us a commission.

27 Essential Math Strategies for Teaching Students of All Ages

Even veteran teachers need to read these.

What are the essential strategies for good, effective math teaching? Everyone wants kids to succeed in math, but how best to do that? In most districts, standardized tests are a high-stakes way to measure students’ understanding, yet few want to teach to the test. Over-reliance on test prep materials and “drill and kill” worksheets can make math repetitive, boring, and devoid of true understanding for kids.

The reality is that motivating, effective instruction and good test scores aren’t mutually exclusive. Being intentional and using creative approaches to your teaching can get students excited about math and successful in their understanding. Here are some essential strategies and attitudes in teaching mathematics that can help make this your class’s best math year ever!

1. You are all mathematicians

Noted math educator Marilyn Burns wrote a classic book entitled Math: Facing an American Phobia (Math Solutions, 1998). The title kind of says it all. In America we have a cultural belief that you have to be born good at math because as Barbie once said, “Math is hard.”

On the other hand, we have a generally held belief that everyone can and should learn to read. If you were to tell a room of adults you hate math, you would get plenty of affirmation. Try telling them you hate reading. You’ll see a different reaction.

As teachers of young children, we need to help our students understand and believe that we are all mathematicians, just like we are all readers. We can do this by giving kids positive and successful experiences with math from an early age and pointing out to them how we all are constantly doing math on a daily basis.

How to teach it:

Try this with your students. Ask them to write down every bit of math they did at home the day before. Did they look at a clock and check the time? Math. Did they use any words reflecting spatial sense like next to , under , over , right , left ? Math. Did they hear anything about weather like the temperature for the day? Math. And it goes on. Make clear to them that they are already daily mathematicians and that in school you are going to help them in becoming even more expert in the field!

Use targeted feedback to support this. Rather than general statements like “That was good,” it’s better to say, “You put those two numbers together perfectly. That is the exact right answer and perfect mathematics!” Now the student knows what was good and can reflect on that.

The reality is everyone can do math and do it well, but as the teacher, you have to believe that to be true and help your students truly experience it and believe it too.

2. You can do it! … You did it!

Becoming expert at anything is usually not easy. There is work involved, but there’s a great feeling of satisfaction and accomplishment when we work hard and see results. Rather than success being a function of how much math talent we’re born with, kids need to hear from teachers that anyone who works hard can succeed. Practice and persistence make you good at math or anything else.

Ask students about experiences they have had with sports. How long did it take to learn to throw a ball? Kick a goal? Make a basket? No one is born with these skills. They take lots of practice. Well, so does math. But just like sports, practice in math can be fun because the results are visible. ADVERTISEMENT

With this in mind, one simple thing you can do at the beginning of the year is to give everyone a math assessment of all the concepts they will be expected to master in the year. Start it off with some skills from the previous year, but put in everything else.

Tell students first that this assessment is to help you know what you have to teach this year. If they all know how to count to 10 already, you won’t spend a lot of time on that, maybe just a little practice. Tell them to circle anything they don’t know how to do yet and want to learn. They are helping you find out what to teach. Explain that these assessments (some teachers call them inventories) don’t get graded, they are only to help you as the teacher to plan. Because that is what it’s really for.

At the end of the year, give students the same assessment again. Score it and hand it back along with the original so they can compare. When they see how much they have learned, they will feel like they received a gold medal in mathematics!

Try it: Free Printable Growth Mindset Posters

3. Assessment (aka: testing) is not a dirty word

Assessment is not something separate from your instruction. In fact, assessment, like that first math assessment of the year mentioned above, drives instruction. It should be integrated into your planning.

Exit tickets or questions, quizzes, open-ended questions, and meaningful homework assignments confirm what students have mastered or not mastered and let you know what needs to happen next.

Additionally, asking students to explain their thinking orally or in writing is a great way to determine their level of understanding. A capable digital resource, designed to monitor your students in real time, can also be an invaluable tool, providing actionable data to inform your instruction along the way if you have access. Remember, it’s not about generating grades. It’s about learning what needs to be taught.

Try it: Free Printable Exit Ticket Templates

4. Rome was not built in a day

Sometimes we get stuck in a mindset of “a lesson a day” in order to get through the content. However, we should keep our pacing flexible, or kids can fall behind. Walk through your classroom as students work on problems and observe the dynamics.

Talk with them individually and ask questions to gauge understanding. In response, make decisions to go faster or slower or put students in flexible groups as needed. Flexible groups could be together for the lesson, the week, the concept, or however long it makes sense. It can help you individualize instruction more easily.

5. You’re motivated = they’re motivated

Generally, students will become excited about a subject if their teacher is excited about it. However, it’s hard to be excited about teaching math if your understanding hasn’t changed since you learned it in elementary school. When you have confidence in your own mathematical expertise, then you can teach math confidently and joyfully.

How to do this? Consider attending a conference on math teaching. Don’t be intimidated. It’s not all math geniuses trading formulas. It’s teachers sharing best practices. Most every state has a branch of NCTM (National Council of Teachers of Mathematics) that provides programs from preschool through high school. It’s very motivating. Or read a book on math-teaching ideas by folks like John Van de Walle, Marilyn Burns, Susan O’Connell, or other leading math educators. Get together with a couple of colleagues and start a book group. These books are full of ideas, lessons, and motivation. We need it just like the kids do.

Try it: Best Education Conferences in 2024-2025

6. The eight math commandments

When the Common Core State Standards were first released, most people focused on the content standards. At the beginning of the document, however, there were eight math-practice standards. These are qualities and attitudes of young mathematicians that are desirable to develop in all kids. They are:

• Make sense of problems & persevere in solving them
• Reason abstractly & quantitatively
• Construct viable arguments & critique the reasoning of others
• Model with mathematics
• Use appropriate tools strategically
• Attend to precision
• Look for & make use of structure
• Look for & express regularity in repeated reasoning

While the document is written for adults, here’s the kid-language version. It makes a great poster and discussion starter:

• I can solve problems without giving up.
• I can think about numbers in many ways.
• I can explain my thinking and try to understand others.
• I can show my work in many ways.
• I can use math tools and explain why I chose them.
• I can work carefully and check my work.
• I can use what I know to solve problems.
• I can solve problems by looking for rules and patterns.

For good lesson ideas and teaching tips for each standard, check out Putting the Practices Into Action by Susan O’Connell and John SanGiovanni (Heinemann, 2013).

7. Talk the math and walk the math

Communicating about math helps students process new learning and build on their thinking. Engage students during conversations and have them describe why they solved a problem in a certain way. “My goal is to get information about what students are thinking and use that to guide my instruction, as opposed to just telling them information and asking them to parrot things back,” says Delise Andrews, who taught math (K–8) and is now a grade 3–5 math coordinator in the Lincoln Public Schools in Nebraska.

Instead of seeking a specific answer, Andrews wants to have deeper discussions to figure out what a student knows and understands. “True learning happens a lot around talking and doing math—not just drilling,” she says. Of course, this math strategy not only requires students to feel comfortable expressing their mathematical thinking, but also assumes that they have been trained to listen respectfully to the reasoning of their classmates.

Learn more:  Free Let’s Talk Math Poster

8. Give students time to reflect

Sometimes as teachers we get so caught up in meeting the demands of the curriculum and the pressure to “get it all done” that we don’t give students the time to reflect on their learning.

Students can be asked to reflect in writing at the end of an assignment or lesson, via class or small-group discussion, or in interviews with the teacher. It’s important to give them the time to think about and articulate the meaning of what they’ve learned, what they still don’t understand, and what they want to learn more about.

This provides useful information for the teacher and helps the student monitor their own progress and think strategically about how they approach mathematics. To keep it simple and build a routine, you can give students an index card at the end of a lesson and ask them to write a thought about each of those three things:

• What I learned.
• What I still don’t understand.
• What I want to learn more about.

Not only will this give you invaluable feedback, but it gives students the clear message that you care about what’s happening with them and their learning.

9. Allow productive struggle

Don’t spoon-feed kids answers and strategies. Pose the question and allow time and attitude for some “bumping around.” That’s what real life is like. We don’t always know how to solve a problem, like buying enough fertilizer for the lawn, but we can figure it out. We might make some mistakes, but we can get there.

Generally, provide as little information as possible but enough so students can be productive. Effective math teaching supports students as they grapple with mathematical ideas and relationships. Allow them to discover what works and experience setbacks along the way as they adopt a growth mindset about mathematics. This also involves wait time. How much time do you allow kids before you expect an answer? We feel time-pressured in our teaching, so we tend to want to “move it along.” Resist this. If no on answers, just wait. Someone will eventually venture a guess. You can work from there, but give them time to think and process.

10. Get hands-on

Developmentally, the first stage for almost any math learning should be physical. Then pictorial, then symbolic. From counting to algebraic equations, the physical comes first. To do that, you need “stuff” to get physical with.

You can use almost anything to model concepts like counting, operations, measurement, data, money. Dried beans work. Cubes work. Tiles work. Buttons work. Almost any set of small objects works. There are also place value models, geometric shapes, number tiles, and so on. Bring out the math tools too! Calculators, scales, rulers, measuring tapes, balances, measuring cups, all of it. Experiencing math ideas in a hands-on way always leads to deeper understanding.

Try it: Best Math Manipulatives for the Classroom

11. Explore!

Whatever you get involved in with math and kids, give them time to explore first. This is particularly true for math tools and materials.

If you’re introducing calculators or scales or rulers or number cards, first make an agreement with the class. Something along the lines of, “You have 10 minutes to play with this, explore it, learn what you can about it, and then we’ll share back what you notice. After that, I’ll be giving you some directions on what I’d like to do with it today.” They’re going to play with it anyway, so you might as well use that inclination to your advantage, and it will also open up their thinking at the beginning and value it.

12. In a group and by yourself

As you plan your lessons, try to allow time for individual work, partner work, and small-group work. Kids need time in all three contexts.

Everyone needs that individual time to work things out for themselves, work at their own pace, and to be properly assessed. Partner groups give students a chance to support one another and learn how to cooperate with others on a small scale in an easily managed environment. Small groups allow for diverse thinking, learning from others, and developing mutual cooperation and listening skills.

13. The math should do something

Kids get excited about math when they get to  solve real-life problems.  

For instance, when teaching 4th graders how to determine area, do this Haunted Mansion project. Kids get a letter from the fictitious owners of the Haunted Mansion Fun House. The owners want a plan for designing their new fun house. It has to include a certain perimeter, area, and volume. Kids can’t wait to learn how to do it and are incredibly proud when they use math to make a model of the fun house.

14. Play math games

When you play a game, the number of repetitions of certain tasks is surprisingly large. Just consider how many times you roll two dice together and add them in a board game like Monopoly. That’s practice, practice, practice, but it doesn’t feel like it. No one complains or even realizes how many times it’s happening. You can find a game or make one for every math concept you will teach. And kids will thank you for it!

Games are an excellent way to make the learning more fun while simultaneously promoting strategic mathematical thinking,  computational fluency , and understanding of operations. Games are especially good for kinesthetic learners and foster a home-school connection when they’re sent home for extra practice.

Try it: First Grade Math Games

15. Establish effective math routines

Students generally feel confident and competent in the classroom when they know what to do and why they’re doing it. Establishing routines in your math class and training kids to use them can make math class efficient, effective, and fun!

For example, consider starting your class with a number sense routine and finishing with reflection on the day’s learning. Rich, productive small-group math discussions don’t happen by themselves, so make sure your students know the “rules of the road” for contributing their ideas and respectfully critiquing the ideas of others.

16. Reward progress math-style

Students—especially those who haven’t experienced success—can have negative attitudes about math. While good instruction and success are the best intrinsic motivators, consider rewarding achievements with certificates, stickers, badges, or rewards as they progress. Remember: They are kids and kids like this stuff.

Make the rewards all math-oriented though. If you give out stickers, you’ll find even stickers that just have numbers on them are motivating. Collect them all, 1 to 100! Or have a Mathematician Certificate of Achievement with Einstein’s picture on it. This helps build a culture that says math is fun, math is cool, and learning math is valued.

Try it: Classroom Rewards and Incentives That Really Work

17. Build the home–school connection

Think about ways to assign meaningful homework. Ask deeper, more open-ended questions, not just practice pages. Yes, practice is important, and you should help kids understand that. There is a need for practice pages, but also have kids engage with people in their homes at least once a week on an interesting question.

Ask questions like:

• What do you think the best way to multiply two numbers is?
• What is the best way to multiply three numbers?
• How would you measure the wall if you had to paint it?
• How do you know if something you buy is a good price?

Make parents aware at the beginning of the year that you are going to be asking one of these questions every week, and make clear that there is no one right answer you are looking for. Explain this process is just so your students will understand that people in their home use math, that it’s valuable, that it’s done in different ways, and that you care about it. Those are huge pluses for making math relevant for kids.

18. Numbers all around us—raising math awareness

Help kids understand and value math by building their awareness of the math all around them. With every math concept you teach, a routine math assignment should be to have students go home and find out where this concept (measurement, money, multiplication, fractions, etc.) is in their home or neighborhood.

For example, learning about patterns? Any in your house? On your clothes? Learning about addition? Does anyone in your house add anything? Ask your parents. Learning geometry? Any shapes in your house? In your neighborhood? Have students report back with written notes about what they found out. Pretty soon, no matter what you teach, they’ll automatically be on the lookout for it and they’ll see how math is very relevant.

19. Read, read, read aloud

Although we don’t often think of reading as a math strategy, there’s almost nothing better to get students ready to learn a new concept than a great read-aloud. It’s fun, it’s engaging, and it can teach us a lot.

Kids love to be read to, and the more we show students how math is connected to the world around us, the more invested they become. It also connects imagination to math and makes for a more creative context. Reading books with math connections helps children see how abstract concepts connect to their lives.

Try it: Amazing Math Picture Books for Young Mathematicians

20. Prove it!

A number of students learn math by rote. They’ve attended special programs or learned online or from family members. They have memorized procedures, but have no real understanding of why they are doing what they are doing. This is OK for a while, but eventually if something in the procedure changes or problems become more complex, or the idea must be applied, it all breaks down.

One way to help with this is when a student tells you something like, “I know 9 x 9 = 81.” Reply, “Ah, so you say. But can you prove it?” If they don’t know what to do next, take some time with your class to model ways to provide proof.

For example, you could draw a picture of 9 groups of 9 dots in each. Or you could use tally marks. Or you might say, “I know 10 x 9 = 90 and 9 less is 81,” and show a multiplication chart. You could use buttons to build arrays. There are a ton of ways for students to show what they know, and yes, it is slower, but unless someone can prove that what they say is true, it makes real conceptual understanding suspect.

21. The art of math

Almost all kids love art, and visual learners need a math strategy that works for them too, so consider integrating art and math instruction for one of the easiest strategies in teaching mathematics.

Many concepts in geometry, such as shapes, symmetry, and transformations (slides, flips, and turns), can be applied in a fun art project. Also consider using art projects to teach concepts like patterns, measurement, ratios, arrays, and really anything.

Try it: Geometric Art Project

22. Teach estimation first

The majority of math we do on a daily basis involves estimation. It’s an important but often neglected skill. Many kids grow up thinking that in math they must have the exact answer or they can’t move forward with whatever they are doing.

When you shop for food, you estimate how much you need of a certain item. You don’t know exactly how many slices of bread your family will eat this week or how much milk they will drink down to the ounce, but you have some idea based on your experience, so you estimate, and you buy about how much you think you will need. That’s what an estimate is. A guess based on experience and what you can see.

Before you do any math with kids, ask them for an estimate before they give you an answer or begin calculations. It will build understanding and number sense, two qualities that will help them throughout their lives.

Try it: Estimation Activities That Take the Guesswork Out of Teaching Math

23. Real math in school

Consider starting some projects in school with your kids where they use math to make things happen.

For example, you could start a class store. Think of all the math involved: counting, adding, subtracting, multiplication, money, data collection … the list goes on. Or how about making a classroom lunch once a week for all to share. Kids will not only see how real, useful, and relevant these skills are, but they will also feel like “Wow. I really did that. I made it happen. No me, no math = no lunch.” It’s that sense of real accomplishment and empowerment we want for all our young mathematicians.

A school garden is another great real-life way to apply math concepts in a fun way while instilling a sense of purpose. Measurement, geometry, and data analysis are obvious topics that can be addressed through garden activities, but also consider using the garden to teach operations, fractions, and decimals. Additionally, garden activities can help promote character education goals like cooperation, respect for the earth, and, if the crops are donated to organizations that serve those in need, the value of giving to others.

Try it: How To Start a School Store

24. Encourage teacher teamwork and reflection

Teaching is a hard job. It’s even harder if you go it completely alone. Collaborate with other teachers to improve your math instruction skills.

Consider meeting with a teacher partner to share and discuss a unit you are both starting. Begin by discussing the goals and what it will look like for kids to achieve them. Work backward from there. Share strategies that have worked and maybe research a little together. Try things out and then share with each other what worked and what didn’t work.

25. Get moving

Kids are built to get up and move. Use that desire to make your math lessons even more fun and motivating. Asking kids to get out of their seats can increase their energy and interest.

For example, you could ask students to:

• Make angles with their arms
• Create a snap/clap sequence that demonstrates different types of patterns
• Complete a shape scavenger hunt in the classroom
• Run or complete other exercises periodically, count them, time them, and graph the results
• Jump on a given number from the ones you chalk on the playground

The possibilities of these strategies in teaching mathematics are limited only by your imagination and the math concepts you need to cover.

Try it: Active Math Games and Activities for Kids Who Love To Move

26. There’s more than one way to bake a cake

We need to be open-minded when it comes to math strategies. There are many viable strategies to solving any problem, including many math problems. Promote open-ended discussions about how different concepts in math can be done.

For example, when adding two two-digit numbers together, you could stack one above the other, do column addition, regroup if you need to, and check the answer by reversing the operation. Is there another way? Could you add the tens first and then the ones and then put them together? Is it easier for you to do it vertically or horizontally? Do pictures or drawings help you?

When you come to a concept, brainstorm with your class about different ways to solve problems in this area. This sharing of ideas promotes flexible thinking and also validates different approaches that are appropriate to different learning styles and levels.

27. Always begin with a question, not a statement

A good way to start any lesson is with a question. A question that gets people thinking. Instead of saying, “Today we are going to learn about multiplication,” what if instead you put a pile of books out on the floor and asked, “What’s the best way to find out how many books there are here?” You might get questions back like, “Can we move them?” That’s a good sign. It shows you’ve already engaged students’ thinking. Questions do that—they provoke thinking.

In this example, some kids will estimate, some will want to count by ones, some will want to skip-count, some will want to group them and do repeated addition, while others will group them and multiply. You can then ask, “What does efficient mean?” Field answers and work toward the idea that efficient means quick and accurate. That’s what multiplication is—it’s a quick and accurate way of finding out how many.

Another good opening question is, “What do you know about ________ ?” Fill in the math topic you are about to start. Have the class brainstorm on this, and write everything they say down on a chart. This will help you assess previous knowledge, give kids a chance to share, expose them to new ideas, validate their thinking, and open the door to exploration.

Think about whatever you’re teaching and consider: What is the main idea here, and what’s a question that gets at it? Lead with that and the rest will follow.

We all want our kids to succeed in math. In most districts, standardized tests measure students’ understanding, yet nobody wants to teach to the test. Over-reliance on test prep materials and “drill and kill” worksheets steal instructional time while also harming learning and motivation. But sound instruction and good test scores aren’t mutually exclusive. Being intentional and using creative approaches to your instruction can get students excited about math. These essential strategies in teaching mathematics can make this your class’s best math year ever!

Try it: Ways To Pose Better Math Questions in Class

Want more articles like this? Be sure to subscribe to our newsletters .

Learn why it’s important to honor all math strategies in teaching math . plus, check out the best math websites for teachers ..

You Might Also Like

8 Ways to Pose Better Questions in Math Class

Get students thinking! Continue Reading

Copyright © 2024. All rights reserved. 5335 Gate Parkway, Jacksonville, FL 32256

Top 9 Math Strategies for Successful Learning (2021 and Beyond)

Written by Ashley Crowe

• Teaching Strategies

• Why are effective Math strategies so important for students?
• Getting students excited about Math problems
• Top 9 math strategies for engaging lessons
• How teachers can refine math strategies

Math is an essential life skill. You use problem-solving every day. The math strategies you teach are needed, but many students have a difficult time making that connection between math and life.

Math isn’t just done with a pencil and paper. It’s not just solving word problems in a textbook. As an educator, you need fresh ways for math skills to stick while also keeping your students engaged. 

In this article, we’re sharing 9 engaging math strategies to boost your students’ learning . Show your students how fun math can be, and let’s freshen up those lesson plans!

Unlike other subjects, math builds on itself. You can’t successfully move forward without a strong understanding of previous materials. And this makes math instruction difficult.

To succeed in math, students need to do more than memorize formulas or drill times tables. They need to develop a full understanding of what their math lessons mean , and how they translate into the real world. To reach that level of understanding, you need a variety of teaching strategies. 

Conceptual understanding doesn’t just happen at the whiteboard. But it can be achieved by incorporating fun math activities into your lessons, including 

• Hands-on practice
• Collaborative projects
• Gamified or game-based learning

Repetition and homework are important. But for these lessons to really stick, your students need to find the excitement and wonder in math.

Creating excitement around math can be an uphill battle. But it’s one you and your students can win! 

Math is a challenging subject — both to teach and to learn. But it’s also one of the most rewarding. Finding the right mix of fun and learning can bring a lot of excitement to the classroom. 

Think about what your students already love doing. Video games? Legos? Use these passions to create exciting math lesson plans your students can relate to. 

Hands-on math practice can engage students that have disconnected from math. Putting away the pencils and textbooks and moving students out of their desks can re-energize your classroom.

If you’re teaching elementary or middle school math, find ways for your students to work together. Kids this age crave peer interaction. So don’t fight it — provide it! 

Play a variety of math games or puzzles . Give them a chance to problem-solve together. Build real-world skills in the classroom while also boosting student confidence. 

And be sure to celebrate all the wins! It is easy to get bogged down with instruction and testing. But even the smallest accomplishments are worth celebrating. And these rewarding moments will keep your students motivated and pushing forward.

Keep reading to uncover all of our top math strategies for keeping your students excited about math. 

1. Explicit instruction

You can’t always jump straight into the fun. Explicit instruction still provides the best foundation for the activities to come. 

Set up your lesson for the day at the whiteboard, along with materials to demonstrate the coming activities. Make sure to also focus on any new vocabulary and concepts. 

Tip: don't stay here for too long. Once the lesson is introduced, move on to the next fun strategy for the day!

2. Conceptual understanding

Helping your students understand the concept behind the lesson is crucial, but not always easy. Even your highest performing students may only be following a pattern to solve problems, without grasping the “why.”

Visual aids and math manipulatives are some of your best tools to increase conceptual understanding. Math is not a two dimensional subject. Even the best drawing of a cone isn’t going to provide the same experience as holding one. Find ways to let your students examine math from all sides.

Math manipulatives don’t need to be anything fancy. Basic wooden blocks, magnets, molding clay and other toys can create great hands-on lessons. No need to invest in expensive or hard-to-find materials. 

Math word problems are also a great time to break out a full-fledged demo. Hot Wheels cars can demonstrate velocity and acceleration. A tape measure is an interactive way to teach area and volume. These materials give your students a chance to bring math off the page and into real life. 

3. Using concepts in Math vocabulary

There’s more than one way to say something. And the more ways you can describe a mathematical concept, the better. Subtraction can also be described as taking away or removing. Memorizing multiplication facts is useful, but seeing these numbers used to calculate area gives them new meaning. 

Some math words are going to be unfamiliar. So to help students get comfortable with these concepts, demonstrate and label math ideas throughout your classroom . Understanding comes more easily when students are surrounded by new ideas. 

For example, create a division corner in your station rotations , with blocks to demonstrate the concept of one number going into another. Use baskets and labels to have students separate the blocks into each part of the division problem: dividend, divisor, quotient and remainder.  

Give students time to explore, and teach them big ideas with both academic and everyday terms. Demystify math and watch their confidence build!

4. Cooperative learning strategies

When students work together, it benefits everyone. More advanced students can lead, helping them solidify their knowledge. And they may have just the right words to describe an idea to others who are struggling.

It is rare in real-life situations for big problems to be solved alone. Cooperative learning allows students to view a problem from various angles. This can lead to more flexible, out-of-the-box thinking. 

After reviewing a word problem together as a class, ask small student groups to create their own problems. What is something they care about that they can solve with these skills? Involve them as much as possible in both the planning and solving. Encourage each student to think about what they bring to the group. There’s no better preparation for the future than learning to work as a team. 

5. Meaningful and frequent homework

When it comes to homework, it pays to think outside of textbooks and worksheets. Repetition is important, but how can you keep it fun?

Create more meaningful homework by including games in your curriculum plans. Encourage board game play or encourage families to play quiz-style games at home to improve critical thinking, problem solving and basic math skills. 

Sometimes you need homework that doesn’t put extra work onto the parents. The end of the day is already full for many families. To encourage practice and give parents a break, assign game-based options like Prodigy Math Game for homework. 

With Prodigy, students can enjoy a fun, video game experience that helps them stay excited and motivated to keep learning. They’ll practice math skills, while their parents have time to fix dinner. Plus, you’ll get progress reports that can help you plan future instruction . Win-win-win!    

Set an Assessment through your Prodigy teacher account today to reinforce what you’re teaching in class and differentiate for student needs. 

Ready to make homework fun?

6. Puzzle pieces math instruction

Some kids excel at math. But others pull back and may rarely participate. That lack of confidence is hard to break through. How can you get your reluctant students to join in?

Try giving each student a piece of the puzzle. When you’re presenting your class with a problem, this creates necessary collaboration to get to the solution. 

Each student is given a piece of information needed to solve the problem. A number, a unit of measurement, or direction — break your problem into as many pieces as possible. 

If you have a large class, break down three or more problems at a time. The first task: find the other students who are working on your problem (try color-coding or using symbols to distinguish each problem’s parts). Then watch the learning happen as everyone plays their own important role. 

7. Verbalize math problems

There’s little time to slow down in the classroom. Instruction has to move fast to keep up with the expected standards. And students feel that, too. 

When possible, try to set aside some time to ask about your students’ math struggles. Make sure they know that they can come to you when they get stuck. Keep the conversation open to their questions as much as possible.

One great way to encourage questions is to address common troubles students have encountered in the past. Where have your past classes struggled? Point these out during your explicit instruction, and let your students know this is a tricky area. 

It’s always encouraging to know you’re not alone in finding something difficult. This also leaves the door open for questions, leading to more discovery and greater understanding.

8. Reflection time

Providing time to reflect gives the brain a chance to process the work completed. This can be done after both group and individual activities.

Group Reflection

After a collaborative activity, save some time for the group to discuss the project . Encourage them to ask:

• What worked?
• What didn’t work?
• Did I learn a new approach?
• What could we have done differently?
• Did someone share something I had never thought of before? 

These questions encourage critical thinking. They also show the value of working together with others to solve a problem. Everyone has different ways of approaching a problem, and they’re all valuable.

Individual Reflection

One way to make math more approachable is to show how often math is used. Journaling math encounters can be a great way for students to see that math is all around. 

Ask them to add a little bit to their journal every day, even just a line or two. Where did they encounter math outside of class? Or what have they learned in class that has helped them at home? 

Math skills easily transfer outside of the classroom. Help them see how much they have grown, both in terms of academics and social emotional learning .

9. Making Math facts fun

As a teacher, you know math is anything but boring. But transferring that passion to your students is a tricky task. So how can you make learning math facts fun?

Play games! Math games are great classroom activities. Here are a few examples:

• Design and play a board game.
• Build structures and judge durability.
• Divide into groups for a quiz or game show. 
• Get kids moving and measure speed or distance jumped.

Even repetitive tasks can be fun with the right tools. That’s why engaging games are a great way to help students build essential math skills. When students play Prodigy Math Game , for example, they learn curriculum-aligned math facts without things like worksheets or flashcards. This can help them become excited to play and learn! 

How teachers can refine Math strategies

Sometimes trying something new can make a huge difference for your students. But don’t stress and try to change too much at once. 

You know your classroom and students best. Pick a couple of your favorite strategies above and try them out. 

If you're looking to freshen up your math instruction, sign up for a free Prodigy teacher account. Your students can jump right into the magic of the Prodigy Math Game, and you’ll start seeing data on their progress right away! 

Share this article

Table of Contents

Classroom Q&A

With larry ferlazzo.

In this EdWeek blog, an experiment in knowledge-gathering, Ferlazzo will address readers’ questions on classroom management, ELL instruction, lesson planning, and other issues facing teachers. Send your questions to [email protected]. Read more from this blog.

Four Teacher-Recommended Instructional Strategies for Math

• Share article

(This is the first post in a two-part series.)

The new question-of-the-week is:

What is the single most effective instructional strategy you have used to teach math?

This post is part of a longer series of questions and answers inviting educators from various disciplines to share their “single most effective instructional strategy.”

Two weeks ago, educators shared their recommendations when it came to teaching writing.

Last month , it was about teaching English-language learners.

There are many more to come!

Today, Cindy Garcia, Danielle Ngo, Patrick Brown, and Andrea Clark share their favorite math instructional strategies.

‘Concrete Representational Abstract’

Cindy Garcia has been a bilingual educator for 14 years and is currently a district instructional specialist for PK-6 bilingual/ESL mathematics. She is active on Twitter @CindyGarciaTX and on her blog:

The single most effective strategy that I have used to teach mathematics is the Concrete Representational Abstract (CRA) approach.

During the concrete step, students use physical materials (real-life objects or models) to explore a concept. Using physical materials allows the students to see and touch abstract concepts such as place value. Students are able to manipulate these materials and make sense of what works and what does not work. For example, students can represent 102, 120, and 201 with base 10 blocks and count each model to see the difference of the value of the digit 2 in each number.

During the representational step, students use pictures, images, or virtual manipulatives to represent concrete materials and complete math tasks. Students are making connections and gaining a deeper understanding of the concept by creating or drawing representations.

During the abstract step, students are now primarily using numbers and symbols. Students working at the abstract stage have a solid understanding of the concept.

The CRA approach is appropriate and applicable to all grade levels. It is not about the age of the student but rather the concept being taught. In 3rd grade, it is beneficial to students to have them use base 10 blocks to create an open-area model, then draw an open-area model, and finally use the multiplication algorithm. In algebra, it is STILL beneficial to practice using algebra tiles to multiply polynomials using an open-area model.

The CRA approach provides students P-12 to have multiple opportunities to explore concepts and make connections with prior concepts. Some teachers try to start teaching a concept at the abstract level, for example, the standard algorithm for multiplication. However, they soon find out that students have difficulty remembering the steps, don’t regroup, or don’t line up digits correctly. One of the main reasons is that students don’t understand this shortcut and they have not had the concrete & representational experiences to see how the shortcuts in the standard algorithm work.

‘Encouraging Discourse’

Danielle Ngo is a 3rd grade teacher and Lower School math coordinator at The Windward School . She has been a teacher for 10 years and works primarily with students who have language-based learning disabilities:

Growing up, so many of us were taught that there is one right answer to every math problem, and that there is one efficient way to arrive at that conclusion. The impetus to return to this framework when teaching math is a tempting one and one I’ve found myself having to fight actively against during my own classroom instruction. In my experience, the most effective way to counter this impulse is to mindfully increase the discourse present during my math lessons. Encouraging discourse benefits our students in several ways, all of which solidify crucial math concepts and sharpen higher-order thinking and reasoning skills:

Distributes math authority in the classroom: Allowing discourse between students—not just between the students and their teacher—establishes a classroom environment in which all contributions are respected and valued. Not only does this type of environment encourage students to advocate for themselves, to ask clarifying questions, and to assess their understanding of material, it also incentivizes students to actively engage in lessons by giving them agency and ownership over their knowledge. Learning becomes a collaborative effort, one in which each student can and should participate.

Promotes a deeper understanding of mathematical concepts: While the rote memorization of a process allows many students to pass their tests, this superficial grasp of math skills does not build a solid foundation for more complex concepts. Through the requisite explanation and justification of their thought processes, discourse pushes students to move beyond an understanding of math as a set of procedural tasks. Rather, rich classroom discussion gives students the freedom to explore the “why’s and how’s” of math—to engage with the concepts at hand, think critically about them, and connect new topics to previous knowledge. These connections allow students to develop a meaningful understanding of mathematical concepts and to use prior knowledge to solve unfamiliar problems.

Develops mathematical-language skills: Students internalize vocabulary words—both their definitions and correct usage—through repeated exposures to the words in meaningful contexts. Appropriately facilitated classroom discourse provides the perfect opportunity for students to practice using new vocabulary terms, as well as to restate definitions in their own words. Additionally, since many math concepts build on prior knowledge, classroom discussions allow students to revisit vocabulary words; use them in multiple, varied contexts; and thus keep the terms current.

‘Explore-Before-Explain’

Patrick Brown is the executive director of STEM and CTE for the Fort Zumwalt school district,in Missouri, an experienced educator, and a noted author :

The current COVID-19 pandemic is a sobering reminder that we are educating today’s students for a world that is increasingly complex and unpredictable. The sequence that we use in mathematics education can be pivotal in developing students’ understanding and ability to apply ideas to their lives.

An explore-before-explain mindset to mathematics teaching means situating learning in real-life situations and problems and using those circumstances as a context for learning. Explore-before-explain teaching is all about creating conceptual coherence for learners and students’ experiences must occur before explanations and practice-type activities.

Distance learning reaffirmed these ideas when I was faced with the challenge of teaching area and perimeter for the first-time to a 3 rd grade learner. I quickly realized that rather than viewing area and perimeter as topics to be explained and then practiced, situating learning in problem-solving scenarios and using household items as manipulatives can illustrate ideas and derive the mathematical formulas and relationships.

Using Lego bricks, we quickly transformed equations and word problems into problem-solving situations that could be built. Student Lego constructions were used as evidence for comparing and contrasting physically how area and perimeter are similar and different as well as mathematical ways to calculate these concepts (e.g., students quickly learned by using Legos that perimeter is the distance around a shape while area is the total shape of an object). Thus, situating learning and having students use data as evidence for mathematical understanding have been critical for motivating and engaging students in distance learning environments.

Using an explore-before-explain sequence of mathematics instruction helps transform traditional mathematics lessons into activities that promote the development of deeper conceptual understanding and transfer learning.

A ‘Whiteboard Wall’

Andrea Clark is a grade 5-7 math and language arts teacher in Austin, Texas. She has a master’s in STEM education and has been teaching for over 10 years:

If you want to increase motivation, persistence, and participation in your math classroom, I recommend a whiteboard wall. Or some reusable dry erase flipcharts to hang on the wall. Or some dry erase paint. Anything to get your students standing up and working on math together on a nonpermanent surface.

The idea of using “vertical nonpermanent surfaces” in the math classroom comes from Peter Liljedahl’s work with the best conditions for encouraging and supporting problem-solving in the math classroom. He found that students who worked on whiteboards (nonpermanent surfaces) started writing much sooner than students who worked on paper. He also found that students who worked on whiteboards discussed more, participated more, and persisted for longer than students working on paper. Working on a vertical whiteboard (hung on the wall) increased all of these factors, even compared with working on horizontal whiteboards.

Adding additional whiteboard space for my students to write on the walls has changed my math classroom (I have a few moveable whiteboard walls covered in dry erase paint as well as one wall with large whiteboards from end to end). My students spent less time sitting down, more time collaborating, and more time doing high-quality math. They were more willing to take risks, even willing to erase everything they had done and start over if necessary. They were able to solve problems that were complex and challenging, covering the whiteboards with their thinking and drawing.

And my students loved it. They were excited to work together on the whiteboards. They were excited to come to math and work through difficult problems together. They moved around the room, talking to other groups and sharing ideas. The fact that the boards were on the wall meant that everyone could see what other groups were doing. I could see where every group was just by looking around the room. I could see who needed help and who needed more time to work through something. But my students could see everything, too. They could get ideas from classmates outside of their group, using others’ ideas to get them through a disagreement or a sticking point. It made formally presenting their ideas easier, too; everyone could just turn and look at the board of the students who were sharing.

I loved ending the math class with whiteboards covered in writing. It reminded me of all of the thinking and talking and collaborating that had just happened. And that was a good feeling at the end of the day. Use nonpermanent vertical surfaces and watch your math class come alive.

Thanks to Cindy, Danielle, Patrick, and Andrea for their contributions!

Please feel free to leave a comment with your reactions to the topic or directly to anything that has been said in this post.

Consider contributing a question to be answered in a future post. You can send one to me at [email protected] . When you send it in, let me know if I can use your real name if it’s selected or if you’d prefer remaining anonymous and have a pseudonym in mind.

You can also contact me on Twitter at @Larryferlazzo .

Education Week has published a collection of posts from this blog, along with new material, in an e-book form. It’s titled Classroom Management Q&As: Expert Strategies for Teaching .

Just a reminder; you can subscribe and receive updates from this blog via email (The RSS feed for this blog, and for all Ed Week articles, has been changed by the new redesign—new ones are not yet available). And if you missed any of the highlights from the first nine years of this blog, you can see a categorized list below.

• This Year’s Most Popular Q&A Posts
• Race & Racism in Schools
• School Closures & the Coronavirus Crisis
• Classroom-Management Advice
• Best Ways to Begin the School Year
• Best Ways to End the School Year
• Student Motivation & Social-Emotional Learning
• Implementing the Common Core
• Facing Gender Challenges in Education
• Teaching Social Studies
• Cooperative & Collaborative Learning
• Using Tech in the Classroom
• Student Voices
• Parent Engagement in Schools
• Teaching English-Language Learners
• Reading Instruction
• Writing Instruction
• Education Policy Issues
• Differentiating Instruction
• Math Instruction
• Science Instruction
• Advice for New Teachers
• Author Interviews
• Entering the Teaching Profession
• The Inclusive Classroom
• Learning & the Brain
• Administrator Leadership
• Teacher Leadership
• Relationships in Schools
• Professional Development
• Instructional Strategies
• Best of Classroom Q&A
• Professional Collaboration
• Classroom Organization
• Mistakes in Education
• Project-Based Learning

I am also creating a Twitter list including all contributors to this column .

The opinions expressed in Classroom Q&A With Larry Ferlazzo are strictly those of the author(s) and do not reflect the opinions or endorsement of Editorial Projects in Education, or any of its publications.

Sign Up for EdWeek Update

Edweek top school jobs.

Sign Up & Sign In

Center for Teaching

Teaching problem solving.

Print Version

Tips and Techniques

Expert vs. novice problem solvers, communicate.

• Have students  identify specific problems, difficulties, or confusions . Don’t waste time working through problems that students already understand.
• If students are unable to articulate their concerns, determine where they are having trouble by  asking them to identify the specific concepts or principles associated with the problem.
• In a one-on-one tutoring session, ask the student to  work his/her problem out loud . This slows down the thinking process, making it more accurate and allowing you to access understanding.
• When working with larger groups you can ask students to provide a written “two-column solution.” Have students write up their solution to a problem by putting all their calculations in one column and all of their reasoning (in complete sentences) in the other column. This helps them to think critically about their own problem solving and helps you to more easily identify where they may be having problems. Two-Column Solution (Math) Two-Column Solution (Physics)

Encourage Independence

• Model the problem solving process rather than just giving students the answer. As you work through the problem, consider how a novice might struggle with the concepts and make your thinking clear
• Have students work through problems on their own. Ask directing questions or give helpful suggestions, but  provide only minimal assistance and only when needed to overcome obstacles.
• Don’t fear  group work ! Students can frequently help each other, and talking about a problem helps them think more critically about the steps needed to solve the problem. Additionally, group work helps students realize that problems often have multiple solution strategies, some that might be more effective than others

Be sensitive

• Frequently, when working problems, students are unsure of themselves. This lack of confidence may hamper their learning. It is important to recognize this when students come to us for help, and to give each student some feeling of mastery. Do this by providing  positive reinforcement to let students know when they have mastered a new concept or skill.

Encourage Thoroughness and Patience

• Try to communicate that  the process is more important than the answer so that the student learns that it is OK to not have an instant solution. This is learned through your acceptance of his/her pace of doing things, through your refusal to let anxiety pressure you into giving the right answer, and through your example of problem solving through a step-by step process.

Experts (teachers) in a particular field are often so fluent in solving problems from that field that they can find it difficult to articulate the problem solving principles and strategies they use to novices (students) in their field because these principles and strategies are second nature to the expert. To teach students problem solving skills,  a teacher should be aware of principles and strategies of good problem solving in his or her discipline .

The mathematician George Polya captured the problem solving principles and strategies he used in his discipline in the book  How to Solve It: A New Aspect of Mathematical Method (Princeton University Press, 1957). The book includes  a summary of Polya’s problem solving heuristic as well as advice on the teaching of problem solving.

Teaching Guides

Quick Links

• Services for Departments and Schools
• Examples of Online Instructional Modules

• Math tutors
• Math classes
• 1st Grade Math Worksheets
• 2nd Grade Math Worksheets
• 3rd Grade Math Worksheets
• 4th Grade Math Worksheets
• 5th Grade Math Worksheets
• 6th Grade Math Worksheets
• 7th Grade Math Worksheets
• 8th Grade Math Worksheets
• Knowledge Base

10 Strategies for Problem-Solving in Math

reviewed by Jo-ann Caballes

Updated on August 21, 2024

It’s not surprising that kids who lack problem-solving skills feel stuck in math class. Students who are behind in problem-solving may have difficulties identifying and carrying out a plan of action to solve a problem. Math strategies for problem-solving allow children to use a range of approaches to work out math problems productively and with ease. This article explores math problem-solving strategies and how kids can use them both in traditional classes and in a virtual classroom. 

What are problem-solving strategies in math?

Problem-solving strategies for math make it easier to tackle math and work up an effective solution. When we face any kind of problem, it’s usually impossible to solve it without carrying out a good plan.In other words, these strategies were designed to make math for kids easier and more manageable. Another great benefit of these strategies is that kids can spend less time cracking math problems. 

Here are some problem-solving methods:

• Drawing a picture or diagram (helps visualize the problem)
• Breaking the problem into smaller parts (to keep track of what has been done)
• Making a table or a list (helps students to organize information)

When children have a toolkit of math problem-solving strategies at hand, it makes it easier for them to excel in math and progress faster. 

How to solve math problems?

To solve math problems, it’s worth having strategies for math problem-solving that include several steps, but it doesn’t necessarily mean they are failproof. They serve as a guide to the solution when it’s difficult to decide where and how to start. Research suggests that breaking down complex problems into smaller stages can reduce cognitive load and make it easier for students to solve problems. Essentially, a suitable strategy can help kids to find the right answers fast. 

Here are 5 math problem-solving strategies for kids:

• Recognize the Problem  
• Work up a Plan  
• Carry Out the Plan  
• Review the Work  
• Reflect and Analyze  

Understanding the Problem 

Understanding the problem is the first step in the journey of solving it. Without doing this, kids won’t be able to address it in any way. In the beginning, it’s important to read the problem carefully and make sure to understand every part of it. Next, when kids know what they are asked to do, they have to write down the information they have and determine what essentially they need to solve. 

Work Out a Plan 

Working out a plan is one of the most important steps to solving math problems. Here, the kid has to choose a good strategy that will help them with a specific math problem. Outline these steps either in mind or on paper.

Carry Out the Plan 

Being methodical at that stage is key. It involves following the plan and performing calculations with the correct operations and rules. Finally, when the work is done, the child can review and show their work to a teacher or tutor.

Review the Work

This is where checking if the answer is correct takes place. If time allows, children and the teacher can choose other methods and try to solve the same problem again with a different approach. 

Reflect and Analyze

This stage is a great opportunity to think about how the problem was solved: did any part cause confusion? Was there a more efficient method? It’s important to let the child know that they can use the insights gained for future reference. 

Ways to solve math problems

The ways to solve math problems for kids are numerous, but it doesn’t mean they all work the same for everybody. For example, some children may find visual strategies work best for them; some prefer acting out the problem using movements. Finding what kind of method or strategy works best for your kid will be extremely beneficial both for school performance and in real-life scenarios where they can apply problem-solving. 

Online tutoring platforms like Brighterly offer personalized assistance, interactive tools, and access to resources that help to determine which strategies are best for your child. Expertise-driven tutors know how to guide your kid so they won’t be stuck with the same fallacies that interfere with effective problem-solving. For example, tutors can assist kids with drawing a diagram, acting a problem out with movement, or working backward. All of these ways are highly effective, especially with a trusted supporter by your side. 

Your child will fall in love with math 
after just one lesson!

Choose 1:1 online math tutoring.

What are 10 strategies for solving math problems?

There are plenty of different problem-solving strategies for mathematical problems to help kids discover answers. Let’s explore 10 popular problem-solving strategies:

Understand the Problem

Figuring out the nature of math problems is the key to solving them. Kids need to identify what kind of issue this is (fraction problem, word problem, quadratic equation, etc.) and work up a plan to solve it. 

Guess and Check

With this approach, kids simply need to keep guessing until they get the answer right. While this approach may seem irrelevant, it illustrates what the kid’s thinking process is. 

Work It Out

This method encourages students to write down or say their problem-solving process instead of going straight to solving it without preparation. This minimizes the probability of mistakes. 

Work Backwords 

Working backward is a great problem-solving strategy to acquire a fresh perspective. It requires one to come up with a probable solution and decide which step to take to come to that solution. 

A visual representation of a math problem may help kids to understand it in full. One way to visualize a problem is to use a blank piece of paper and draw a picture, including all of the aspects of the issue. 

Find a Pattern 

By helping students see patterns in math problems, we help them to extract and list relevant details. This method is very effective in learning shapes and other topics that need repetition. 

It may be self-explanatory, but it’s quite helpful to ask, “What are some possible solutions to this issue?”. By giving kids time to think and reflect, we help them to develop creative and critical thinking.

Draw a Picture or Diagram

Instead of drawing the math problem yourself, ask the kid to draw it themselves. They can draw pictures of the ideas they have been taught to help them remember the concepts better.

Trial and Error Method

Not knowing clear formulas or instructions, kids won’t be able to solve anything. Ask them to make a list of possible answers based on rules they already know. Let them learn by making mistakes and trying to find a better solution. 

Review Answers with Peers

It’s so fun to solve problems alongside your peers. Kids can review their answers together and share ideas on how each problem can be solved. 

Help your kid achieve their full math potential

The best Brighterly tutors are ready to help with that.

Math problem-solving strategies for elementary students

5 problem-solving strategies for elementary students include:

Using Simple Language 

Ask students to explain the problem in their own words to make sure they understand the problem correctly.

Using Visuals and Manipulatives 

Using drawing and manipulatives like counters, blocks, or beads can help students grasp the issue faster. 

Simplifying the Problem

Breaking the problem into a step-by-step process and smaller, manageable steps will allow students to find the solution faster. 

Looking for Patterns 

Identifying patterns in numbers and operations is a great strategy to help students gain more confidence along the way. 

Using Stories

Turning math problems into stories will surely engage youngsters and make them participate more actively. 

To recap, students need to have effective math problem-solving strategies up their sleeves. Not only does it help them in the classroom, but it’s also an essential skill for real-life situations. Productive problem-solving strategies for math vary depending on the grade. But what they have in common is that kids have to know how to break the issue into smaller parts and apply critical and creative thinking to solve it. 

If you want your kid to learn how to thrive in STEM and apply problem-solving strategies to both math and real life, book a free demo lesson with Brighterly today! Make your child excited about math!

Jessica is a a seasoned math tutor with over a decade of experience in the field. With a BSc and Master’s degree in Mathematics, she enjoys nurturing math geniuses, regardless of their age, grade, and skills. Apart from tutoring, Jessica blogs at Brighterly. She also has experience in child psychology, homeschooling and curriculum consultation for schools and EdTech websites.

As adults, we take numbers for granted, but preschoolers and kindergartners have no idea what these symbols mean. Yet, we often demand instant understanding and flawless performance when we start teaching numbers to our children. If you don’t have a clue about how to teach numbers for kids, browse no more. You will get four […]

May 19, 2022

Teaching strategies aren’t something that is set in stone and continue to evolve every year. Even though traditional educational strategies like teachers teaching in front of the classroom seemed to work for decades with little to no adjustments, the digital age has brought along numerous challenges. Teaching methods for kids require new strategies, so educators […]

Math programs from 1st to 8th grade

Meet the best tutors for interactive learning.

Choose kid's grade

Math Program Boost Your Child's Math Abilities! Ideal for 1st-8th Graders, Perfectly Synced with School Curriculum!

What do we offer?

Related posts.

40 Best Math Jokes For Kids

Are you a parent looking for ways to make math more engaging and enjoyable for your child? Check this article to find 40 math jokes for adults that you can use to make lessons with young students more fun! Importance of funny math jokes Funny math jokes are an important part of the study process […]

Apr 29, 2022

How to Teach Addition: tips from Brighterly

Addition is one of the most fundamental operations in math. It’s often one of the first things parents and teachers will teach kids because it provides the foundation for many other math concepts and operations. Whether you’re a parent looking to help your kid learn and understand addition or a kindergarten teacher looking to enhance […]

Apr 05, 2022

How to Teach Kids Division?

Parents can try to explain division to a child in their own way or turn to specialized educational platforms. For instance, the innovative education platform Brighterly offers a wide range of activities to learn math, including fun ways to teach division. As the topic belongs to one of the most important and core, kids should […]

Want your kid to excel in math?

Kid’s grade

We use cookies to help give you the best service possible. If you continue to use the website we will understand that you consent to the Terms and Conditions. These cookies are safe and secure. We will not share your history logs with third parties. Learn More

• Our Mission

A Math Word Problem Framework That Fosters Conceptual Thinking

This strategy for selecting and teaching word problems guides students to develop their understanding of math concepts.

Word problems in mathematics are a powerful tool for helping students make sense of and reason with mathematical concepts. Many students, however, struggle with word problems because of the various cognitive demands. As districtwide STEAM professional development specialists, we’ve spent a lot of time focusing on supporting our colleagues and students to ensure their success with word problems. We found that selecting the right word problems, as well as focusing on conceptual understanding rather than procedural knowledge, provides our students with real growth.

As our thinking evolved, we began to instill a routine that supports teaching students to solve with grit by putting them in the driver’s seat of the thinking. Below you’ll find the routine that we’ve found successful in helping students overcome the challenges of solving word problems.

Not all word problems are created equal

Prior to any instruction, we always consider the quality of the task for teaching and learning. In our process, we use word problems as the path to mathematics instruction. When selecting the mathematical tasks for students, we always consider the following questions:

• Does the task align with the learning goals and standards?
• Will the task engage and challenge students at an appropriate level, providing both a sense of accomplishment and further opportunities for growth?
• Is the task open or closed? Open tasks provide multiple pathways to foster a deeper understanding of mathematical concepts and skills. Closed tasks can still provide a deep understanding of mathematical concepts and skills if the task requires a high level of cognitive demand. 
• Does the task encourage critical thinking and problem-solving skills?
• Will the task allow students to see the relevance of mathematics to real-world situations?
• Does the task promote creativity and encourage students to make connections between mathematical concepts and other areas of their lives?

If we can answer yes to as many of these questions as possible, we can be assured that our tasks are rich. There are further insights for rich math tasks on NRICH and sample tasks on Illustrative Mathematics and K-5 Math Teaching Resources .

Developing conceptual understanding

Once we’ve selected the rich math tasks, developing conceptual understanding becomes our instructional focus. We present students with Numberless Word Problems and simultaneously use a word problem framework to focus on analysis of the text and to build conceptual understanding, rather than just memorization of formulas and procedures. 

• First we remove all of the numbers and have students read the problem focusing on who or what the problem is about; they visualize and connect the scenario to their lives and experiences. 
• Next we have our students rewrite the question as a statement to ensure that they understand the questions.
• Then we have our students read the problem again and have them think analytically. They ask themselves these questions: Are there parts? Is there a whole? Are things joining or separating? Is there a comparison? 
• Once that’s completed, we reveal the numbers in the problem. We have the students read the problem again to determine if they have enough information to develop a model and translate it into an equation that can be solved.
• After they’ve solved their equation, we have students compare it against their model to check their answer.  

Collaboration and workspace are key to building the thinking

To build the thinking necessary in the math classroom , we have students work in visibly random collaborative groups (random groups of three for grades 3 through 12, random groups of two for grades 1 and 2). With random groupings, we’ve found that students don’t enter their groups with predetermined roles, and all students contribute to the thinking.

For reluctant learners, we make sure these students serve as the scribe within the group documenting each member’s contribution. We also make sure to use nonpermanent vertical workspaces (whiteboards, windows [using dry-erase markers], large adhesive-backed chart paper, etc.). The vertical workspace provides accessibility for our diverse learners and promotes problem-solving because our students break down complex problems into smaller, manageable steps. The vertical workspaces also provide a visually appealing and organized way for our students to show their work.  We’ve witnessed how these workspaces help hold their attention and improve their focus on the task at hand.

Facilitate and provide feedback to move the thinking along

As students grapple with the task, the teacher floats among the collaborative groups, facilitates conversations, and gives the students feedback. Students are encouraged to look at the work of other groups or to provide a second strategy or model to support their thinking. Students take ownership and make sense of the problem, attempt solutions, and try to support their thinking with models, equations, charts, graphs, words, etc. They work through the problem collaboratively, justifying their work in their small group. In essence, they’re constructing their knowledge and preparing to share their work with the rest of the class. 

Word problems are a powerful tool for teaching math concepts to students. They offer a practical and relatable approach to problem-solving, enabling students to understand the relevance of math in real-life situations. Through word problems, students learn to apply mathematical principles and logical reasoning to solve complex problems. 

Moreover, word problems also enhance critical thinking, analytical skills, and decision-making abilities. Incorporating word problems into math lessons is an effective way to make math engaging, meaningful, and applicable to everyday life.

You are using an outdated browser. Please upgrade your browser to improve your experience.

6 Simple (But Effective) Instructional Strategies for Mathematics

As a mathematics teacher, it’s easy to dream about the dynamite lessons you could plan and deliver if only you had a little more time up your sleeve.

But we don’t live in a perfect world. With time at a premium, it’s not always possible to prepare cutting-edge resources and coordinate lengthy student-focused activities.

That doesn’t mean your teaching has to suffer. There’s still plenty you can do to drive engagement and foster conceptual understanding in your day-to-day lesson.

Here are 6 simple yet effective instructional strategies for mathematics that you can weave into your daily practice.

1. Make conceptual understanding a priority

For students to use mathematics flexibly and grapple with complex problems, they need more than facts and procedures.

They need a deep understanding of mathematical  concepts  themselves.

Here’s how you make conceptual understanding a priority in your classroom:

Use visual strategies

Making a concept visual allows students to see how an abstract concept translates to a physical scenario. Use illustrated problems or hands-on activities, and encourage students to use visual methods of their own (e.g. drawing) when solving problems.

Seeing a problem in different ways also builds the brain’s neural networks, increasing understanding and retention.

Use the schema approach

The schema is the underlying pattern behind a mathematical concept. All subtraction problems, for example, revolve around a certain amount of something being taken away from an original amount. Once students grasp the schema, they’ll be able to notice it in a diverse array of different problems.

To do this, put similar word problems (e.g. addition ones) side by side and help students discover what they have in common. See if they can express this in words that might apply to other problems of the same type.

Explicitly teach the mathematics vocabulary of a concept

Show the different ways a concept might be expressed in words. Addition, for example, might be expressed as two quantities “together” or a “combined amount”. Once they broaden their math(s) vocabulary, they’ll be able to use concepts much more flexibly.

• Here are some fun ways to build mathematical vocab:
• Display words on posters around the classroom.
• Have students bookmark a mathematics dictionary on their browser (link to ours).
• Have students write down a mathematical word, which they then describe to a partner without using the word itself. The partner has to guess which mathematical concept it is.

2. Set meaningful homework that builds on class learning

You hear the bell ring and – in a last-minute panic – yell out an order to complete exercise 15.2, odd number questions, and every second column.

We’ve all been there. After all your lesson planning, meaningful homework sometimes slips through the cracks.

But if you integrate homework into your lesson plans , you’ll find it much easier to set activities that build deep understanding and engage students that much more.

Think about how your students might reflect on or connect new knowledge at home, rather than just blindly practicing a process.

For example, they could:

• Teach someone else in the family about what they’ve learned
• Find a real-life application of the lesson’s concept somewhere in the home
• Put theory into practice with a hands-on activity (e.g. creating a timetable, cooking)
• Ask qualitative or ‘value’ questions of family members where appropriate.

Mathletics has targeted curriculum activities to ensure your students are progressing within their zone of learning

3. use cooperative learning strategies.

Cooperative learning has three major benefits in mathematics:

• It encourages students to express their mathematical thinking, which in turn gives them greater clarity of thought and self-awareness of their own problem-solving strategies.
• Communicating with others exposes students to different mathematical approaches, which they can use to think more flexibly.
• It mirrors the way mathematics is done outside the classroom, where people with different strengths work together to solve challenging real-world problems.

Here’s how you can use cooperative learning strategies effectively in your classroom:

The “puzzle pieces” approach to group work

Use the “puzzle pieces” approach, where each learner is given a unique piece of information to share with the rest of the group to solve a problem. That way every student has to get involved, and everyone has something to contribute regardless of ability level. (Tip: find some examples of puzzle piece activities in our article on math enrichment .)

Take time to reflect

Build-in reflection time after a collaborative activity for students to reflect on what worked, which strategies they found helpful, and how being exposed to other ways of reasoning has made them think differently.

Be strategic when allocating groups

A mix of ability levels will mean top-level students can consolidate their understanding by guiding the activity, while others can learn from more experienced peers. That way, students never miss out on learning, even if they’re always helping others (in fact, research suggests that teaching others yields the highest retention of any strategy).

4. Use strategic questioning

Strategic questions can help turn a regular ‘chalk and talk’ lesson into a deep learning experience, or scaffold learning acting as students advance into more challenging territory. Try using open-ended questions such as:

“Tell me how you solved that”

Instead of congratulating a student when they get an answer correct and moving on, ask them to communicate their approach. This achieves two things:

• The student is encouraged to reflect on their own thought process in detail. Instead of just “doing the math(s)” automatically, they’ll understand exactly the steps they took – and begin to see how these might be adapted to future, more challenging problems.
• Other students get the opportunity to see how they could have solved the problem, even if they struggled to do so originally.

“Is there any other way of solving this?”

Asking students to elaborate on different approaches to the same question highlights that there is no single, correct way of doing the mathematics. Moreover, students might discover some new mental mathematics tips or strategies from their peers that they can use in future activities.

“Does this problem remind you of anything else we’ve done before?”

Before students start shrugging their shoulders in response to an unfamiliar problem, ask them if it reminds them of anything they’ve done before.

They’ll start to notice previously encountered concepts underneath the surface. This habit of checking for familiarity is what produces flexible and agile mathematical thinkers.

“Where could you use this…” or “where would you see this used in the real world?”

These questions drive home the relevance of the learning. Instead of procedural knowledge alone, students will also come away with an understanding of how to apply that knowledge.

5. Focus on real problem-solving and reasoning

In the world beyond the classroom, mathematics takes the form of complex problems as opposed to straightforward questions with just one answer. For this reason, the most effective instruction equips students with the problem-solving and reasoning skills they’ll need for real life.

But this doesn’t mean an arbitrary word problem with apples and oranges. Instead, the best problems are real . That means they:

• Are open-ended. Instead of funnelling students to a particular solution, keep it open to different approaches.
• Approximate relevant real-world scenarios, or (even better) invite students to get hands-on with real items.
• Encourage students to collaborate and explore different perspectives.
• Don’t spell out exactly what students need to do. Let them trial different procedures until they settle on a strategy that works instead.

Use these examples of great problem-solving tasks .

Get access to 700+ unique problem solving and reasoning activities with a free trial

6. use mixed modes of assessment.

A variety of formative and summative assessment types will allow you to:

• Assess conceptual learning, as well as fact recall
• Build on what students know, instead of just assessing what they don’t
• Notice gaps in the learning before the final test

Here are some assessment types that provide an alternative to standard timed testing:

• Reflections
• Peer assessments
• “Teach the class” activities

Tip: Learning doesn’t have to cease for assessment to take place. Try and integrate the two, e.g. by assessing students’ collaborative abilities while they do a group task.

Join millions of students across the globe to celebrate  World Maths Day!

More instructional strategies for mathematics, mathematics activities.

• Fun math activities
• At home math activities
• STEM activities for elementary students

Concept-specific instructional strategies

• How to teach addition
• How to teach multiplication
• How to teach subtraction with regrouping
• How to teach addition with regrouping

Other instructional strategies for mathematics

• Math enrichment strategies
• Strategies to support struggling math students
• Mental math strategies
• Problem-solving strategies

You might like...

Teaching Problem-Solving Skills

Many instructors design opportunities for students to solve “problems”. But are their students solving true problems or merely participating in practice exercises? The former stresses critical thinking and decision­ making skills whereas the latter requires only the application of previously learned procedures.

Problem solving is often broadly defined as "the ability to understand the environment, identify complex problems, review related information to develop, evaluate strategies and implement solutions to build the desired outcome" (Fissore, C. et al, 2021). True problem solving is the process of applying a method – not known in advance – to a problem that is subject to a specific set of conditions and that the problem solver has not seen before, in order to obtain a satisfactory solution.

Below you will find some basic principles for teaching problem solving and one model to implement in your classroom teaching.

Principles for teaching problem solving

• Model a useful problem-solving method . Problem solving can be difficult and sometimes tedious. Show students how to be patient and persistent, and how to follow a structured method, such as Woods’ model described below. Articulate your method as you use it so students see the connections.
• Teach within a specific context . Teach problem-solving skills in the context in which they will be used by students (e.g., mole fraction calculations in a chemistry course). Use real-life problems in explanations, examples, and exams. Do not teach problem solving as an independent, abstract skill.
• Help students understand the problem . In order to solve problems, students need to define the end goal. This step is crucial to successful learning of problem-solving skills. If you succeed at helping students answer the questions “what?” and “why?”, finding the answer to “how?” will be easier.
• Take enough time . When planning a lecture/tutorial, budget enough time for: understanding the problem and defining the goal (both individually and as a class); dealing with questions from you and your students; making, finding, and fixing mistakes; and solving entire problems in a single session.
• Ask questions and make suggestions . Ask students to predict “what would happen if …” or explain why something happened. This will help them to develop analytical and deductive thinking skills. Also, ask questions and make suggestions about strategies to encourage students to reflect on the problem-solving strategies that they use.
• Link errors to misconceptions . Use errors as evidence of misconceptions, not carelessness or random guessing. Make an effort to isolate the misconception and correct it, then teach students to do this by themselves. We can all learn from mistakes.

Woods’ problem-solving model

Define the problem.

• The system . Have students identify the system under study (e.g., a metal bridge subject to certain forces) by interpreting the information provided in the problem statement. Drawing a diagram is a great way to do this.
• Known(s) and concepts . List what is known about the problem, and identify the knowledge needed to understand (and eventually) solve it.
• Unknown(s) . Once you have a list of knowns, identifying the unknown(s) becomes simpler. One unknown is generally the answer to the problem, but there may be other unknowns. Be sure that students understand what they are expected to find.
• Units and symbols . One key aspect in problem solving is teaching students how to select, interpret, and use units and symbols. Emphasize the use of units whenever applicable. Develop a habit of using appropriate units and symbols yourself at all times.
• Constraints . All problems have some stated or implied constraints. Teach students to look for the words "only", "must", "neglect", or "assume" to help identify the constraints.
• Criteria for success . Help students consider, from the beginning, what a logical type of answer would be. What characteristics will it possess? For example, a quantitative problem will require an answer in some form of numerical units (e.g., $/kg product, square cm, etc.) while an optimization problem requires an answer in the form of either a numerical maximum or minimum.

Think about it

• “Let it simmer”.  Use this stage to ponder the problem. Ideally, students will develop a mental image of the problem at hand during this stage.
• Identify specific pieces of knowledge . Students need to determine by themselves the required background knowledge from illustrations, examples and problems covered in the course.
• Collect information . Encourage students to collect pertinent information such as conversion factors, constants, and tables needed to solve the problem.

Plan a solution

• Consider possible strategies . Often, the type of solution will be determined by the type of problem. Some common problem-solving strategies are: compute; simplify; use an equation; make a model, diagram, table, or chart; or work backwards.
• Choose the best strategy . Help students to choose the best strategy by reminding them again what they are required to find or calculate.

Carry out the plan

• Be patient . Most problems are not solved quickly or on the first attempt. In other cases, executing the solution may be the easiest step.
• Be persistent . If a plan does not work immediately, do not let students get discouraged. Encourage them to try a different strategy and keep trying.

Encourage students to reflect. Once a solution has been reached, students should ask themselves the following questions:

• Does the answer make sense?
• Does it fit with the criteria established in step 1?
• Did I answer the question(s)?
• What did I learn by doing this?
• Could I have done the problem another way?

If you would like support applying these tips to your own teaching, CTE staff members are here to help.  View the  CTE Support  page to find the most relevant staff member to contact. 

• Fissore, C., Marchisio, M., Roman, F., & Sacchet, M. (2021). Development of problem solving skills with Maple in higher education. In: Corless, R.M., Gerhard, J., Kotsireas, I.S. (eds) Maple in Mathematics Education and Research. MC 2020. Communications in Computer and Information Science, vol 1414. Springer, Cham. https://doi.org/10.1007/978-3-030-81698-8_15
• Foshay, R., & Kirkley, J. (1998). Principles for Teaching Problem Solving. TRO Learning Inc., Edina MN.  (PDF) Principles for Teaching Problem Solving (researchgate.net)
• Hayes, J.R. (1989). The Complete Problem Solver. 2nd Edition. Hillsdale, NJ: Lawrence Erlbaum Associates.
• Woods, D.R., Wright, J.D., Hoffman, T.W., Swartman, R.K., Doig, I.D. (1975). Teaching Problem solving Skills.
• Engineering Education. Vol 1, No. 1. p. 238. Washington, DC: The American Society for Engineering Education.

Catalog search

Teaching tip categories.

• Assessment and feedback
• Blended Learning and Educational Technologies
• Career Development
• Course Design
• Course Implementation
• Inclusive Teaching and Learning
• Learning activities
• Support for Student Learning
• Support for TAs
• Learning activities ,

5 Strategies for Successful Problem Solving

• Powerful teaching strategies
• December 26, 2023
• Michaela Epstein

Blog > 5 Strategies for Successful Problem Solving

Problem solving can change the way students see maths – and how they see themselves as maths learners.

But, it's tough to help all students get the most out of a task.

To help, here are  5 Strategies for Problem Solving Success.

These are 5 valuable lessons I've learned from working with teachers across the globe .  You can use these strategies with all your students, no matter their level.

5 Strategies for Problem Solving Success

Your own enthusiasm is quickly picked up by your students. So, choose a problem, puzzle or game that you’re excited and curious about.

How do you know what will spark your curiosity? Do the task yourself!

(That’s why,  in the workshops I run , we spend a lot of time  actually  exploring problems. It’s a chance to step into students' shoes and experience maths from their perspective.)

Often, curriculum content becomes the goal of problem solving. For example, adding fractions, calculating areas or solving quadratic equations.

But, this is a mistake! Here's why-

Low floor, high ceiling tasks give students choices. Choices about what strategies to use, tools to draw on – and even what end-points to get to.

The most valuable goals focus on building confidence and capability in problem solving. For example:

• To make and break conjectures
• To use and evaluate different strategies
• To organise data in meaningful ways
• To explain and justify their conclusions.

The start of a task is what will get your students curious and hungry to get underway.

Consider: What's the least information your students will need?

At  ​our Members' online PL sessions​ , we look at one of four possibilities for launching a problem:

• Present a mystery to explore
• Present an example and non-example
• Run a demonstration game
• Show how to use a tool.

Keep the launch short – under 5 minutes. This is just enough to keep students’ attention AND share essential information.

Let’s face it, problem solving is hard, no matter your age or mathematical skill set.

Students aren’t afraid of hard work – they’re afraid of feeling or looking stupid. And, when those tricky maths moments do come, you can help.

Using questions, tools and other prompts can bring clarity and boost confidence.

(Here's a  free question catalogue  you might find handy to have in your back pocket.)

This careful support will help your students find problem solving far less daunting. Instead, it can become a chance for wonderous mathematical exploration.

Picture this: Your students are elbows deep in a problem, there’s a buzz in the air – oh, and only a minute until the bell.

The  most important  stage of a problem solving task – right at the end – is often the one that gets dropped off.

Why does ‘wrapping up’ matter?

In the last 10 minutes of a problem, students can share conjectures, strategies and solutions. It's also a chance to consider new questions that may open up further exploration.

In wrapping up, important learning will happen. Your students will observe patterns, make connections and clarify conjectures. You might even notice ‘aha’ moments.

Five strategies for problem solving success:

• Choose a task that YOU'RE keen on,
• Set a goal for strengthening problem solving skills,
• Plan a short launch to make the task widely accessible,
• Use questions, tools and prompts to support productive exploration, and
• Wrap up to create space for pivotal learning.

Join the Conversation

Dear Michaela, Greetings !! Thank you for sharing the strategies for problem solving task. These strategies will definitely enhance the skill in the mindset of young learners. In India ,Students of Grade 9 and Grade 10 have to learn and solve lot of theorems of triangle, Quadrilateral, Circle etc. Being an educator I have noticed that most of the students learn the theorems and it’s derivation by heart as a result they lack in understanding the application of these theorems.

I will appreciate if you can share your insights as how to make these topics interesting and easy to grasp.

Once again thanks for sharing such informative ideas.

Leave a comment

Cancel reply.

Your email address will not be published. Required fields are marked *

Don’t miss a thing!

Sign up to our mailing list for inspiring maths teaching ideas, event updates, free resources, and more!

Mathseeds School Edition

Start your free trial today.

7 Effective Strategies for Teaching Elementary Math

FEB 01, 2018

Teaching math in a mixed-ability classroom should take into account different learning abilities.

Teaching in today's mixed-ability classroom can be a challenge. These days, it's not uncommon to find a wide range of abilities in the one classroom—from students struggling to grasp new concepts, to those who are way ahead of their peers from day one.

This factor has contributed to a range of problems for early math learners, including a large achievement gap between students. Read more about how students can benefit from technology that supports differentiated instruction .

While individual students do benefit from different learning styles, there are a range of effective strategies which can help all students to succeed.

Additionally, the highly engaging, self-paced Mathseeds program offers a research-based solution for mixed-ability K–2 math classrooms, making math fun, interactive, and personalized for young learners. Start your free trial now .

Here are seven effective strategies for teaching elementary math:

1. Make it hands-on

Elementary math can be difficult because it involves learning new, abstract concepts that can be tricky for children to visualize.

Try to imagine what it's like for a five-year-old to see an addition problem for the very first time. Since it's a totally new concept to them, it can be hard for them to visualize a scenario where one quantity is added to another.

Manipulatives are hands-on tools that make math a lot easier for young children to understand. Tools like Lego, clay, and wooden blocks can all be used in the classroom to demonstrate how math ideas work.

For example, Lego is a great way to demonstrate number building, operations, fractions, sorting, patterns, 3D shapes, and more.

2. Use visuals and images

While students will come across countless graphs and visuals in their math textbooks, research shows this isn't the only place they should be utilized.

According to the National Council of Teachers of Mathematics, the most powerful way to use graphics in elementary math is in conjunction with specific practice or guidance, either from a teacher or another classroom tool such as Mathseeds .

3. Find opportunities to differentiate learning

It's important that students feel comfortable and are given the opportunity to learn new math ideas at their own pace, without feeling rushed. But while the idea that 'given enough time, every student will learn' is nothing new, it's easier said than done.

Mastery learning is about giving students as much time as they need to grasp a specific skill or concept. It involves varying the time you give each student to succeed.

Technology-based classroom tools offer a powerful way to differentiate learning while teaching elementary math, which is an effective way to help students in mixed-ability classrooms to succeed. Learn more here .

4. Ask students to explain their ideas

Have you ever noticed how much more confident you feel about a concept after explaining it to someone else?

Meta-cognition is the process of thinking about your options, choices, and results, and it has a big impact on the way students learn.

Before assigning a math problem, ask students to brainstorm problem-solving strategies they can use. Encourage students to work together to suggest different strategies in a respectful way.

This process can be carried out at every stage of problem solving when teaching elementary math. Once students have offered an answer, ask them to verbalize step-by-step how they got that answer.

5. Incorporate storytelling to make connections to real-world scenarios

When it comes to igniting the interest of young minds, not much comes close to a good story.

Incorporate story problems into your classroom lessons allow students to see how certain math concepts can apply to real life. Story problems are also a good way to help students understand how to use math in everyday life, and see the relevance of math.

Mathseeds provides colorful end-of-lesson books as part of its online program. Many of these are designed so students read the problem, work through it independently, and then turn to the next page to see the solution.

6. Show and tell new concepts

Elementary math teachers should normally begin each lesson with a 'show and tell.' Telling is the process of sharing information and knowledge with students, while showing involves modeling how to do something.

These days, teachers can really kick 'show and tell' up a notch with an interactive whiteboard, using animations, and videos to clearly show and tell specific math concepts in an engaging and interesting way.

7. Let your students regularly know how they're doing

Feedback is an important part of teaching elementary math and improving students' results.

Let your students know how they have performed on a specific task, along with helpful ways that they can further improve and extend their skills.

Remember, feedback is different to praise. Focus your feedback on the task itself (rather than the student) and make sure they have a clear understanding of what they did well and how they can improve next time. In Carol Dweck's research around what's known as the 'growth mindset', she writes:

“The growth mindset was intended to help close achievement gaps, not hide them. It is about telling the truth about a student's current achievement and then, together, doing something about it, helping him or her become smarter.”

Do you teach elementary math? Mathseeds is the research-based online math program specifically designed for students in grades K–2. Created by a highly experienced team of elementary teachers, Mathseeds provides self-paced lessons, automated reporting, and a range of teaching tools to help your elementary math students succeed. Sign up for a free trial today .

Back to Articles

Previous Article

Next Article

• ‐ Content Overview
• ‐ Correlation Charts
• ‐ White Paper
• ‐ Testimonials
• Blake eLearning
• Privacy Policy
• Refund Policy
• Do Not Sell My Info - CA Resident Only
• ‐ Brochures and Guides
• ‐ Technical Requirements
• ‐ FAQs

Start your FREE TRIAL today!

Information

• Author Services

Initiatives

You are accessing a machine-readable page. In order to be human-readable, please install an RSS reader.

All articles published by MDPI are made immediately available worldwide under an open access license. No special permission is required to reuse all or part of the article published by MDPI, including figures and tables. For articles published under an open access Creative Common CC BY license, any part of the article may be reused without permission provided that the original article is clearly cited. For more information, please refer to https://www.mdpi.com/openaccess .

Feature papers represent the most advanced research with significant potential for high impact in the field. A Feature Paper should be a substantial original Article that involves several techniques or approaches, provides an outlook for future research directions and describes possible research applications.

Feature papers are submitted upon individual invitation or recommendation by the scientific editors and must receive positive feedback from the reviewers.

Editor’s Choice articles are based on recommendations by the scientific editors of MDPI journals from around the world. Editors select a small number of articles recently published in the journal that they believe will be particularly interesting to readers, or important in the respective research area. The aim is to provide a snapshot of some of the most exciting work published in the various research areas of the journal.

Original Submission Date Received: .

• Active Journals
• Find a Journal
• Proceedings Series
• For Authors
• For Reviewers
• For Editors
• For Librarians
• For Publishers
• For Societies
• For Conference Organizers
• Open Access Policy
• Institutional Open Access Program
• Special Issues Guidelines
• Editorial Process
• Research and Publication Ethics
• Article Processing Charges
• Testimonials
• Preprints.org
• SciProfiles
• Encyclopedia

Article Menu

• Subscribe SciFeed
• Recommended Articles
• Google Scholar
• on Google Scholar
• Table of Contents

Find support for a specific problem in the support section of our website.

Please let us know what you think of our products and services.

Visit our dedicated information section to learn more about MDPI.

JSmol Viewer

Examples of problem-solving strategies in mathematics education supporting the sustainability of 21st-century skills.

1. Introduction

2. scope of 21st-century skills, 3. a short overview of mathematical problem solving.

• Since additional mathematics courses are not an optimal solution, it is more useful to implement the teaching of problem-solving strategies in the existing mathematics education.
• Specific noncognitive and general skills (that are typically underpromoted in education) are highly expected in work. Many of them belong to a high cognitive level, so it is worth paying attention to their improvement during mathematics lessons.
• It is essential to study different facets of some mathematical notions, since they help to understand and design conceptual models that represent the basis of processes and systems in IT fields.
• Mathematics should not be an isolated discipline. Students have to be able to connect knowledge from different mathematical disciplines; for example, to connect algebra and geometry to other knowledge.
• Employers highly favor the ability to apply one’s knowledge and experience to novel, unfamiliar situations. This is presumed to be most effectively fostered when learning occurs in work-based contexts or when replicated in schools. International studies such as the TIMSS (Trends in International Mathematics and Science Study) and PISA (PISA is the OECD’s Program for International Student Assessment) emphasize this dimension in mathematics education using nonroutine tasks from real life.

4. Problem-Solving Activities and Strategies to Develop 21st-Century Skills

4.1. examples and discussions. how pólya’s heuristic principles work in the case of a special problem.

• Step 1. Understanding the Problem
• If the weighing result is that the scales do balance, it means that all coins on the scales are good, and the other coins not used for the given weighing remain suspect.
• If the scales do not balance, it means that all other coins that were not weighted are good, while those weighted are suspect.
• In this latter case, the students need to formulate an additional idea and name this key idea.
• If the scales do not balance, it is needed to distinguish the suspect coins on the two scales and separate them as suspected of being heavier and suspected of being lighter.
• Step 2. Making a Plan
• Planning the First Weighing
• Planning the Second Weighing
• There is no use in measuring suspect coins three by three; they will surely not balance, and the last weighing has to be used for three coins suspected of being lighter and three coins suspected of being heavier.
• There is no use in measuring suspect coins two by two; e.g., in case they balance, one remains with two suspect coins, but one does not know if they are heavier or lighter.
• There is also no use in measuring suspect coins one by one.
• If one tries to analyze other cases, they will get stuck as well. Possible cases are: three suspect against three good coins, or four suspect against four good coins.
• The Second Weighing in Case 1-4-2
• Planning the Third Weighing
• One can separate S 4
• One can separate L 2 , L 3 , and L 4
• One can separate H 1 , H 2 , and H 3
• One can separate L 1 and H 4
• Step 3. Executing the Plan
• Step 4. Feedback

4.2. Examples and Discussions. Problems for Training Pre-Service and In-Service Teachers

4.2.1. multiplication of two natural numbers.

• Step 2. Devising the Plan
• Step 3. Carrying Out the Plan
• Step 4. Looking Back

4.2.2. Introduction of the Binary Number System

• Step 1. Understanding of the Problem

5. Discussion and Conclusions

• The rapidly changing environment due to technological disruption, globalization, and climate change, which requires the development of new transversal skills through education.
• Cross-curricular integration helps students and learners to remember math knowledge better and to link it to real-life situations, allowing them to connect different subject areas.

Author Contributions

Acknowledgments, conflicts of interest.

Click here to enlarge figure

• − problem tasks;
• − historical notes;
• − various small projects supporting interdisciplinary relationships, e.g., mathematics and art, Euclid, mathematics and space, mathematics and center of gravity, mathematics and the game billiards;
• − information documenting the current and historical use of mathematics.
• Davis, J.P. Applied Mathematics as Social Contract. Math. Mag. 1988 , 61 , 139–147. [ Google Scholar ] [ CrossRef ]
• Brynjolfsson, E.; McAfee, A. Race against the Machine: How the Digital Revolution Is Accelerating Innovation, Driving Productivity, and Irreversibly Transforming Employment and The Economy ; Digital Frontier Press: Lexington, MA, USA, 2011; Available online: http://b1ca250e5ed661ccf2f1-da4c182123f5956a3d22aa43eb816232.r10.cf1.rackcdn.com/contentItem-5422867-40675649-ew37tmdujwhnj-or.pdf (accessed on 12 September 2020).
• English, D.; Gainsburg, J. Problem Solving for the 21st Century Mathematics Curriculum. Available online: https://www.researchgate.net/publication/42424489_Problem_Solving_for_the_21st_Century (accessed on 23 September 2020).
• OECD. Education Policy Analysis ; OECD Publishing: Paris, France, 2001. [ Google Scholar ] [ CrossRef ]
• Ananiadoui, K.; Claro, M. 21st Century Skills and Competences for New Millennium Learners in OECD Countries ; OECD Education Working Papers, EDU/WKP(2009)20: Paris, France, 2009; p. 41. [ Google Scholar ] [ CrossRef ]
• EC. COM (2016) 381 Final. A New Skills Agenda for Europe. Brussels. Available online: https://eur-lex.europa.eu/legal-content/EN/TXT/PDF/?uri=CELEX:52016DC0381&from=EN (accessed on 25 September 2020).
• EC. European Skills Agenda for Sustainable Competitiveness, Social Fainess and Resilience. Available online: https://ec.europa.eu/social/main.jsp?langId=en&catId=89&furtherNews=yes&newsId=9723 (accessed on 25 September 2020).
• EC. European Skills Competencies and Occupation. 2020. Available online: https://ec.europa.eu/esco/portal/skill?uri=http%3A%2F%2Fdata.europa.eu%2Fesco%2Fskill%2F30d49832-84bd-4d97-9441-aef97a76a8d0&conceptLanguage=en&full=true#&uri=http://data.europa.eu/esco/skill/30d49832-84bd-4d97-9441-aef97a76a8d0 (accessed on 30 September 2020).
• BattelleforKids (Ed.) A Network of Battelle for Kids. Available online: https://www.battelleforkids.org/networks/p21 (accessed on 28 September 2020).
• NRC. Exploring the Intersection of Science Education and 21st Century Skills: A Workshop Summary. Available online: https://www.nap.edu/read/12771/chapter/8#p2001a08c9970070001 (accessed on 27 August 2020).
• ATC21S. 2012. Available online: http://www.atc21s.org/ (accessed on 27 August 2020).
• AES. What Are 21st Century Skills? Available online: https://www.aeseducation.com/blog/what-are-21st-century-skills (accessed on 9 September 2020).
• Binkley, M.; Erstad, O.; Herman, J.; Raizen, S.; Ripley, M.; Miller-Rici, M.; Rumble, M. Defining Twenty-First Century Skills ; Springer: Dordrecht, The Netherlands, 2012. [ Google Scholar ] [ CrossRef ]
• Generation Ready. 2020. Available online: https://www.generationready.com/mathematics-as-a-complex-problem-solving-activity/ (accessed on 12 September 2020).
• Ouedraogo, N.; Ouakouak, L.M.; Salem, T. Effects of Employee Creative Problem-solving on innovation outcomes and non-financial performance the Moderating Role of Culture and Communication. Int. J. Innov. Manag. 2020 , 24 , 28. [ Google Scholar ] [ CrossRef ]
• NSTA. Quality Science Education and 21st Century Skills ; Association, N.S., Ed.; NSTA: Arlington, VA, USA, 2020; Available online: https://www.nsta.org/nstas-official-positions/quality-science-education-and-21st-century-skills (accessed on 27 September 2020).
• Designed in Cooperation with the Nation’s Math Educators. Available online: https://files.eric.ed.gov/fulltext/ED543032.pdf (accessed on 28 September 2020).
• Jang, H. Identifying 21st century STEM competencies using workplace data. J. Sci. Educ. Technol. 2016 , 25 , 284–301. [ Google Scholar ] [ CrossRef ]
• Koenig, A.J. Assessing 21st Century Skills: Summary of a Workshop ; Council, N.R., Ed.; The National Academies Press: Washington, DC, USA, 2011. [ Google Scholar ] [ CrossRef ]
• Pehkonen, E. Teaching Mathematics via Problem Solving. In A Life’s Time for Mathematics Education and Problem Solving. Festschrift on the Occasion of András Ambrus’ 75th Birthday ; Stein, M., Ed.; WTM-Verlag: Münster, Germany, 2017; pp. 344–354. [ Google Scholar ]
• NBE. Perusopetuksen Opetussuunnitelman Perusteet 2014. Available online: https://www.oph.fi/sites/default/files/documents/perusopetuksen_opetussuunnitelman_perusteet_2014.pdf (accessed on 28 September 2020).
• NCTM. Principles and Standards for School Mathematics. Available online: https://www.nctm.org/Standards-and-Positions/Principles-and-Standards/ (accessed on 7 September 2020).
• Rosli, R.; Goldsby, D.; Capraro, M.M. Assessing Students’ Mathematical Problem-Solving and Problem-Posing Skills. Asian Soc. Sci. 2013 , 9 , 54–60. [ Google Scholar ] [ CrossRef ] [ Green Version ]
• Hejný, M. The process of discovery in teaching focusing on building schemes. In International Symposium Elementary Mathematics Teaching-Semt ; Novotná, J., Moraová, H., Eds.; Charles University, Faculty of Education: Prague, Czech Republic, 2011; pp. 150–157. [ Google Scholar ]
• Mason, J. Generating Worthwhile Mathematical Tasks in Order to Sustain and Develop Mathematical Thinking. Sustainability 2020 , 12 , 5727. [ Google Scholar ] [ CrossRef ]
• Pólya, G. How to Solve It ; Princeton University Press: Princeton, NJ, USA; Oxford, UK, 1945. [ Google Scholar ]
• Schoenfeld, H.A. Mathematical Problem Solving ; Academic Press INC. (London) Ltd.: London, UK, 1985. [ Google Scholar ] [ CrossRef ]
• Voskoglou, G.M. Problem Solving in Mathematics Education: Recent Trends and Development. Quaderni di Ricerca in Didattica” (Scienze Matematiche), 2008. pp. 22–28. Available online: https://www.researchgate.net/publication/228489790_Problem_Solving_in_Mathematics_Education_Recent_Trends_and_Development (accessed on 7 September 2020).
• Voskoglou, G.M. Ch 4. Problem-solving from Polya to nowadays: A review and future perspectives. In Progress in Education ; Nova Publishers: Hauppauge, NY, USA, 2011; Volume 12, pp. 65–82. [ Google Scholar ]
• Kalmykova, Z. Processes of Analysis and synthesis in the solution of arithmetic problems. In Analysis and Synthesis as Problem Solving Methods ; Kilpatrick, J., Wirszup, I., Kantowski, M., Eds.; School Mathematics Study Group Stanford University and Survey of Recent East Europe Mathematical Literature, University of Chicago: Chicago, IL, USA, 1975; Volume XI. [ Google Scholar ]
• Walle, V.D. Teaching Mathematics through Problem Solving, Chapter 2. 2014. Available online: https://www.pearsonhighered.com/assets/preface/0/1/3/4/013480208X.pdf (accessed on 26 August 2020).
• Klerlein, J.; Hervey, S. Mathematics as a Complex Problem-Solving Activity: Promoting Students’ Thinking through Problem-Solving. Generation Ready White Paper. 2019. Available online: https://36kf1rfh5v23ru41h2gm84pz-wpengine.netdna-ssl.com/wp-content/uploads/2019/02/Mathematics-as-a-Complex-Problem-Solving-Activity.pdf (accessed on 26 August 2020).
• Rahman, M. 21st Century Skill “Problem Solving”: Defining the Concept. Asian J. Interdiscip. Res. 2019 , 2 , 64–74. [ Google Scholar ]
• Evans, S.; Swan, M. Developing Students’ Strategies for Problem Solving in Mathematics: The Role of Pre-Designed. Available online: https://www.educationaldesigner.org/ed/volume2/issue7/article25/index.htm (accessed on 8 September 2020).
• Lester, K.F.; Cai, J. Can Mathematical Problem Solving Be Taught? Preliminary Answers from 30 Years of Research. In Posing and Solving Mathematical Problems ; Felmer, P., Pehkonen, E., Kilpatrick, J., Eds.; Springer International Publishing AG Switzerland: Berlin/Heidelberg, Germany, 2016; pp. 117–136. [ Google Scholar ] [ CrossRef ]
• Schoenfeld, H.A. Problem Solving, Teaching and More toward a Theory of Goal-Directed Behavior. Available online: http://math.unipa.it/~grim/cieaem/cieaem59/cikkek_pdf/plenary_pdf/p%2004.pdf (accessed on 19 September 2020).
• Hung, L.P.; Seokhee, C. Nurturing Mathematical Creativity in Schools. Turk. J. Gift. Educ. 2018 , 8 , 65–82. [ Google Scholar ]
• Susilo, H.; Kristiani, N.; Sudrajat, K.A. Development of 21st century skills at the senior high school: Teachers’ perspective. In AIP Conference Proceedings ; Habiddin, H., Majid, S., Suhadi, I., Farida, N., Dasna, I., Eds.; AIP Publishing: Baltimore, MD, USA, 2020; Volume 2215, Article number 030018. [ Google Scholar ] [ CrossRef ]
• Sudrajat, A.K.; Susilo, H.; Rohman, F. Student perspective on the importance of developing critical thinking and collaboration skills for prospective teacher students. AIP Conf. Proc. 2020 , 2215 , 030015. [ Google Scholar ] [ CrossRef ]
• Chu, S.; Reynolds, R.; Tavares, N.; Notari, M.; Lee, C. 21st Century Skills Development through Inquiry-Based Learning, from Theory to Practice ; Springer: Singapore, 2017. [ Google Scholar ] [ CrossRef ]
• Bai, B.; Song, H. 21st century skills development through inquiry-based learning from theory to practice. Asia Pac. J. Educ. 2018 , 38 . [ Google Scholar ] [ CrossRef ]
• Dishon, G.; Gilead, T. Adaptability And Its Discontents: 21st-Century Skills and the Preparation for an Unpredictable Future. Br. J. Educ. Stud. 2020 , 1–21. [ Google Scholar ] [ CrossRef ]
• NCTM. The Math Forum. Available online: http://mathforum.org/library/drmath/view/55618.html (accessed on 8 September 2020).
• Antonick, G. The Twelve-Coin Problem. Available online: https://wordplay.blogs.nytimes.com/2014/07/21/12coin/ (accessed on 14 November 2020).
• GeekForGeeks. Available online: https://www.geeksforgeeks.org/decision-trees-fake-coin-puzzle/ (accessed on 14 November 2020).
• Coldwell, N. A Collection of Quant Riddles with Answers. Available online: http://puzzles.nigelcoldwell.co.uk/one.htm# (accessed on 14 November 2020).
• Tuska, A. George Polya’s Influence on Mathematics Competitions in the USA. Available online: https://www.uni-miskolc.hu/~matsefi/HMTM_2020/papers/HMTM_2020_Tuska_Polya.pdf (accessed on 14 November 2020).
• Back, A.; Kovács, L.; Marton, R.; Ruszt, B.; Debrenti, E. Problem Solving in Elementary Mathematics Education. Available online: https://www.uni-miskolc.hu/~matsefi/Summer_University_2020/annexes/ (accessed on 14 November 2020).
• Lein, A.E.; Jitendra, A.K.; Harwell, M.R. Effectiveness of Mathematical Word Problem Solving Interventions for Students With Learning Disabilities and/or Mathematics Difficulties: A Meta-Analysis. J. Educ. Psychol. 2020 , 112 , 1388–1408. [ Google Scholar ] [ CrossRef ]
• Dagiene, V.; Sentance, S.; Stupuriene, G. Developing a Two-Dimensional Categorization System for Educational Tasks in Informatics. Informatica 2017 , 28 , 23–44. [ Google Scholar ] [ CrossRef ] [ Green Version ]
• Menchinskaya, A.M.; Moro, I.N. Questions in the Method and Psychology of Teaching Arithmetic in the Elementary Grades. Moscow 1965. Available online: http://files.eric.ed.gov/fulltext/ED184842.pdf (accessed on 13 November 2020).
• Cajori, F. A History of Mathematics ; Macmillan: New York, NY, USA, 1919. [ Google Scholar ]
• Benediktová, M. Philosophical Aspects of Al-Khwarizmi’s Arithmetical and Algebraic Tractatus. Acta Fak. Filoz. Západočeské Univerzity V Plzni 2010 , 3 , 77–97. (In Czech) [ Google Scholar ]
• Al-Khwarizmi. Aritmetický a algebraický traktát komentované Petrem Vopěnkou ; OPS: Kenosha, WI, USA, 2009. [ Google Scholar ]
• Vajkovics, I. Elementa Arithmeticae Numericae et Literalis Practicae et Theoricae in Usum Discentium Proposita. Available online: https://www.uni-miskolc.hu/~matsefi/HMTM_2020/annexes/HMTM_2020_K%C3%B6rtesi_Imre_Vajkovics.pptx (accessed on 14 October 2020).
• UNESCO & UNEVOC. Transversal Skills-UNESCO TVETipedia Glossary. (U.-U. I. Training, Producer) 2020. Available online: https://unevoc.unesco.org/home/TVETipedia+Glossary/filt=all/id=577 (accessed on 14 November 2020).
• ECB. European Central Bank. Available online: https://www.ecb.europa.eu/stats/policy_and_exchange_rates/euro_reference_exchange_rates/html/index.en.html (accessed on 14 November 2020).
• Sriraman, B.; English, L. Problem solving for the 21st century. In Theories of Mathematics Education ; English, L., Sriraman, B., Eds.; Springer: Heidelberg, Germany, 2010; pp. 263–290. [ Google Scholar ] [ CrossRef ] [ Green Version ]
• Atance, M.C.; O’Neill, K. Episodic future thinking. Trends Cogn. Sci. 2001 , 5 , 533–539. [ Google Scholar ] [ CrossRef ]
• Maciejewski, W. Future-Oriented Thinking and Activity in MAthematical Problem Solving. In Mathematical Problem Solving ; Liljedahl, P., Santos-Trigo, M., Eds.; ICME-13 Monographs ed.; Springer: Cham, Switzerland, 2019. [ Google Scholar ] [ CrossRef ]
• Math Kangaroo in USA. Available online: http://www.mathkangaroo.us/mk/default.html (accessed on 28 September 2020).
• Bebras International Challenge on Informatics and Computational Thinking. Available online: http://www.bebras.org/ (accessed on 28 September 2020).
• Mathematical Duels. Available online: https://jcmf.cz/?q=cz/node/584 (accessed on 28 September 2020).
• Hill, F.; Mammarella, I.C.; Devine, A.; Caviola, S.; Passolunghi, M.C.; Szűcs, D. Maths anxiety in primary and secondary school students: Gender differences, developmental changes and anxiety specificity. Learn. Individ. Differ. 2016 , 48 , 45–53. [ Google Scholar ] [ CrossRef ]
• Osaďan, R.; Severini, E.; Valkóová, V. Applying of teaching materials in teaching maths at primary school-gender aspect. Online J. Prim. Presch. Educ. 2019 , 3 , 27–36. [ Google Scholar ] [ CrossRef ]

Share and Cite

Szabo, Z.K.; Körtesi, P.; Guncaga, J.; Szabo, D.; Neag, R. Examples of Problem-Solving Strategies in Mathematics Education Supporting the Sustainability of 21st-Century Skills. Sustainability 2020 , 12 , 10113. https://doi.org/10.3390/su122310113

Szabo ZK, Körtesi P, Guncaga J, Szabo D, Neag R. Examples of Problem-Solving Strategies in Mathematics Education Supporting the Sustainability of 21st-Century Skills. Sustainability . 2020; 12(23):10113. https://doi.org/10.3390/su122310113

Szabo, Zsuzsanna Katalin, Péter Körtesi, Jan Guncaga, Dalma Szabo, and Ramona Neag. 2020. "Examples of Problem-Solving Strategies in Mathematics Education Supporting the Sustainability of 21st-Century Skills" Sustainability 12, no. 23: 10113. https://doi.org/10.3390/su122310113

Article Metrics

Article access statistics, further information, mdpi initiatives, follow mdpi.

Subscribe to receive issue release notifications and newsletters from MDPI journals

• PRINT TO PLAY
• DIGITAL GAMES

Problem-Solving Strategies

October 16, 2019

There are many different ways to solve a math problem, and equipping students with problem-solving strategies is just as important as teaching computation and algorithms. Problem-solving strategies help students visualize the problem or present the given information in a way that can lead them to the solution. Solving word problems using strategies works great as a number talks activity and helps to revise many skills.

Problem-solving strategies

1. create a diagram/picture, 2. guess and check., 3. make a table or a list., 4. logical reasoning., 5. find a pattern, 6. work backward, 1. create a diagram/draw a picture.

Creating a diagram helps students visualize the problem and reach the solution. A diagram can be a picture with labels, or a representation of the problem with objects that can be manipulated. Role-playing and acting out the problem like a story can help get to the solution.

Alice spent 3/4 of her babysitting money on comic books. She is left with $6. How much money did she make from babysitting?

2. Guess and check

Teach students the same strategy research mathematicians use.

With this strategy, students solve problems by making a reasonable guess depending on the information given. Then they check to see if the answer is correct and they improve it accordingly.  By repeating this process, a student can arrive at a correct answer that has been checked. It is recommended that the students keep a record of their guesses by making a chart, a table or a list. This is a flexible strategy that works for many types of problems. When students are stuck, guessing and checking helps them start and explore the problem. However, there is a trap. Exactly because it is such a simple strategy to use, some students find it difficult to consider other strategies. As problems get more complicated, other strategies become more important and more effective.

Find two numbers that have sum 11 and product 24.

Try/guess  5 and 6  the product is 30 too high

  adjust  to 4 and 7 with product 28 still high

  adjust  again 3 and 8 product 24

3. Make a table or a list

Carefully organize the information on a table or list according to the problem information. It might be a table of numbers, a table with ticks and crosses to solve a logic problem or a list of possible answers. Seeing the given information sorted out on a table or a list will help find patterns and lead to the correct solution.

To make sure you are listing all the information correctly read the problem carefully.

Find the common factors of 24, 30 and 18

Logical reasoning is the process of using logical, systemic steps to arrive at a conclusion based on given facts and mathematic principles. Read and understand the problem. Then find the information that helps you start solving the problem. Continue with each piece of information and write possible answers.

Thomas, Helen, Bill, and Mary have cats that are black, brown, white, or gray. The cats’ names are Buddy, Lucky, Fifi, and Moo. Buddy is brown. Thoma’s cat, Lucky, is not gray. Helen’s cat is white but is not named Moo. The gray cat belongs to Bill. Which cat belongs to each student, and what is its color?

A table or list is useful in solving logic problems.

Since Lucky is not gray it can be black or brown. However, Buddy is brown so Lucky has to be black.

Buddy is brown so it cannot be Helen’s cat. Helen’s cat cannot be Moo, Buddy or Lucky, so it is Fifi.

Therefore, Moo is Bill’s cat and Buddy is Mary’s cat.

5. Find a pattern.

Finding a pattern is a strategy in which students look for patterns in the given information in order to solve the problem. When the problem consists of data like numbers or events that are repeated then it can be solved using the “find a pattern” problem-solving strategy. Data can be organized in a table or a list to reveal the pattern and help discover the “rule” of the pattern.

 The “rule” can then be used to find the answer to the question and complete the table/list.

Shannon’s Pizzeria made 5 pizzas on Sunday, 10 pizzas on Monday, 20 pizzas on Tuesday, and 40 pizzas on Wednesday. If this pattern continues, how many pizzas will the pizzeria make on Saturday?

6. Working backward

Problems that can be solved with this strategy are the ones that  list a series of events or a sequence of steps .

In this strategy, the students must start with the solution and work back to the beginning. Each operation must be reversed to get back to the beginning. So if working forwards requires addition, when students work backward they will need to subtract. And if they multiply working forwards, they must divide when working backward.

Mom bought a box of candy. Mary took 5 of them, Nick took 4 of them and 31 were given out on Halloween night. The next morning they found 8 pieces of candy in the box. How many candy pieces were in the box when mom bought it.

For this problem, we know that the final number of candy was 8, so if we work backward to “put back” the candy that was taken from the box we can reach the number of candy pieces that were in the box, to begin with.

The candy was taken away so we will normally subtract them. However, to get back to the original number of candy we need to work backward and do the opposite, which is to add them.

8 candy pieces were left + the 31 given out + plus the ones Mary took + the ones Nick took

8+31+5+4= 48   Answer: The box came with 48 pieces of candy.

Selecting the best strategy for a problem comes with practice and often problems will require the use of more than one strategies.

Print and digital activities

I have created a collection of print and digital activity cards and worksheets with word problems (print and google slides) to solve using the strategies above. The collection includes 70 problems (5 challenge ones) and their solution s and explanations.

sample below

How to use the activity cards

Allow the students to use manipulatives to solve the problems. (counters, shapes, lego blocks, Cuisenaire blocks, base 10 blocks, clocks) They can use manipulatives to create a picture and visualize the problem. They can use counters for the guess and check strategy. Discuss which strategy/strategies are better for solving each problem. Discuss the different ways. Use the activities as warm-ups, number talks, initiate discussions, group work, challenge, escape rooms, and more.

Ask your students to write their own problems using the problems in this resource, and more, as examples. Start with a simple type. Students learn a lot when trying to compose a problem. They can share the problem with their partner or the whole class. Make a collection of problems to share with another class.

For the google slides the students can use text boxes to explain their thinking with words, add shapes and lines to create diagrams, and add (insert) tables and diagrams.

Many of the problems can be solved faster by using algebraic expressions. However, since I created this resource for grades 4 and up I chose to show simple conceptual ways of solving the problems using the strategies above. You can suggest different ways of solving the problems based on the grade level.

Find the free and premium versions of the resource below. The premium version includes 70 problems (challenge problems included) and their solutions

There are 2 versions of the resource

70 google slides with explanations + 70 printable task cards

70 google slides with explanations + 11 worksheets

You might also like

Multiplying fractions/mixed numbers/simplifying

Adding and subtracting fractions

AM/PM, 24-hour clock, Elapsed Time – ideas, games, and activities

Teaching area, ideas, games, print, and digital activities

Multi-Digit Multiplication, Area model, Partial Products algorithm, Puzzles, Word problems

Place Value – Representing and adding 2/3 digit numbers with manipulatives

Multiplication Mission – arrays, properties, multiples, factors, division

Fractions Games and activities – Equivalence, make 1, compare, add, subtract, like, unlike

Diving into Division -Teaching division conceptually

Expressions with arrays

Decimals, Decimal fractions, Percentages – print and digital

Solving Word Problems- Math talks-Strategies, Ideas and Activities-print and digital

Check out our best selling card games now available at amazon.com and amazon.ca.

Chicken Escape

A multiplayer card game that makes mental math practice fun! Chicken Escape is a fast-paced multiplayer card game. While playing…

Dragon Times – A math Adventure card game

Dragon Times is an educational fantasy card game that aims to motivate children to practice multiplication and division facts while…

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

• View all journals
• Explore content
• About the journal
• Publish with us
• Sign up for alerts
• Open access
• Published: 05 September 2024

The effectiveness of training teachers in problem-based learning implementation on students’ outcomes: a mixed-method study

• Nawaf Awadh K. Alreshidi   ORCID: orcid.org/0000-0002-7934-4724 1 &
• Victor Lally 2  

Humanities and Social Sciences Communications volume  11 , Article number:  1137 ( 2024 ) Cite this article

Metrics details

The aim of this study was to understand the effect of training teachers in problem-based learning (PBL) implementation on students’ outcomes. Mixed methods were used to analyse the quasi-experimental study data. 127 students were divided into three groups: Group A ( N  = 52) was taught by a trained teacher using the PBL teaching strategy, group B ( N  = 39) was taught by an untrained teacher using traditional teaching methods, and group C ( N  = 36) was taught by an untrained teacher using the PBL teaching strategy. The results showed that students whose teachers received training in PBL implementation significantly improved in terms of applying knowledge compared with students whose teachers used traditional teaching methods. The findings also provide robust evidence to show that using PBL teaching methods significantly improves students’ attitudes towards mathematics compared with traditional teaching methods, regardless of the teacher training effect. The key element in training teachers in PBL to improve students’ application of mathematics is training teachers in using metacognitive strategies that facilitate students’ learning processes.

Similar content being viewed by others

Fostering twenty-first century skills among primary school students through math project-based learning

A meta-analysis to gauge the impact of pedagogies employed in mixed-ability high school biology classrooms

Secondary school students’ attitude towards mathematics word problems

Introduction.

Problem-based learning (PBL) is a teaching strategy in which a facilitator assists students to solve real-world problems as they work in small groups; the facilitator’s aim is to help the students to gain new knowledge and improve their problem-solving skills (see Barrows, 1986 ; Goodman, 2010 ). PBL aims to improve students’ knowledge application (Hmelo, 1998 ; Hmelo and Lin, 2000 ; Schmidt et al., 1996 ), and attitudes towards learning the subject (Hung, 2006 ; Westwood, 2011 ).

In mathematics, PBL is an instructional strategy that contextualises mathematics knowledge (i.e., real-life problems) in a way that helps students to understand where, when and how to apply knowledge. In PBL, when students encounter a real-life problem, they should identify what they have already learned about the problem (i.e., activating their prior knowledge) and establish what they need to know in order to solve the problem (i.e., missing information). They have to search for missing information and then combine it with what they already know (i.e., relevant prior knowledge), applying this to a new context (Bokonjic et al., 2007 ). Therefore, using a PBL teaching strategy in mathematics should reflect on students’ improvement in applying mathematics. Applying mathematics is the concept of using mathematics in real life (Mumcu, 2016 ).

Contextualising knowledge can be prepared by embedding learning opportunities in real-life contexts, which could it also be of interest for students, and it shows students the value of the function of the subject matter in the real world (Hung, 2006 ; Westwood, 2011 ). In the mathematics context, the content of PBL settings (real-life problems) shows the function of mathematics in reality and gives meaning to learning mathematics (Westwood, 2011 ). This should place value on learning mathematics for students, leading to an increase in positive attitudes towards learning mathematics. Attitudes towards mathematics is a negative or positive emotional disposition toward mathematics (Zan and Di Martino, 2007 ). In a systematic review and meta-analysis, Suparman et al. ( 2021 ) determined that PBL is one of the best teaching strategies for primary school mathematics teachers to enhance students’ mathematical abilities. However, students’ learning processes need to be facilitated by teachers in their approach to solving problems (Collins et al., 1989 ; Hmelo-Silver and Barrows, 2006 ; Hung, 2011 ). Thus, it is essential for teachers to be able to do this effectively to produce a noticeable improvement in students’ outcomes. This might require teachers to complete training in facilitation processes. To date, little is known about how the training of teachers in PBL implementation affects students’ outcomes. The results of the present study will help educational decision-makers to understand how training teachers in implementing PBL affects students’ mathematical applications and attitudes towards mathematics.

This article begins with a review of previous studies on PBL, followed by a discussion of teacher training in PBL implementation. The experiment conducted as part of this research examined the effects of training teachers on students’ knowledge application in mathematics and students’ attitudes towards mathematics.

Previous studies in problem-based learning

The overall review of empirical studies shows that PBL tends to significantly improve knowledge application (Abdalqader and Khalid, 2014 ; Primadoni et al., 2020 ; Tong et al., 2021 ; Wirkala and Kuhn, 2011 ; Wong and Day, 2009 ) and generate positive attitudes among students compared with traditional teaching methods (TTM; i.e., teacher-centred instruction) in kindergarten to 12th grade (K–12) settings (Goodnough and Cashion, 2006 ; Lou et al., 2011 ; Merritt et al., 2017 ; Nowak, 2001 ; Tong et al. 2021 ). For example, a quasi-experimental study including control groups conducted by Tong et al. ( 2021 ) examined the effectiveness of PBL on 10th-grade students’ mathematical application knowledge and their attitudes towards mathematics. The results showed that the students taught by the PBL group improved significantly in the application of knowledge and attitudes towards mathematics compared to the students taught by conventional methods. The real-life problems used with PBL are expected to drive students’ curiosity and capture their interest (Schmidt et al. 2009 ); therefore, PBL pedagogy and content could enhance students’ interest and promote their knowledge application.

Most of the literature pertaining to PBL has been conducted in the field of medicine and its allied contexts at universities. A limited number of studies have been carried out in K–12 contexts, and very few studies have been conducted in primary schools see (Alshhrany and Mohammed ( 2010 ); Eviyanti et al., 2017 ). Additional empirical research is needed to investigate the effects of PBL on the outcomes of younger students.

Training in PBL implementation

Although training teachers to implement PBL is generally viewed as critical for improving students’ achievement (Arani et al., 2023 ; Barrows, 1996 ; Fernandes, 2021 ; Hmelo-Silver and Barrows, 2006 ; Leary et al., 2009 ; Wosinski et al., 2018 ) the effects of teacher training on students’ performance are still ambiguous. The agreement on the importance of training is supported by literature outside of PBL, where reports have shown that the most effective teachers are trained in how to use facilitation skills (Leary et al., 2009 ). A meta-analysis was conducted to investigate the relationship between teacher training and students’ learning outcomes, and 94 studies were selected for inclusion in the study. The results showed a significant relationship between teacher training and students’ achievement. The study suggested that untrained teachers have similar student outcomes to those of teachers who use TTM (Leary et al., 2013 ). The researchers concluded that the facilitator may be a key factor in students’ outcomes. In another study, Tawfik and Kolodner ( 2016 ) revisited PBL’s foundations from a case-based reasoning perspective suggested that novices must be trained to facilitate scaffolding students during PBL. Maxwell et al., ( 2005 ) suggested that PBL instruction can improve learning compared with conventional methods when teachers are trained well in PBL. El-Aziz El Naggar et al., ( 2013 ) found that training was necessary to improve facilitators’ skills in collaborative learning and self-directed environments. However, there is a lack of research studies that have experimentally examined the effects of teacher training on student learning. More primary research is required to measure the effects on students’ outcomes of training teachers in PBL.

The aim of training teachers in PBL is to develop teachers in their professional role (Friedman and Woodhead, 2008 ; Villegas-Reimers, 2003 ). Both teachers and students have a role in PBL. To delineate the role of teachers, first, we have to identify the role of students. In PBL, the role of students is to go through the PBL process. Students work in small groups to understand the problem, identify and learn what they need to know and generate hypotheses to solve the problem (Hmelo-Silver, 2004 ). The role of students also involves questioning, researching and using critical thinking in an active way to solve problems (Cerezo, 2004 ). Students are required to take responsibility for their learning and engage in meaning-making in terms of their knowledge (English and Kitsantas, 2013 ). For effective engagement in PBL, students must be responsible for their learning, and they must actively participate in constructing knowledge and making meaningful processes (English and Kitsantas, 2013 ). However, many students cannot easily shift into this role because they have developed ingrained habits from the typical traditional classroom experiences, and they rely on the passive receiving of knowledge (English and Kitsantas, 2013 ; Hung, 2011 ; Ronis, 2008 ). To shift effectively to the new role, students must develop self-regulated learning (SRL) skills (English and Kitsantas, 2013 ).

SRL refers to the extent to which the learner is motivationally, metacognitively and behaviourally active in their learning processes (Zimmerman, 1989 ). Self-regulated learners can set goals and plans, identify appropriate strategies, and self-monitor and self-evaluate their learning; they are intrinsically motivated to learn. Thus, for effective learning in PBL, SRL is an essential skill (English and Kitsantas, 2013 ). In PBL, teachers can consciously activate students’ behaviours, leading to SRL. When it comes to promoting students’ skills to be able to do this, the role of teachers is to structure activities to stimulate students’ motivation, encourage reflection and facilitate their learning processes through guidance, scaffolding feedback and prompting independent thinking (English and Kitsantas, 2013 ). The role of the teacher in PBL is to facilitate collaborative knowledge construction by students, monitor learning processes, model desired behaviours and concentrate students’ efforts on critical thinking (Hmelo-Silver and Barrows, 2006 , 2008 ); this can be done by raising awareness of students’ higher cognitive thinking (Barrows, 1998 ).

Effective teachers should know how to facilitate groups’ learning processes (Dolmans et al., 2002 ; El-Aziz El Naggar et al., 2013 ). To enhance cooperation and production within groups, teachers should use intervention strategies, such as making decisions on what, when and how to intervene (Bosse et al., 2010 ). Teachers may need to be trained to implement such strategies in such a way as to facilitate tutorial processes, since it is teachers’ responsibility to guide students’ learning (Yew et al., 2011 ). In this study, we attempt to understand the effect of training in implementing PBL on students’ outcomes. We address the following questions:

How do trained and untrained teachers in PBL techniques implement PBL?

What are the effects of teacher training in implementing PBL on students’ mathematical applications?

What are the effects of teacher training in implementing PBL on students’ attitudes towards mathematics?

Study design

A quasi-experimental design was adopted in this study as the main quantitative approach to minimise bias in estimating the difference between traditional instruction and PBL classes. In addition, a qualitative approach was used during the intervention using field observation notes and after the intervention using interviews, as a secondary approach (see Fig. 1 ).

The figure illustrates the study design; mathematical test and attitudes towards mathematics were applied before and after the intervention, while during the quasi-experimental implementation, field observation notes were taken, and at the end of the intervention semi-structured interviews were conducted with the teachers.

Figure 1 illustrates the study design; during the quasi-experimental implementation, field observation notes documenting the authors’ observations were taken with the aim of observing how teachers implemented PBL, while semi-structured interviews were conducted with both types of the teachers who only implemented PBL (trained and untrained teachers) after the implementation of PBL as a supplement, with the aim of being used as part of the triangulation method for the author’s observations in how teachers implemented PBL.

School and participating students

The school was located in an urban district in a major city, Hail, which is situated in the north of Saudi Arabia. The school was randomly selected from ten private schools. Then, seven of the third-grade classes out of nine in the selected school were randomly chosen. The third grade is an important level, as it is the final grade of lower primary school. The classes were instructed by three teachers; one taught three classes, and the others taught two classes each. These classes comprised the three following groups: group A (three classes taught by a trained teacher using a PBL teaching strategy), group B (two classes taught by an untrained teacher using TTM) and group C (two classes taught by an untrained teacher using a PBL teaching strategy; see the study design in Table 1 ).

Ethical approval was obtained, and all participants signed consent forms to participate. They were informed that they could withdraw any time with no need to justify their decision, nor would there be any consequences of withdrawal.

In total, 127 pupils participated in the study, and their ages ranged from eight to nine years old. They were in the last semester of the third grade. Most of the students at the school were Saudis; in each group, two to four students had Arab backgrounds, such as from Syria, Egypt and Sudan. All students had a middle-class socioeconomic status. Academic school records and pre-test’ scores were used to ensure that the groups were similar in terms of mathematical achievement. Within each group, students showed a wide range of academic achievements; the students spanned from very low to very high achievers. There were no special education pupils within the groups.

Three teachers were randomly selected from one large primary school to take part in this study. The first teacher was randomly selected to receive training courses in using the PBL teaching strategy. The second teacher did not receive any training, but he was provided with PBL materials—specifically, design problems and guidelines for implementing PBL; he was asked to conduct self-directed learning (SDL) to implement PBL in his classrooms. The aim of including a trained and an untrained teacher using PBL was to measure the effects of training teachers on students’ outcomes. The third teacher was not trained in PBL and was asked to teach students using TTM.

The teachers had similar characteristics in terms of qualifications, experience and expertise, as well as in their beliefs and perspectives on PBL and TTM. They are all male and they believed that the aim of teaching mathematics is to conduct real-life problem solving, and they considered active learning to be important for students. They had been teaching mathematics to third-grade school students for 10 years. They all had a first degree in mathematics. They were all Egyptians and aged in their late thirties. According to the teachers and the administration of the school, the teachers had all attended the same training courses in different aspects of education, such as active learning. However, none of them had ever been trained in using PBL teaching strategies.

The topic covered in the classes was ‘data display’. It covered representation through codes, interpretation of representation through codes, representation in columns and interpretation of representation in columns. The content was new to the students. The instruction took place during ten class sessions (45 min each) comprising four sessions per week over for two and a half weeks, with a total of 7.5 h for each group. To control for the time factor, all groups, whether PBL or traditional, were given the same amount of time.

Instruments

Six multiple-choice questions, short answer questions, fill-in table questions and drawing tests were applied at the beginning of the study (pre-test) and in the final experiment (post-test). Mathematics items were selected from Trends in International Mathematics and Science Study (TIMSS) 2003 , 2007 and 2011 (see Mullis et al., 2012 ). The TIMSS items that were selected matched the objectives of lessons for knowledge application exactly; they had already been examined for the purpose of the test. We chose TIMSS mathematics items because they were verified as appropriate for the students’ ages. The students had nearly finished the third grade, and the curriculum for that grade contained many TIMSS topics (see TIMSS, n.d. ). Each item on the test received a score of either one or zero. An example of the items is given in Appendix A . The measure ‘attitudes towards mathematics’ of TIMSS 2007 (Mullis et al., 2008 ) contains four items, as follows:

I would like to take more mathematics in school

I enjoy learning mathematics.

Mathematics is boring (reverse-coded).

I like mathematics.

This measure was adopted and assumed to meet the standard of a valid and reliable test (see, Mullis et al., 2008 ). Attitudes were assessed using four items applied twice as pre- and post-measures; four items with 4-point Likert scales (disagree a lot, disagree a little, agree a little, and agree a lot) were presented. Each item score ranged from 1 to 4. The total marks ranged from the number of items of the measure to multiply them by 4; the measure consisted of four items, so the total scores ranged from 4 to 16. Some items were reverse-coded; for example, for ‘mathematics is boring’, ‘disagree a lot’ would receive a score of 4, whereas ‘agree a lot’ would receive a score of 1.

The face validity method was used to assess the validity of the tests and attitude measures. Eight arbitrators checked and gave their opinions on the adequacy, clarity, and relevance of the items’ content. The opinions of the arbitrators were considered and included in the preparation of the final image of the tests and attitudes. However, no changes were reported, and face validity confirmed the tests’ validity. In addition, test-retest reliability was used to assess the reliability of the tests and attitude measures. The levels of reliability were acceptable, with a score of 0.86 for the mathematics test and 0.88 for the attitude measure. For further reliability, Cronbach’s alpha was used for each scale of the test and attitudes and for the whole test and attitudes. The results show that all items correlated with a good degree of total scales (no items scored less than 0.3), and the reliability for the test was 0.747, whereas that for attitude was 0.808. Therefore, the measures became high valid for the purposes of this study.

In qualitative methods, filed observation and semi-structured interview were used to assess teachers’ performance in PBL implementation. After filed observations completed, post- semi-structured interviews were conducted for the teachers to confirm the results of author observations of how teachers implemented PBL as a supplement for the methodological triangulation of the filed observations. Methodological triangulation involves a researcher using more than one method, such as interviews and observations, for collecting data to understand a phenomenon deeply (Flick et al., 2004 ; Neuman, 2000 ). The teachers’ responses to the questions in the semi-structured interviews were analysed and compared with the analysed observation data to enhance the validity of the study and to gain a deeper understanding of social events. As Neuman ( 2000 ) commented, “Looking at something from several different points gives a more accurate view of it” (p. 521).

The data obtained from qualitative methods were deductively analysed. Prior to conducting data collection from filed work. A structured categorisation matrix was developed by the authors based on a literature review (see Barrows, 1998 ; English and Kitsantas, 2013 ; Hmelo-Silver and Barrows, 2006 , 2008 ). It aimed to assess PBL implementation conducted by teachers and consisted of two main categories: understanding the problem and using metacognitive strategies (see Appendix B ). Field observation notes were used to describe how the teachers implemented PBL. In this study, field observation notes consisted of two parts: descriptive and reflective information (Patton, 1990 ). The descriptive part involved documenting the factual data obtained from inside the classroom. The main author moved between groups to make sure everything was proceeding well; the intention was to monitor the implementation of the study, and the authors had a diary that was used to document any observations, particularly the observations that took place during lessons and were made inside mathematics classrooms. The main focus was on teachers’ performance, particularly with respect to teacher intervention, individual and collective student practices, student responses, group interaction and PBL processes. In the reflective section, the authors reflected on the meaning of the observations outside of the classroom (see Appendix C ). At the end of the experiment, ten lessons by each teacher were observed.

Semi-structured interview questions were developed according to analysed data of class observations which includes: The three main questions:

How was PBL implemented in your teaching strategies?

How did you assess your students in relation to understanding the problem?

How did you support your students to solve the problem?

In semi-structured interview, tape recordings were used for the interviews with each teacher, which ranged from 13 to 23 min in length. The interviews were conducted in Arabic, transcribed and subsequently translated into English by the authors.

The data were deductively coded (i.e., both the interview and observation) by the main author, and according to the identified categories mentioned above. When a deductive content analysis is used, a categorisation matrix is developed; following this, the data are coded according to the categories (Polit and Beck, 2004 ). In addition, if a structured matrix is chosen, only aspects that fit the matrix are selected from the data (Patton, 1990 ).

Professional development

The PBL programme used in this study aimed to train teachers by focusing on how to implement PBL in mathematics classrooms. The programme continued to provide feedback during the implementation after each session, taking advantage of the literature recommendations. Therefore, the trained teacher learned how to facilitate groups’ learning processes and guide students’ learning by adopting strategies such as posing meta-cognitive questions and focusing on the process of learning to model students’ learning strategies. The teacher was trained in intervention strategies, such as making decisions based on what, when and how intervention should occur to enhance cooperation. The programme included examples of PBL implementations. Teacher training lasted for one week (8–10 h), and daily meetings took place during the course of the training to provide an opportunity to present feedback and resolve unexpected problems. The programme for training the teacher to implement PBL in his class was developed by the author. It was expected that, following the teacher’s completion of the programme, the teacher would be able to do the following:

provide scaffolding and feedback as needed

prompt independent thinking

facilitate collaborative knowledge construction for students

monitor learning processes

model desired behaviours

concentrate students’ efforts on critical thinking.

use intervention strategies, such as making decisions on what, when and how to intervene

The programme included three real-life sessions, each lasting 45 min. The teacher was asked to implement the PBL strategy using an ill-structured problem, which was taken from a mathematics textbook and related to the topics that the students had been studying. A group of students from outside the study sample was selected to assess the teacher’s performance and establish whether he was able to implement PBL effectively. This was followed by providing the teacher with extensive feedback, which lasted more than an hour for each session.

The students were trained in two sessions in how to deal with the PBL teaching strategy.

Problem-based learning implementation

Problems were presented to the students. Students worked in small groups of four to six members. They discussed their understanding of the problems, and then the teacher discussed the understanding of the problem with the whole class. This was followed by students solving the problems. Finally, the teacher discussed the solution with all the students.

In this study, the six core characteristics of PBL mentioned by Barrows ( 1996 ) were adopted. These are as follows:

The student is the centre of the learning.

Learning occurs in small groups of students.

At the beginning of the learning, the students are presented with authentic problems.

The problems are used as a means of developing problem-solving skills.

New knowledge is gained through SDL. (Barrows, 1996 )

From the literature review (see Barrows, 1986 ; Gallagher and Stepien, 1996 ; Hung et al., 2008 ), six characteristics were adopted in the problems after reviewing the literature related to the problem of PBL. These were as follows:

the role of students as stakeholders

ill-structured problems

real-life problems

age-appropriate problems

clear and short problems

not too difficult problems

Statistical analysis (quantitative analysis)

The study used mixed-factor analysis of variance (ANOVA) models (Field, 2013 ; Howell, 2012 ) within one factor (time: pre- and post-tests and between). Tukey’s post hoc test (Field, 2013 ; Howell, 2012 ) was applied when appropriate and where significant results were observed—that is, an effect size (partial eta squared [η p 2 ]). The effect size, classified as Cohen suggested, could be small 0.01; medium, 0.06; or large, 0.14. All analyses were performed on IBM SPSS v22 and at a 5% (0.05) level of significance.

A quasi-experimental design was adopted in this study as the main quantitative approach, while a qualitative approach was used during the intervention using class observation notes and interviews, as a secondary approach. In total, 127 pupils participated in the study. They were in the last semester of the third grade. Ethical approval was obtained, and all participants signed consent forms to participate. Three teachers were randomly selected from one large primary school to take part in this study. The first teacher was randomly selected to receive training courses in using the PBL teaching strategy. The second teacher was not trained and asked to conduct SDL to implement PBL in his classrooms. The third teacher was not trained in PBL and was asked to teach students using TTM. The topic covered in the classes was ‘data display’. The content was new to the students. The instruction took place during 10 class sessions. Instruments of the study include mathematics test and attitudes towards mathematics were prepared and verified. Applying a pre-test (a measure of attitudes towards mathematics and an exam to measure mathematics application). Conducting the study took about 2 and a half weeks. Applying for a post-test (a measure of attitudes towards mathematics and an exam to measure mathematics application). During the intervention, class observations were carried out for each lesson.

Problem-based learning implementation of trained and untrained teachers

Unlike the untrained teacher, the trained teacher properly implemented PBL. The differences between their performances lay in differences in ‘giving students sufficient time to understand the problem’ and ‘using more metacognitive strategies to coach students in relation to their thinking skills’.

Table 2 and Fig. 2 summarise the difference between trained and untrained teachers after analysing both the teachers’ interviews and the author’s observations. The two following themes were extracted from the data analyses: ‘understanding the problem’ and ‘using meta-cognitive teaching skills’. These themes are detailed below.

This figure illustrates the difference between trained and untrained teachers' performances in PBL implementation.

Understanding the problem

The trained teacher did not allow students to solve the problem until they demonstrated their understanding of it. The author frequently noted that the trained teacher prevented the students from solving the problem until they demonstrated their understanding of it. When the trained teacher was asked how he knew that the students understood the problem, he replied, ‘I frequently asked random students… : ‘could you please explain to us the problem in your own words?’ If they did not do very well, I asked them how they could understand the problem more deeply? I waited longer … for them to solve the problem and gave them more time to reflect on their understanding and discuss with their group to deeply understand the problem’. The author observed that the teacher frequently and asked ransom students the following question: ‘Could [you] explain the problem [to us in] your own words’. Some students could, while others could not. Then, he encouraged them to understand the problem by asking them the following questions: ‘How can you understand the problem deeply? and Could you identify the obstacles and discuss [them] with your [respective] groups?’ Later, he again asked them whether they could explain the problem. However, the untrained teacher’s students had been given a shorter amount of time to understand the problem than those who were with the trained teacher (author’s observation).

In all lessons, the untrained teacher asked students whether they understood the problem; he often proceeded after hearing anyone shout ‘yes’ (author’s observation). The untrained teacher confirmed this when he was asked how he knew that his students had understood the problem before carrying on: ‘I always ask my students, if they do not understand the problem, to stop me any time and feel free to ask’. He did not ask his students to explain the problem in their own words (author’s observation). It was noted that the trained teacher gave more time for understanding the problem and questioned his students’ understanding more than the untrained teacher did.

Using meta-cognitive teaching skills

The trained teacher used more metacognitive strategies than the untrained teacher. Throughout all the lessons, the author observed that the trained teacher facilitated his students’ learning processes via PBL by using meta-cognitive strategies. He confirmed this in stating:

They [the students] work within groups to solve the problem, and I monitor them and coach their thinking with meta-cognitive questions …. For example, I ask students: what they did so far, and what next, did they consider this or that … and so on…. Sometimes, I think aloud and model right behaviours to let them engage in learning processes.

It was observed that students gradually began to depend on their own selves to solve the problems when they found their teacher pushed them to be independent. The trained teacher confirmed the following:

I did not want my students to depend on me. I never give them the solution, but encouraged them to depend on their own effort … And I found coaching their thinking improved their independence.

In contrast, the untrained teacher showed less ability to use meta-cognitive strategies through implementing PBL (author’s observation). The untrained teacher said: ‘They [the students] worked with their groups to solve the problem, and I helped them to solve the problem by indirectly explaining any difficulties, for example, by giving them some examples’. He explained the difficulties and led his students to solve the problem. He did not explain the solution directly, but he gave similar examples, which led them to the correct answer (author’s observation). In some ways, this strategy may be considered a metacognitive activation strategy.

The author observed that students frequently asked their teachers to give them more examples to understand how to solve the problems. The untrained teacher confirmed this: ‘My students are allowed to ask me to give examples to solve the problems, and I always meet their needs’.

Knowledge application in mathematics

From Table 3 , it can be seen that the improvement in the ‘applying achievement’ mean scores increased in all groups. From the mixed-measures ANOVA, as shown in Table 4 , it was found that a statistically significant improvement occurred for the average of students’ scores in knowledge application, F (2, 121) = 76.795, p  = 0.000, with a large effect size at 0.388 (see row 1). However, when time was interacted with the groups (PBL with trained teacher, PBL with untrained teacher and TTM) the result showed a statistically significant effect, F (3, 121) = 4.333, p  = 0.015. The partial eta squared effect size for this statistically significant result was medium, at 0.067 (see row 2). This effect shows that there was an effect on at least one group, but further analysis was needed to identify which group(s) might be affected. Tukey’s post hoc test was applied to determine which of the groups was statistically significantly different from the others. This test found that the mean scores of the group of students taught using the PBL teaching strategy by the trained teacher were statistically significantly different only from the scores of the students taught using TTM, p  = 0.009 (see row 3). This indicates that the average of the PBL group’s scores with the trained teacher significantly improved more than the average of the traditional group’s scores did in ‘applying mathematics’.

Attitudes towards mathematics

From Table 5 , it can be seen that the mean score for ‘attitudes towards mathematics’ increased in groups A and C, while the scores of group B, the traditional group, decreased.

From the mixed-measures ANOVA analysis, as shown in Table 6 , there was no statistically significant improvement occurring for the average of students’ scores in attitudes towards mathematics, F (2, 121) = 0.480, p  = 0.490 (see row 1). However, when time was interacted with groups (PBL with trained teacher, PBL with untrained teacher, and TTM), the result showed a statistically significant effect, F (3, 121) = 12.486, p  = 0.000. The partial eta squared effect size for this statistically significant result was large, at 0.171 (see row 2). Tukey’s post hoc test was applied to determine which of the groups was significantly different from the others in attitudes towards mathematics. This test showed that using PBL with the trained teacher group was significantly different from using TTM, p  = 0.000; using PBL with the untrained teacher group was also significantly different from using TTM, p  = 0.008. However, there was no statistically significant difference between using PBL with the trained and untrained teachers (see row 3). This means that there was a statistically significant difference between the groups attributed to the types of treatment (PBL and TTM) in ‘attitudes towards mathematics’ and in favour of the PBL group, regardless of the different abilities of teachers in PBL implementation.

The study aimed to assess the effect of teacher training on students’ knowledge application and attitudes towards mathematics. The trained teacher demonstrated his ability to facilitate his students’ learning processes by using more metacognitive strategies than the untrained teacher. This result was expected, as many scholars think that training teachers on PBL implementation is critical for success (Barrows, 1996 ; Hmelo-Silver and Barrows, 2006 ; Leary et al., 2009 ; Wosinski et al., 2018 ). The results of the analyses of the interview data and the class observations were convergent. No noticeable difference was identified between the data analyses of class observation and the teachers’ interviews. Below, we consider how the teacher training affected student outcomes. Below, we consider how the teacher training affected student outcomes.

The current study’s quantitative results suggest that when PBL is taught by a teacher who can facilitate the students’ learning processes by using more meta-cognitive strategies, this could improve the application of mathematical knowledge of third-grade students’ significantly more than when they are taught using TTM (see Table 4 ). PBL theorists claim that, when compared with TTM, PBL is more successful in improving knowledge application (Hmelo-Silver, 2004 ; Hmelo-Silver and Barrows, 2008 ). This is because, with PBL, students engage in SDL by using their meta-cognitive learning strategies to solve real-life and ill-structured problems as a way of learning (Chin and Chia, 2006 ). This should reflect some improvement in the students’ ‘application’ ability over TTM (Fogarty, 1994 ). However, for such a method to be effective, skilled teachers who are also able to effectively use meta-cognitive strategies must be present to activate students’ meta-cognitive learning strategies. The trained teacher in PBL is better able to do so.

The role of the teacher in PBL is to facilitate learning processes (Hmelo-Silver and Barrows, 2006 , 2008 ). The shift to PBL requires new teaching roles and skills (Wilkerson and Hundert, 1997 ). Teachers can facilitate PBL processes if they are using meta-cognitive strategies, such as ‘thinking aloud with students’ and ‘modelling behaviours’ (Delisle, 1997 ). In the current study, these skills were shown effectively by the trained teacher; consequently, such strategies were reflected in the improvements to the students’ ‘application’ achievements. However, when students were taught by an untrained teacher, their learning processes were less facilitated. He only responded to difficulties they were experiencing by explaining similar situations (i.e., an example). Even though this approach is considered a metacognitive activation strategy, the students’ solutions were led by these examples. Thus, the teacher’s performance is an important factor that will affect the application of mathematical knowledge among third-grade students.

In terms of teacher training, the findings of the present study are supported by the results of the meta-analysis conducted by Leary et al. ( 2013 ), which showed a statistically significant positive relationship between teacher training and student achievement. The study also suggested that untrained teachers resulted in student outcomes similar to those attained by teachers who use TTM. This is also supported by the results of the current study. Moreover, this study’s findings are in line with those of Maxwell et al. ( 2005 ); these researchers’ conclusion suggests that PBL instruction can improve learning more than TTM can when teachers are well trained in using the PBL strategy. However, the results of the current study support the conclusions of several studies that found students taught via PBL outperformed students taught via TTM in terms of application knowledge (see Tong et al., 2021 ; Wirkala and Kuhn, 2011 ; Wong and Day, 2009 ).

The current study’s results suggested that PBL could significantly improve third-grade students’ attitudes towards mathematics compared with TTM (see Table 6 ). This is supported by the findings of (Lou et al., ( 2011 ) and Tong et al. ( 2021 ). For example, Tong et al. ( 2021 ) suggested that students taught via PBL improved their attitudes towards mathematics more significantly than those taught via TTM. The reason for this is that the students liked active learning and working in groups. This idea was supported by Goodnough and Cashion ( 2006 ), who suggested that young students like this strategy because it encourages active learning, supports working in groups and provides students with a variety of learning approaches and methods. In addition, real-life problems that interest students can be used to motivate students to engage deeply in learning processes when students fully understand them. These kinds of problems are expected to drive students’ curiosity and capture their interest, resulting in more effective student engagement in SDL in order to solve the problems (Schmidt et al., 2009 ).

In this study, the role of the problem was to motivate the students in all lessons taught by teachers trained in implementing PBL. Students became intrinsically motivated when they worked on tasks that stimulated their interests and sense of satisfaction or that challenged them (Hmelo-Silver, 2004 ). The possible reason for this is that the untrained teachers did not give students sufficient time to understand the problem, in contrast with the trained teacher (teachers’ interview and author’s observations).

In sum, PBL could be an effective teaching strategy for improving students’ attitudes towards learning mathematics; this effect is probably due to PBL content (i.e., real-life problems) and the nature of the PBL environment (i.e., eliciting active learning). In addition, PBL could be an effective teaching strategy for improving students’ mathematics application when students’ processes are effectively facilitated; without such facilitation, the effect of PBL instruction will not differ from that of TTM.

Limitations of the study

This study had several limitations. Because of the study design, results could be generated only for young students and for learning mathematics. The sample selection was not completely random, which could also decrease the opportunity to generalise the results of this study. Because of the gender segregation system that is currently operational in Saudi Arabia, the study participants were all male students. Therefore, the results of this study should be generalised with caution, taking these contextualising factors into account.

This study attempted to assess how training teachers in PBL implementation affects student outcomes, including knowledge application and students’ attitudes towards learning mathematics compared with TTM. Overall, the third-grade students who were taught using PBL showed more positive attitudes towards learning mathematics, regardless of whether they were taught by trained or untrained teachers. The study provides evidence that supports the necessity of training teachers to implement PBL effectively, as this will improve students’ mathematics application.

Data availability

The datasets generated during and/or analysed during the current study are available from the corresponding author on reasonable request.

Abdalqader K (2014) The effect of problem-based learning strategy in constructing proofs of solid geometry problems and attitudes toward math among female tenth graders in Gaza Governorates. Int J Res Educ Psychol 2:2210–1780

Alshhrany M (2010) The effect of using Wheatly’s Model for teaching a mathematics on sixth grade’s achievement in and attitudes towards math, Umm Al-Qura University

Arani SMN, Zarei AA, Sarani A (2023) Problem-based language learning: why aren’t teachers using it? Soc Sci Humanit Open 8(1):100668

Google Scholar  

Barrows HS (1996) Problem‐based learning in medicine and beyond: a brief overview. N Dir Teach Learn 1996(68):3–12

Article   Google Scholar  

Barrows HS (1986) Taxonomy of problem based learning methods. Med Educ 20(6):481–486

Article   CAS   PubMed   Google Scholar  

Barrows HS (1998) The essentials of problem-based learning. J Dent Educ 62(9):630–633

Bokonjic D, Mimica M, Pranjic N (2007) Problem based learning. In: Bokonjić D, Steiner T, Sonntag HG (eds) Manual of teaching and learning in medicine. Available at: http://www.bristol.ac.uk/medine . Accessed

Bosse HM, Huwendiek S, Skelin S, Kirschfink M, Nikendei C (2010) Interactive film scenes for tutor training in Problem-Based Learning (PBL): dealing with difficult situations. BMC Med Educ 10(1):52

Article   PubMed   PubMed Central   Google Scholar  

Cerezo N (2004) Problem-based learning in the middle school: a research case study of the perceptions of at-risk females. RMLE Online 27(1):1–13

Article   MathSciNet   Google Scholar  

Chin C, Chia LG (2006) Problem‐based learning: using Ill‐structured problems in biology project work. Sci Educ 90(1):44–67

Collins A, Brown JS, Newman SE (1989) Cognitive apprenticeship: teaching the crafts of reading, writing, and mathematics. In: LB Resnick (ed.), Knowing, learning, and instruction: essays in honor of Robert Glaser. Hillsdale NJ: Erlbaum, p 453–494

Delisle R (1997) How To Use Problem-Based Learning in The Classroom. Association for Supervision and Curriculum Development, Alexandria, VA

Dolmans DH, Gijselaers WH, Moust JH, Grave WSD, Wolfhagen IH, Vleuten CPVD (2002) Trends in research on the tutor in problem-based learning: conclusions and implications for educational practice and research. Med Teach 24(2):173–180

Article   PubMed   Google Scholar  

El-Aziz El Naggar MAA, Maklady FAH, Hamam AM, Omar AS (2013) Effectiveness of implementing a tutor training workshop for problem based learning class tutors at the Faculty of Medicine. Suez Canal Univ Intel Prop Rights 1(1):2

English MC, Kitsantas A (2013) Supporting student self-regulated learning in problem- and project-based learning. Interdiscip J Probl -Based Learn 7(2):6

Eviyanti CY, Surya E, Syahputra E, Simbolon M (2017) Improving the students’ mathematical problem solving ability by applying problem based learning model in VII grade at SMPN 1 Banda Aceh Indonesia. Int J Nov Res Educ Learn 4(2):138–144

Fernandes HV (2021) From student to tutor: a journey in problem-based learning. Curr Pharm Teach Learn 13(12):1706–1709

Field A (2013) Discovering statistics using IBM SPSS statistics. 4th Ed. London. Sage Publications

Flick D, Kardorff EV, Steinke I (2004) A Comparison To Qualitative Research. Sage, London

Fogarty R (1994) The mindful school: how to teach for metacognitive reflection. IRI/Skylight Publishing, Inc., 200 East Wood Street, Suite 274, Palatine, IL 60067

Friedman A, Woodhead S (2008) Approaches to CPD Measurement. Professional Associations Research Network. Retrieved on 26 October, 2008 From website: http://www.ifac.org/education/meeting-filedl.php?FID=3653

Gallagher SA, Stepien WJ (1996) Content acquisition in problem-based learning: depth versus breadth in American Studies. J Educ Gifted 19(3):257–275

Goodman RJB (2010) Problem-based learning: merging of economics and mathematics. J Econ Financ 34(4):477–483

Goodnough K, Cashion M (2006) Exploring problem‐based learning in the context of high school science: design and implementation issues. Sch Sci Math 106(7):280–295

Hmelo CE (1998) Problem-based learning: effects on the early acquisition of cognitive skill in medicine. J Learn Sci 7:173–208

Hmelo CE, Lin X (2000) Becoming self-directed learners: strategy development in problem-based learning. In: D Evensen & CE Hmelo (eds), Problem-based learning: a research perspective on learning interactions, Mahwah, NJ: Erlbaum, p 227–250

Hmelo-Silver CE, Barrows HS (2006) Goals and strategies of a problem-based learning facilitator. Interdiscip J Probl -Based Learn 1(1):4

Hmelo-Silver CE, Barrows HS (2008) Facilitating collaborative knowledge building. Cognit Instr 26(1):48–94

Hmelo-Silver CE (2004) Problem-based learning: what and how do students learn? Educ Psychol Rev 16(3):235–266

Howell D (2012) Statistical methods for psychology. 8th edn. Belmont, CA: Wadsworth, Cengage Learning

Hung W (2011) Theory to reality: a few issues in implementing problem-based learning. Educ Technol Res Dev 59(4):529–552. https://doi.org/10.1007/s11423-011-9198-1

Hung W (2006) The 3C3R model: a conceptual framework for designing problems in PBL. Interdiscip J Probl -Based Learn 1(1):6

Hung W, Jonassen DH, Liu R (2008) Problem-based learning. Handb Res Educ Commun Technol 3:485–506

Leary H, Walker A, Shelton BE, Fitt MH (2013) Exploring the relationships between tutor background, tutor training, and student learning: a problem-based learning meta-analysis. Interdiscip J Probl -Based Learn 7(1):6

Leary HM, Walker AE, Fitt MH, Shelton BE (2009) Expert Versus novice tutors: impacts on student outcomes in problem-based learning. Utah State University. ITLS Faculty Publications

Lou SJ, Shih RC, Diez CR, Tseng KH (2011) The Impact of problem-based learning strategies on STEM knowledge integration and attitudes: an exploratory study among female taiwanese senior high school students. Int J Technol Des Educ 21(2):195–215

Maxwell NL, Mergendoller JR, Bellisimo Y (2005) Problem-based learning and high school macroeconomics: a comparative study of instructional methods. J Econ Educ 36(4):315–329

Merritt J, Lee MY, Rillero P, Kinach BM (2017) Problem-based learning in K-8 mathematics and science education: A literature review. Interdiscip J Probl Based Learn 11(2):3–15. https://doi.org/10.7771/1541-5015.1674

Mullis IVS, Martin MO, Foy P (2008) TIMSS 2007 International Mathematics Report: Findings from IEA‟s Trends in International Mathematics and Science Study for the Fourth and Eighth Grades. Chestnut Hill, MA: TIMSS and PIRLS International Study Center, Boston College

Mullis IV, Martin MO, Foy P, Arora A (2012) TIMMS 2011 International Results in Mathematics. International Association for the Evaluation of Educational Achievement. Herengracht 487, Amsterdam, 1017 BT, The Netherlands

Mullis IV, Martin MO, Smith TA, International Association for the Evaluation of Educational Achievement (2003) TIMSS: Assessment frameworks and specifications 2003. https://pirls.bc.edu/timss2003i/PDF/t03_AF_preface.pdf‏

Mumcu HY (2016) Using mathematics, mathematical applications, mathematical modelling, and mathematical literacy: a theoretical study. J Educ Pract 7(36):80–96

Neuman W (2000) Social research methods: qualitative and quantitative approaches. 4th edn. Boston Mass and London: Ally and Bacon

Nowak JA (2001) The implications and outcomes of using problem-based learning to teach middle school science. Ph.D. Indiana University

Patton MQ (1990) Qualitative Evaluation and Research Methods. Sage Publications, Newbury Park

Polit DF, Beck CT (2004) Nursing Research. Principles and Methods. Lippincott Williams & Wilkins, Philadelphia, PA

Primadoni AB, Suharini E, Mulyono M (2020) Problem solving ability of the fourth grade students in problem based learning on two dimensional figures. J Prim Educ 9(2):155–161

Ronis DL (2008) Problem-based learning for math and science: integrating inquiry and the internet. 2nd edn. California: Corwin Press

Schmidt HG, Machiels-Bongaerts M, Hermans H, ten Cate TJ, Venekamp R, Boshuizen HPA (1996) The development of diagnostic competence: comparison of a problembased, an integrated, and a conventional medical curriculum. Acad Med 71:658–664

Schmidt HG, Van der Molen HT, Te Winkel WW, Wijnen WH (2009) Constructivist, problem-based learning does work: A meta-analysis of curricular comparisons involving a single medical school. Educ Psychol 44(4):227–249

Suparman S, Tamur M, Yunita Y, Wijaya TT, Syaharuddin S (2021) Using problem-based learning to enhance mathematical abilities of primary school students: A systematic review and meta-analysis. JTAM (J Teor Dan Aplikasi Matematika) 5(1):144–161

Tawfik AA, Kolodner JL (2016) Systematizing scaffolding for problem-based learning: a view from case-based reasoning. Interdiscip J Probl -Based Learn 10(1):6

Tong DH, Uyen BP, Nhu LKLTQ (2021) Application of Problem-Based Learning to Teaching the Relationships Within A Triangle And Solution Of Triangles. Int J Educ Change 7(7):486–503. https://doi.org/10.5281/zenodo.5137984

TRENDS IN INTERNATIONAL MATHEMATICS AND SCIENCE STUDY (TIMSS). (n.d.). National center for education statistics. Retrieved June 1, 2024, from https://nces.ed.gov/timss/released-questions.asp

Villegas-Reimers E (2003) Teacher Professional Development: An International Review of the Literature. International Institute for Educational Planning, Paris

Westwood P (2011) The problem with problems: potential difficulties in implementing problem-based learning as the core method in primary school mathematics. Aust J Learn Difficulties 16(1):5–18

Wilkerson L, Hundert EM (1997) Becoming a problem-based tutor: Increasing self-awareness through faculty development. In: Boud D, Feletti G (eds) The Challenge of Problem-Based Learning, 1st edn. Routledge, pp 160–172. https://doi.org/10.4324/9781315042039

Wirkala C, Kuhn D (2011) “Problem-based learning in K–12 Education is it effective and how does it achieve its effects?”. Am Educ Res J 48(5):1157–1186

Wong KKH, Day JR (2009) A comparative study of problem-based and lecture-based learning in junior secondary school science. Res Sci Educ 39(5):625–642

Wosinski J, Belcher AE, Dürrenberger Y, Allin AC, Stormacq C, Gerson L (2018) Facilitating problem-based learning among undergraduate nursing students: a qualitative systematic review. Nurse Educ today 60:67–74

Yew EH, Chng E, Schmidt HG (2011) Is learning in problem-based learning cumulative? Adv Health Sci Educ 16(4):449–464

Zan R, Di Martino P (2007) Attitude toward mathematics: overcoming the positive/negative dichotomy. Mont Math Enthus 3(1):157–168

Zimmerman BJ (1989) A social cognitive view of self-regulated academic learning. J Educ Psychol 81(3):329

Download references

Author information

Authors and affiliations.

College of Education, University of Ha’il, Ha’il, Saudi Arabia

Nawaf Awadh K. Alreshidi

College of Education, University of Glasgow, Glasgow, UK

Victor Lally

You can also search for this author in PubMed   Google Scholar

Contributions

The authors confirm contribution to the paper across all sections. Both authors reviewed the results and approved the version of the manuscript.

Corresponding author

Correspondence to Nawaf Awadh K. Alreshidi .

Ethics declarations

Competing interests.

The authors declare no competing interests.

Ethical statements

Approval was obtained. The procedures used in this study adhere to the tenets of the Declaration of Helsinki. The approval obtained from the college ethics committee for non-clinical research involving human subject, at university of Glasgow, Number: 1105870A.

Informed consent

All participants include: the teachers, the students, and the students’ parents signed consent forms to participate.

Additional information

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Supplementary information

Rights and permissions.

Open Access This article is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License, which permits any non-commercial use, sharing, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if you modified the licensed material. You do not have permission under this licence to share adapted material derived from this article or parts of it. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by-nc-nd/4.0/ .

Reprints and permissions

About this article

Cite this article.

Alreshidi, N.A.K., Lally, V. The effectiveness of training teachers in problem-based learning implementation on students’ outcomes: a mixed-method study. Humanit Soc Sci Commun 11 , 1137 (2024). https://doi.org/10.1057/s41599-024-03638-6

Download citation

Received : 03 December 2023

Accepted : 19 August 2024

Published : 05 September 2024

DOI : https://doi.org/10.1057/s41599-024-03638-6

Share this article

Anyone you share the following link with will be able to read this content:

Sorry, a shareable link is not currently available for this article.

Provided by the Springer Nature SharedIt content-sharing initiative

Quick links

• Explore articles by subject
• Guide to authors
• Editorial policies

Collaborative Learning Strategies for Better Classroom Interaction

Collaborative learning is all about students working together to achieve shared goals. It’s not just about group work—it’s about meaningful interaction that helps students learn better. When students collaborate effectively, they engage more with the material and with each other, which leads to better outcomes for everyone. This guide will show you how to use collaborative learning strategies to improve classroom interaction and make learning more engaging and effective.

What is Collaborative Learning

Collaborative learning is a teaching method where students work together in small groups to achieve a common goal. Instead of learning individually, students actively share ideas, discuss concepts, and support each other’s understanding of the material. This approach emphasizes teamwork and student participation, moving away from traditional teacher-centered instruction.

In collaborative learning, students are often grouped in pairs or small teams. They engage in joint intellectual efforts, whether searching for solutions, exploring new ideas, or creating projects. These activities focus on students interacting with the course material in a hands-on way, rather than just passively listening to lectures.

This method represents a shift from the conventional model where the teacher is the central source of knowledge and students primarily listen and take notes. Instead, teachers adopting collaborative learning approaches act more as facilitators or coaches. They design engaging and interactive learning experiences, guiding students through their exploration and application of the material. This encourages deeper understanding and more active involvement in the learning process.

Key Principles of Collaborative Learning

• Shared responsibility: In collaborative learning, every student in the group is responsible for contributing to the task. This creates a sense of accountability and encourages students to work together effectively.
• Active engagement: Students are actively involved in their learning. They ask questions, explain their thinking, and engage in discussions with their peers, which helps deepen their understanding of the subject.
• Diverse perspectives: Collaboration brings together different viewpoints. When students work in groups, they learn to consider ideas that may be different from their own, leading to a richer learning experience.
• Communication and interaction: Collaborative learning promotes strong communication skills. Students must articulate their thoughts clearly, listen to others, and build on each other’s ideas to solve problems or complete tasks.

Why Use Collaborative Learning?

Collaborative learning is used because it helps students learn better by working together. When students share ideas and help each other, they can understand the material more deeply. This method also builds important skills like teamwork, communication, and problem-solving, which are useful in real life.

By discussing and explaining things to each other, students can see different viewpoints and clear up any confusion they might have. Working in groups also makes learning more enjoyable and engaging, as students are more involved in the process. Instead of just listening to the teacher, they take an active role in their own learning.

What Are Collaborative Learning Strategies?

Collaborative learning strategies are methods or approaches used by educators to help students work together in groups to achieve common learning goals. These strategies are designed to encourage interaction, teamwork, and the sharing of ideas among students. The focus is on learning as a collective process, where students help each other understand concepts and solve problems, rather than just working individually.

Key Components of Collaborative Learning Strategies

• Group work: Students are divided into small groups to work on tasks or projects together. The size of the group can vary, but it’s usually kept small enough to ensure that everyone participates.
• Shared goals: Each group is given a clear, common goal that they need to achieve together. This could be completing a project, solving a problem, or understanding a specific concept.
• Interdependence: Students rely on each other to succeed. Each member of the group has a role or responsibility, and their contributions are crucial to the group’s overall success. This creates a sense of accountability within the group.
• Active participation: Collaborative learning strategies require all students to be actively involved. Whether it’s discussing ideas, solving problems, or presenting their work, everyone has a role to play.
• Teacher as a facilitator: The teacher guides the learning process, providing support and direction when needed, but allowing students to take the lead. The teacher’s role is to encourage collaboration and ensure that the group is working effectively.

Benefits of Collaborative Learning Strategies in the Classroom

Collaborative learning strategies offer several benefits in the classroom. By working together, students not only improve their understanding of the material but also develop important social and critical thinking skills.

Improved understanding

Collaborative learning helps students understand material better. When they work together, they explain concepts to each other, which reinforces their own knowledge. This shared learning experience often leads to a deeper grasp of the subject matter.

Enhanced critical thinking

Working in groups encourages students to think critically. They must analyze different viewpoints, discuss various solutions, and evaluate ideas together. This process helps them develop stronger problem-solving skills and a more comprehensive understanding of the topic.

Stronger social skills

Collaborative learning builds important social skills. Students practice communicating clearly, listening to others, and working as a team. These skills are valuable not only in school but also in future careers and everyday life.

Increased engagement

Group activities make learning more interactive and fun. Students are more likely to be engaged and motivated when they are actively participating and working with their peers. This increased engagement can lead to better retention of information and a more enjoyable learning experience.

Greater accountability

In a collaborative setting, each student has a role to play and is responsible for their part of the work. This shared responsibility encourages students to stay on task and contribute to the group’s success, fostering a sense of accountability and teamwork.

12 Collaborative Learning Strategies to Foster Stronger Teamwork

To build stronger teamwork in the classroom, various collaborative learning strategies can be used. These methods encourage students to work together, share ideas, and support each other in achieving common goals.

1. Group discussions

Group discussions involve students talking about a topic or question in small groups. This technique allows students to share their ideas, listen to others, and build a collective understanding of the subject. It helps students articulate their thoughts and learn from diverse perspectives.

How to use it

• Form groups - Divide the class into small groups, typically with 3-5 students each. Make sure the groups are balanced in terms of skills and abilities.
• Assign a topic or question - Provide each group with a topic or question related to the lesson. Make sure it is clear and relevant to what they are learning.
• Set guidelines - Explain how the discussion should be conducted. Encourage students to listen to each other, share their ideas, and build on what others say.
• Monitor progress - Walk around the classroom to listen to the discussions and offer guidance if needed. Ensure that all students are participating and staying on topic.
• Share findings - After the discussion, have each group share their main points or conclusions with the class. This allows students to learn from other groups and see different perspectives.
• Reflect and summarize - End the discussion by summarizing the key points and connecting them to the lesson. Encourage students to reflect on what they learned from the group discussion.
• Ready to use
• Fully customizable template
• Get Started in seconds

2. Role assignments

Role assignments mean giving each student a specific job or responsibility within the group, such as a leader, recorder, or presenter. By clearly defining roles, each student knows what they are responsible for, which helps the group stay organized and ensures everyone contributes.

• Define roles - Decide on the roles needed for the group task. Common roles include leader, note-taker, timekeeper, and presenter. Clearly explain what each role involves.
• Assign roles - Assign a role to each student in the group. Ensure that each student understands their responsibilities and how they contribute to the group’s success.
• Provide guidance - Give students instructions on how to fulfill their roles. For example, the leader might organize the group’s activities, while the note-taker records important points.
• Encourage collaboration - Have students work together, with each member fulfilling their role. Encourage them to support one another and communicate effectively.
• Monitor and support - Observe the groups to ensure that everyone is participating and that the roles are being carried out effectively. Offer help if needed.
• Review roles - After the activity, review how well the roles worked. Discuss with the group what went well and what could be improved for next time.

3. Peer teaching

Peer teaching involves students explaining concepts or lessons to each other. After learning a topic, students take turns teaching their peers about different aspects. This method reinforces their own understanding and builds their communication and teaching skills.

• Divide the material - Break the lesson into sections or topics. Each section should be manageable and relevant to the overall lesson.
• Assign topics - Assign each student or pair of students a different section of the material to learn and teach to their peers.
• Prepare to teach - Give students time to study their assigned section and prepare how they will explain it to others. They can use notes, visual aids, or examples.
• Teach peers - Have students present their section to the rest of the class. They should explain the material clearly and answer any questions from their peers.
• Encourage interaction - After each presentation, allow time for questions and discussion. This helps ensure that all students understand the material.
• Provide feedback - Offer feedback on both the teaching process and the content covered. Praise effective explanations and suggest improvements if needed.
• Reflect on learning - After all sections have been taught, review the key points as a class. Discuss what was learned and how peer teaching helped understand the material better.

Read more about different types of graphic organizers for reading, writing, teaching, learning and brainstorming.

4. Project-based learning

Project-based learning requires students to work together on a project that involves creating a final product, such as a presentation, report, or model. This strategy encourages collaboration as students must plan, research, and work together to complete the project, helping them develop teamwork and problem-solving skills.

• Choose a project - Select a project that relates to the lesson and requires students to use what they’ve learned. The project should be engaging and challenging but achievable.
• Form groups - Divide students into small groups. Each group will work together on the project, so make sure they are balanced in skills and abilities.
• Define roles and tasks - Assign roles within each group, such as researcher, writer, designer, or presenter. Clearly outline the tasks each role will handle to ensure everyone knows their responsibilities.
• Set goals and deadlines - Establish clear goals for the project and set deadlines for each phase. This helps groups stay on track and manage their time effectively.
• Provide resources and support - Give students the resources they need, such as materials, information, and tools. Offer support and guidance as they work on their project.
• Monitor progress - Check in with each group regularly to see how they are progressing. Offer feedback and help if they encounter any problems.
• Present the projects - Have each group present their project to the class. This allows students to share their work and learn from each other’s projects.
• Reflect and evaluate - After the presentations, reflect on the project process with the class. Discuss what worked well and what could be improved. Provide feedback on both the process and the final product.

5. Think-pair-share

Think-pair-share is a technique where students first think about a question or problem individually. They then pair up with a classmate to discuss their ideas before sharing their thoughts with the whole class. This approach promotes individual thinking, peer interaction, and class-wide sharing of ideas.

• Pose a question - Start by asking a clear and relevant question related to the lesson. Make sure it’s something that requires thoughtful consideration.
• Think individually - Give students a few moments to think about their answer or ideas on their own. This allows them to formulate their thoughts without immediate influence from others.
• Pair up - Have students pair up with a classmate. They should share their thoughts and discuss their answers with each other. This step helps them clarify their ideas and hear different perspectives.
• Share with the class - After discussing in pairs, invite pairs to share their ideas or answers with the whole class. This provides an opportunity for students to learn from each other and see a range of viewpoints.
• Facilitate discussion - Encourage a class discussion based on the shared ideas. Ask follow-up questions to deepen the conversation and connect it to the lesson.
• Reflect - Conclude by summarizing the main points and discussing how they relate to the lesson. Encourage students to reflect on what they learned from both their partner and the class discussion.

6. Jigsaw technique

The jigsaw technique divides a topic into several sections. Each student is assigned a different section to learn and then teach to their group. Once each student has taught their part, the group pieces together the complete topic. This method helps students become experts in their section and supports collaborative learning as they share their knowledge.

• Divide the topic - Break the topic into several sections or parts. Each section should cover a different aspect of the overall subject.
• Form expert groups - Create small groups where each group is assigned one section of the topic. These groups, called “expert groups,” focus on learning their specific section.
• Research and learn - Have the expert groups study their assigned section. They can use textbooks, articles, or other resources to become knowledgeable about their part of the topic.
• Reform groups - After learning their sections, reform new groups where each member represents a different expert group. These new groups will now have members who are experts on different sections of the topic.
• Share knowledge - In the new groups, each student teaches the other members about their section. This way, all group members learn about each part of the topic from their peers.
• Discuss and integrate - Encourage the new groups to discuss the information and put together the complete picture of the topic. This helps them understand how each part connects to the others.
• Present findings - Have each group present what they’ve learned to the class. This allows everyone to hear about each section and understand the entire topic.
• Reflect - After presentations, discuss the topic as a class. Reflect on what was learned and how the different sections fit together.

7. Collaborative problem-solving

Collaborative problem-solving involves presenting a problem or challenge for the group to solve together. Students discuss and brainstorm possible solutions, working together to reach a consensus. This strategy encourages critical thinking, teamwork, and the application of problem-solving skills.

• Present a problem - Start by giving the class a clear, engaging problem or challenge related to the lesson. The problem should be open-ended and require thoughtful discussion.
• Form groups - Divide the students into small groups. Each group will work together to find a solution to the problem.
• Discuss and brainstorm - Have each group discuss the problem and brainstorm possible solutions. Encourage them to consider different approaches and ideas.
• Develop a solution - Ask the groups to choose the best solution from their brainstormed ideas and develop a plan to address the problem. They should outline their reasoning and how their solution will work.
• Present solutions - Have each group present their solution to the class. They should explain their approach and how they arrived at their answer.
• Evaluate and discuss - After all groups have presented, discuss the different solutions as a class. Compare the approaches and consider the strengths and weaknesses of each solution.
• Reflect on the process - Reflect on the collaborative process. Discuss what worked well in the group discussions and what could be improved for future problem-solving activities.

8.Group brainstorming

Group brainstorming is a technique where students generate ideas on a topic together. Students contribute their thoughts and build on each other’s ideas to come up with a variety of solutions or approaches. This method promotes creativity and helps students consider different perspectives.

Explore more group brainstorming strategies to drive innovation.

• Introduce the topic - Start by presenting a clear and relevant topic or question for the brainstorming session. Make sure it’s something that encourages creative thinking.
• Form groups - Divide the class into small groups, ideally 3-5 students per group. Each group will brainstorm ideas together.
• Set guidelines - Explain the rules for brainstorming: encourage all ideas, avoid criticism, and build on each other’s thoughts. The goal is to generate as many ideas as possible.
• Brainstorm ideas - Give groups time to discuss and list their ideas. They can use a whiteboard or paper to write down their thoughts as they come up.
• Share ideas - After brainstorming, have each group share their ideas with the class. This allows everyone to see the range of ideas generated and contributes to the overall discussion.
• Discuss and refine - Discuss the ideas as a class. Identify the most promising ones and explore how they can be developed or combined.
• Reflect on the process - Reflect on the brainstorming session. Discuss what worked well and how the group process helped in generating ideas.

Learn more about how to brainstorm effectively with our brainstorming guide .

Debates involve students preparing arguments for or against a particular issue. They work in teams to research and develop their positions before presenting their arguments to the class. This technique enhances teamwork, encourages critical thinking, and improves public speaking skills.

• Choose a topic - Select a relevant and engaging topic for the debate. It should be something with clear sides or viewpoints, and relevant to the lesson.
• Divide into teams - Split the class into two or more teams, each representing a different side of the issue. Assign each team a position to argue for or against.
• Research and prepare - Give each team time to research their assigned position. They should gather evidence and prepare arguments to support their side of the debate.
• Set up the debate - Arrange a time for each team to present their arguments. Establish ground rules, such as time limits for speaking and guidelines for respectful communication.
• Hold the debate - Allow each team to present their arguments and respond to opposing points. Encourage students to listen carefully and engage with each other’s ideas.
• Facilitate discussion - After the debate, facilitate a class discussion about the arguments presented. Discuss the strengths and weaknesses of each side and any new insights gained.
• Reflect on the experience - Reflect on the debate process with the class. Talk about what was learned, how the debate helped in understanding the topic, and what could be improved.

10. Peer review

Peer review requires students to evaluate and provide feedback on each other’s work. After completing an assignment, students review their peers' work and offer constructive criticism. This method helps students improve their work through feedback and fosters a collaborative learning environment.

• Set clear guidelines - Explain what students should look for when reviewing their peers' work, such as clarity, accuracy, and completeness. Provide a checklist or rubric if needed.
• Pair up students - Assign each student a peer to review. Ensure that everyone knows who they will be reviewing and who will be reviewing their work.
• Review work - Have students read and evaluate their peer’s work based on the guidelines provided. They should note strengths and areas for improvement.
• Give feedback - Ask students to provide constructive feedback to their peers. They should offer specific suggestions for how to improve and highlight what was done well.
• Discuss feedback - Allow time for students to discuss the feedback they received and give. This can be done in pairs or small groups, focusing on understanding and applying the feedback.
• Revise and improve - Encourage students to use the feedback to revise and improve their own work. They should consider the suggestions and make changes as needed.
• Reflect on the process - After the peer review, discuss what students learned from giving and receiving feedback. Reflect on how the feedback helped them improve their work and how they can use it in future assignments.

Team building activities

Team building activities are exercises designed to strengthen relationships and improve teamwork among students. Activities such as trust exercises or group games help students build trust, improve communication, and work together more effectively.

• Choose an activity - Pick a team-building activity that fits the class size, age, and objectives. Activities should be fun and encourage cooperation, such as problem-solving tasks, games, or challenges.
• Explain the purpose - Start by explaining the goal of the activity. Let students know that the purpose is to improve teamwork and communication, not just to have fun.
• Divide into teams - Split the class into small teams. Make sure the teams are balanced in terms of skills and abilities to ensure everyone can contribute.
• Set up the activity - Provide clear instructions on how the activity will be conducted. Explain the rules and any materials needed.
• Participate and facilitate - Have students complete the activity while you observe and facilitate. Offer guidance and support if needed, but let students take the lead in working together.
• Debrief and discuss - After the activity, gather the class and discuss what happened. Ask students to reflect on how they worked together and what they learned about teamwork.
• Apply lessons learned - Encourage students to apply the teamwork skills they practiced in the activity to their regular classwork. Reinforce the importance of collaboration in achieving common goals.

Collaborative technology tools

Collaborative technology tools include digital platforms like shared documents, online whiteboards, or group chat applications. These tools allow students to work together in real-time or remotely, making it easier to collaborate on projects, share ideas, and provide feedback.

• Choose the right tool - Select a collaborative tool that fits your classroom needs. Popular options include online whiteboards, shared document editors, and communication platforms.
• Introduce the tool - Show students how to use the tool. Explain its features and how it can help them work together on tasks or projects.
• Set clear goals - Define what you want students to achieve using the tool. Set clear objectives for how the tool should be used in their collaborative work.
• Form groups - Divide students into small groups, if needed. Each group will use the tool to collaborate on their tasks or projects.
• Provide guidance - Offer support as students begin using the tool. Help them with any technical issues and remind them of best practices for online collaboration, such as clear communication and respecting others’ contributions.
• Monitor progress - Keep track of how students are using the tool. Check in regularly to see how they are collaborating and if they need any help.
• Review and reflect - After the task or project is complete, review how the tool helped with the collaboration. Discuss what worked well and what could be improved for future use.
• Encourage feedback - Ask students to provide feedback on their experience using the tool. This helps in understanding their needs and making improvements.

Best Practices for Implementing Collaborative Learning Strategies

Implementing collaborative learning strategies effectively involves careful planning and execution. Here are some best practices to ensure success:

• Clearly define objectives - Set clear goals for what you want to achieve with collaborative learning. Ensure that the objectives align with your lesson plans and learning outcomes.
• Choose appropriate strategies - Select collaborative learning strategies that fit your classroom’s needs and the specific goals of the lesson. Consider the students’ age, skill level, and the subject matter.
• Organize groups effectively - Form groups that are balanced in terms of skills and abilities. Mix students with different strengths to promote diverse perspectives and equitable participation.
• Provide clear instructions - Explain the tasks and expectations to students clearly. Make sure they understand their roles, responsibilities, and the purpose of the collaborative activity.
• Foster a positive environment - Create a supportive classroom atmosphere where students feel comfortable sharing their ideas and collaborating with others. Encourage respectful communication and teamwork.
• Monitor and support - Observe group interactions and offer support as needed. Provide guidance to help students stay on track and address any challenges they may encounter.
• Use technology effectively - Incorporate collaborative technology tools that enhance group work. Ensure that students are familiar with the tools and can use them effectively.
• Encourage reflection - After collaborative activities, have students reflect on their experience. Discuss what worked well, what could be improved, and how they can apply their learning to future group work.
• Assess and evaluate - Evaluate both the process and the outcomes of the collaborative activities. Use assessments to gauge individual contributions and group effectiveness.
• Provide feedback - Offer constructive feedback on the collaborative process and the results. Recognize achievements and provide suggestions for improvement.

Using Creately for Enhancing Collaborative Learning in the Classroom

Creately is a visual collaboration tool that helps make collaborative learning easier and more effective. Using Creately in the classroom helps students work together more efficiently, share ideas clearly, and manage projects effectively. It makes collaborative learning more interactive and productive.

Interactive Diagrams

Creately allows students to create and edit diagrams together in real-time. They can work on flowcharts, mind maps, and other visual aids, making it easier to brainstorm and organize ideas collectively.

Shared Workspaces

Students can collaborate in shared workspaces, where they can see and edit the same document or diagram simultaneously. This feature ensures everyone is on the same page and can contribute to the project.

Commenting and Feedback

Students and teachers can leave comments on specific parts of the work. This feature helps in providing instant feedback, asking questions, and discussing ideas directly on the document.

Templates and Examples

Creately offers a range of templates for different types of projects, like project planning or SWOT analysis and graphic organizers for writing, reading, note-taking and much more. These templates help students start their work quickly and stay organized.

Easy Integration

Creately integrates with other tools like Google Drive and Microsoft Teams. This makes it easy for students to share their work and collaborate across different platforms.

Real-Time Collaboration

With real-time updates, students can see changes made by their peers immediately. This keeps everyone synchronized and helps in making quick adjustments.

Visual Communication

Creately’s visual tools help in presenting ideas clearly. Students can use charts, diagrams, and other visuals to explain complex concepts more effectively.

Access Control

Teachers can control who can view or edit the documents. This ensures that only authorized members of the group can make changes and helps in managing group work securely.

Collaborative learning strategies can greatly enhance the classroom experience by encouraging teamwork and active participation. Techniques like group discussions, peer teaching, and project-based learning help students learn from each other and build important skills.

To make these strategies effective, set clear goals, choose the right methods, and support students throughout the process. This approach not only improves learning but also helps students develop skills they’ll need in the real world, such as communication and problem-solving. Embracing collaborative learning creates a more engaging and successful educational experience for everyone.

Smith, B., Macgregor, J., Goodsell, A., Maher, M. and Tinto, V. (1992). What is collaborative learning? Washington center for improving the quality of undergraduate education what is collaborative learning? *. [online] Available at: https://teach.ufl.edu/wp-content/uploads/2016/07/WhatisCollaborativeLearning.pdf .

Cornell University (2022). Collaborative learning. [online] Center for Teaching Innovation. Available at: https://teaching.cornell.edu/teaching-resources/active-collaborative-learning/collaborative-learning .

Laal, M. and Ghodsi, S.M. (2011). Benefits of Collaborative Learning. Procedia - Social and Behavioral Sciences, [online] 31(31), pp.486–490. doi: https://doi.org/10.1016/j.sbspro.2011.12.091 .

Join over thousands of organizations that use Creately to brainstorm, plan, analyze, and execute their projects successfully.

FAQs About Collaborative Learning Strategies

What are the key features of collaborative learning, how does collaborative learning work.

• Group assignments: The teacher assigns a task that requires teamwork, such as a project, problem-solving activity, or discussion. Each group works together to complete the task.
• Roles and responsibilities: In some cases, students may be assigned specific roles within the group (e.g., leader, note-taker, presenter). This ensures that everyone contributes and the group stays organized.
• Guidance and support: The teacher acts as a facilitator, providing guidance and support when needed, but allowing students to take charge of their learning. The goal is to encourage independence and collaboration among the students.

What is the difference between cooperative vs collaborative learning?

• Cooperative Learning: Involves students working together on a specific task, with each member contributing to achieve a common goal. It often involves structured roles and tasks.
• Collaborative Learning: Focuses on the process of working together to build knowledge and understanding through shared interaction and discussion. It emphasizes mutual learning and shared responsibility.

What is the role of the teacher in collaborative learning?

The teacher’s role in collaborative learning includes:

• Facilitator: Guiding and supporting groups as they work together, ensuring that they stay on task and communicate effectively.
• Planner: Designing and structuring collaborative activities that align with learning objectives.
• Monitor: Observing group interactions and providing feedback to enhance the learning process.
• Mediator: Resolving any conflicts or issues that arise during group work.
• Evaluator: Assessing both the process and the outcomes of collaborative activities to ensure that students meet learning goals.

What are the benefits of collaborative learning?

• Enhances critical thinking: Students discuss various viewpoints, deepening their understanding.
• Improves communication skills: Students practice clear expression and active listening.
• Fosters teamwork: Group work teaches effective collaboration and shared responsibility.
• Builds social skills: Encourages positive interactions and skills like empathy and conflict resolution.
• Increases engagement: Makes learning more dynamic and motivates active participation.
• Enhances problem-solving skills: Promotes creative and strategic thinking through group problem-solving.
• Supports diverse perspectives: Brings together different viewpoints, enriching the learning experience.

More Related Articles

Amanda Athuraliya is the communication specialist/content writer at Creately, online diagramming and collaboration tool. She is an avid reader, a budding writer and a passionate researcher who loves to write about all kinds of topics.

The Best Soft Skills Training Strategies to Boost Team Performance

Soft skills are key non-technical abilities like leadership, communication, teamwork, and problem-solving. Investing in soft skills training for your team can lead to better collaboration, employee satisfaction, and productivity.

Soft skills are key non-technical abilities like leadership, communication, teamwork, and problem-solving. These skills are crucial for enhancing workplace relationships and improving overall team performance.

While these skills may come naturally to some individuals, offering soft skills training on an organizational level can give employees and the overall business an edge. Investing in soft skills training for your team can lead to better collaboration, employee satisfaction, and productivity.

This article explores effective soft skills training strategies to boost your team’s performance. Looking for more tactics? Read our e-book: Top 3 Soft Skills Your Employees Need In the New World of Work .

Key Takeaways

• Soft skills are non-technical abilities such as communication, teamwork, problem-solving, and emotional intelligence, which are essential for enhancing workplace relationships and overall performance.
• On an organizational level, investing in soft skills training is key for improving business outcomes.
• Effective and engaging methods for teaching soft skills include role-playing exercises, story-based learning, and gamification.
• To implement successful soft skills training programs, be sure to assess skill gaps, select appropriate delivery methods, and leverage technology appropriately.

What is soft skills training?

Soft skills training is designed to develop essential non-technical abilities like:

• Communication
• Problem-solving
• Leadership 
• Emotional intelligence

These skills are vital for building stronger workplace relationships and boosting collaboration. Unlike hard skills, which are specific to certain job functions and can be easily measured through exams or certifications, soft skills are more personal and often harder to quantify.

However, just because soft skills are hard to quantify doesn’t mean they can’t be developed. Employees’ personal and professional growth relies on an organization’s investment in soft skills training programs.

When effectively leveraged, this type of training can help individuals improve their social interactions, adaptability, and behavior, which in turn enhances their overall performance. In fact, soft skills significantly contribute to career success, accounting for roughly 85% of an individual’s achievement over their career span.

Developing soft skills is an ongoing process that involves continuous effort, experience, practice, and self-reflection. It’s about cultivating transferable abilities across various roles and industries, making them some of the most valuable assets in today’s workforce.

Differentiating soft skills from hard skills

Before discussing key soft skills strategies for your organization, it’s important to understand the differences between soft skills and hard skills.

Hard skills, also known as technical skills, are job-related competencies that are often a prerequisite for employment in certain fields. They’re critical for performing specific job functions and can be acquired through degrees, courses, or on-the-job training. Examples of hard skills, also known as technical skills, include graphic design, data analysis, and search engine optimization.

However, hard skills alone are not enough to ensure success in the workplace. This is where soft skills come into play. Unlike hard skills, soft skills are non-technical and relate to interactions and work performance. They include personal qualities and traits like teamwork, adaptability, and emotional intelligence, all of which impact how individuals work and collaborate with others.

Interestingly, when soft skills are effectively developed, they can help employees apply and prove their hard skills even more powerfully. They can also improve the strength of an overall team and organization by boosting collaborative potential.

What are the benefits of soft skills training?

Soft skills training programs offer numerous benefits with the power to transform individual performance and overall organizational success. Notably, these programs can greatly improve employee performance. For example, one study found that a 12-month soft skills training program across five factories improved return on investment by roughly 250 percent .

Another key benefit of soft skills training is its ability to improve interpersonal relationships. This, in turn, leads to better teamwork and a stronger sense of community within the workplace. When employees communicate effectively and empathize with one another, it creates a more positive work environment and enhances collaboration. This can even lead to benefits such as improved employee retention, as participants feel more valued and motivated in their roles.

Soft skills training is particularly crucial for specific industries and job functions, especially those that interact with customers regularly. By training employees to respond empathetically in their communication, businesses can improve the strength of their customer service and respond to customer needs more effectively. This can improve brand reputation and lead to increased customer loyalty and satisfaction.

3 essential soft skills to develop

Now, let’s focus on three crucial soft skills: communication, collaboration, and time management. Each plays a pivotal role in ensuring efficient operations, effective teamwork, and a positive work culture.

1. Communication skills

Effective communication is the cornerstone of successful teamwork and client relations. Strong communication skills enable employees to:

• Interact efficiently with clients, partners, and each other
• Build rapport
• Practice active listening skills
• Speak confidently and concisely
• Provide constructive feedback more effectively

Bolstering interpersonal communication in these ways can also lead to increased client satisfaction and loyalty. Being able to deliver information clearly and concisely can help keep things clear, expedite conversations, and resolve potential conflicts.

Presentation skills are another vital aspect of communication, involving the ability to:

• Deliver information in a structured and engaging manner
• Use visual aids effectively to enhance an audience’s understanding
• Adapt the presentation style to suit the audience’s needs and preferences

With opportunities to polish their presentation skills, employees can communicate more effectively—both within their teams and with external stakeholders.

2. Teamwork and collaboration

Like communication skills, strong collaboration skills are essential for effective teamwork, innovation, and achieving collective goals. Teamwork skills allow employees to gain insight into their strengths and weaknesses within a team, and provide an opportunity to improve communication with others for better outcomes.

Collaboration skills also involve:

• The ability to take accountability for errors, and communicate any plans for resolving them
• Conflict mediation skills
• A shared commitment to working in a group
• The ability to foster creativity and innovation

3. Time management

Efficient time management is crucial for meeting deadlines, avoiding stress, and enhancing reliability. Good time management skills help individuals prioritize tasks, allocate time effectively, and maintain a positive approach to challenges, thereby increasing efficiency.

One helpful technique for improving time management skills is time blocking, which involves allocating specific blocks of time for different tasks. This approach can help employees stay focused, avoid procrastination, and ensure that all tasks are completed on time, ultimately improving personal productivity and overall team performance.

Because it is often impacted by external factors, time management can be one of the most challenging to train on. However, fostering a work culture where employees receive training to learn to prioritize tasks, set boundaries, and manage their time more efficiently can pay dividends in the long run.

Effective methods for teaching soft skills

Effective soft skills training requires an engaging approach encouraging active participation and real-world application. Below, we’ll cover three of the most effective methods: role-playing exercises, story-based learning, and gamification.

Role-playing exercises

Role-playing exercises allow employees to participate in scenarios to practice and enhance specific soft skills. These exercises help employees understand different perspectives and improve their problem-solving abilities by working through realistic workplace situations.

Scenarios used in role-playing can be tailored to address specific challenges employees face in their roles, providing immediate feedback and opportunities for improvement. For example, a customer service team might act out common scenarios from the perspective of both the service agent and the client to form a deeper understanding of how these interactions might play out.

Using role-playing in e-learning can be a very effective way to work through scenarios with employees at scale. With the right e-learning software, you can set up simulations and branching logic to help employees understand cause and effect while also aiding in knowledge retention.

Story-based learning

Story-based learning uses narratives or storytelling methods to convey essential lessons and concepts. This can be a highly valuable tool in soft skills training. By reflecting on their personal experiences or envisioning scenarios with fictional characters, employees can extract valuable insights and apply them to real-life situations.

Narratives in story-based learning often mirror the challenges of the job, making lessons more relatable and memorable. This method helps illustrate the consequences of different actions and decisions, enhancing employees’ critical thinking and problem-solving abilities.

Gamification

To make your soft skills courses more engaging and motivating, try incorporating game design elements like point scoring, leaderboards, and rewards. These gamification elements encourage participation and make the training experience more enjoyable for participants.

Interactive games can simulate real-life scenarios your employees might encounter, allowing them to practice and refine their soft skills in a controlled, low-risk environment. Be sure to offer opportunities for constructive feedback in your gamified training to allow participants to hone their skills over time.

How to implement soft skills training programs

To implement a soft skills program effectively and at scale, it’s important to follow a framework. Below, we’ll cover the key steps to doing so, including assessing skill gaps, choosing the right delivery method, and promoting continuous learning and feedback.

By following these steps, you can ensure that your training is tailored to meet the specific needs of your organization and employees.

1. Assess skill gaps

Identifying existing skill gaps among employees is a crucial first step for tailoring training programs efficiently. Organizations can pinpoint opportunities for soft skills development by speaking with employees at all levels and consulting with managers.

Assessing skill gaps helps ensure that your training addresses specific needs and enhances your team’s overall performance. This is essential for creating targeted and impactful training programs.

2. Choose the right delivery method

To ensure your employees can effectively engage with and retain material, it’s key to select the appropriate delivery method for your soft skills training. This may vary depending on the needs of your organization or team.

For example, you may want to create a dedicated soft skills course that allows employees to access training regularly in bite-size chunks without interfering with their day-to-day work. You can also use micro-learning, which breaks down training into small and actionable segments, to allow for immediate application of soft skills.

3. Encourage continuous learning and feedback

Encouraging regular feedback and self-reflection helps employees identify areas for improvement and fosters a learning mindset. This culture of continual learning is essential for addressing mistakes and setting new goals.

Utilizing an e-learning platform like Articulate 360 can help you provide consistent and personalized learning experiences with opportunities for feedback.

Leveraging technology in soft skills training

Technology—specifically online learning platforms—is a key way to enhance the accessibility and effectiveness of soft skills training. These platforms provide flexible and engaging training environments that can be tailored to meet the specific needs of employees.

Below, we’ll explore how platforms like Articulate 360 can be used to develop soft skills.

E-learning platforms for soft skill development

When it comes to soft skills training, e-learning platforms offer the following benefits:

• Access to training regardless of an employee’s geographical location or time constraints
• Interactive multimedia modules for an engaging learning experience
• Videos for visual and auditory learning
• Multi-device access

These platforms provide learners with a flexible and convenient way to develop their soft skills, making it easier for employees to fit training into their schedules.

Articulate 360 capabilities

Articulate 360, the leading e-learning platform, offers a platform designed to help you create engaging, interactive courses tailored to specific soft skills. Some key capabilities include:

• Engaging learner experiences : Articulate 360 lets you build interactive, effective, and engaging sales training that can include branching scenarios, interactive activities, knowledge checks, and a wide range of assessments.
• Intuitive authoring for ALL course creators : With Articulate 360’s intuitive UI and integrated AI Assistant, you and your cross-functional collaborators can easily create effective sales training to boost sales performance.
• Quizzes and knowledge checks : Provide your learners with immediate feedback, helping them identify areas for improvement and track their progress.
• Helpful Templates: Get a head start on course creation with a library of templates on key sales topics such as prospecting, pipeline management, objection handling, and deal negotiation.
• Seamless collaboration and reviews: Collaborate on course creation by inviting colleagues to create and edit content, improving the quality of your sales training. Collect and approve in-context feedback, simplifying and accelerating the entire course review and approval process.

By leveraging the capabilities of platforms like Articulate 360, organizations can ensure continuous development and a more dynamic approach to soft skills training.

Measuring the impact of soft skills training

To ensure the effectiveness of your soft skills training, b e sure to close the loop by evaluating its impact. This can be done through performance metrics, employee feedback, and observed behavioral changes. Pre- and post-assessments can gauge initial and post-training performance levels, providing a clear picture of the training’s impact.

You can also provide employees with opportunities for self-assessment, peer feedback, and supervisor feedback, or track improvements in key areas like productivity, collaboration, and communication after training. Including 360-degree feedback allows for assessment from multiple perspectives, ensuring a comprehensive evaluation.

Evaluation methods for soft skills training programs include:

• Knowledge checks and quiz results from online training programs
• Surveys to gather subjective insights into the effectiveness of the training
• Observing real-life applications of the skills learned
• Assessing knowledge retention rates to measure the long-term impact of the training

These evaluation methods help organizations refine and improve their soft skills training programs by utilizing various soft skills training methods.

Real-life examples of successful soft skills training

Real-life soft skills training examples can provide valuable insights into the implementation and positive results of soft skills training programs. For instance, Google’s Project Oxygen program demonstrated that managers who effectively communicated and supported employee well-being were key to maintaining high-performing teams.

IBM’s Leadership Development Program focuses on enhancing soft skills such as emotional intelligence, collaboration, and communication among its leaders.

Zappos invested in training programs prioritizing customer service skills, which enhanced employee communication and problem-solving abilities, leading to higher customer satisfaction. These case studies highlight the common benefits of soft skills training programs, such as:

• Improved communication
• Better leadership
• Enhanced problem-solving abilities
• Increased employee engagement and satisfaction.

The impact of employee soft skills training

Investing in soft skills training programs is essential for enhancing employee performance, fostering better workplace relationships, and driving overall organizational success. By understanding the key benefits, differentiating between soft and hard skills, and focusing on developing essential soft skills like communication, teamwork, and time management, organizations can create a more dynamic and effective workforce.

Looking for more strategies to improve employee soft skills? Read our e-book: Top 3 Soft Skills Your Employees Need In the New World of Work .

You may also like

How E-Learning Enhances Employee Retention

Learn how e-learning can boost employee retention through personalized, flexible, and continuous learning opportunities that foster loyalty and productivity.

Bring E-Learning to Life With Interactive Scenarios

Discover how to transform e-learning with interactive decision-making scenarios. Engage learners, build real-world skills, and make online courses memorable.

Articulate Wins 2024 Employer of Choice Award

We are thrilled to announce that the Minority Corporate Counsel Association has awarded Articulate with the 2024 Employer of Choice Award.