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Teaching with Jillian Starr

teaching little stars to shine brightly

FREE Number Talks

First grade teachers, access 20 FREE Number Talk Prompts to enhance your place value unit and get your students engaged in conversation.

9 Powerful Strategies to Engage Students in Math Discourse 

Have you ever had students who can compute with ease, but then struggle to talk about the math they’re doing? Engaging in math discourse is a skill, and one that we get to help develop as teachers.

If you’ve followed me for a bit, you know that I adore diving into all things math. From teaching it, to talking about it, writing about it, and reading about it… math is something I am passionate about! I was recently reading Visible Learning for Math by John Hattie (highly recommend!), and I was so excited to see what an impact discussion in a math class has on math learning.

I won’t go into the nerdy details like effect sizes but suffice it to say, it is one of the most impactful things that you can do to help kids learn math!

The Benefits of Math Discourse

There are many benefits of getting students to engage in math discourse. Early in the school year, one of our highest priorities is building the classroom community. Having kids discussing math with one another and sharing their math thinking is a great way to build community. When kids discuss math with one another and share their mathematical thinking, they not only practice active listening and other effective communication skills, but they also get the opportunity to “try on” new ideas. 

Beyond the first weeks of school, math discourse helps to challenge the idea that there is only one way to think about math. By sharing their various perspectives, students are exposed to different strategies and perspectives while studying the same problem or concept. In fact, during math discussions, students will look for patterns, compare different ideas and strategies, and make connections between them, all leading to a deeper understanding of math.

That’s not everything though! Math discourse also supports students’ academic language development. They can practice using new vocabulary words in context, which of course benefits all students, but it is also critical in supporting the language development for multilingual learners. A win-win! With so many benefits, it is no wonder that classroom discussions make such an impact on math learning!

Of course, getting kids to talk about math isn’t quite so easy. As teachers, we’ve all had the experience of asking kids to talk to their partners and having kids mumble something and then go silent or start talking instead about what they want to do about recess. So let’s talk about strategies for getting kids to share their mathematical thinking and truly engage in math discourse.

Structures to Support Math Discourse

There are different ways to structure discussions during math. You can have kids responding to teacher questions, talking to a partner, or talking in small groups, among other structures. Here are two of my favorite structures for encouraging math discourse:

Think-Pair-Share

During a think-pair-share, the teacher poses a question or problem to the whole class. Students then take a few moments to think about their responses. Then they pair up with a partner and discuss the question together. When we are just getting started with this routine, I make it a point to remind students that both of them should share their thinking and that when their partner is sharing, they should be listening.

Finally, students are their responses – the best part! This part is when students get to practice sharing their math thinking with the larger group. Sometimes I ask students to share their own thinking but often, I ask them to share what their partner shared or ask them to respond to a prompt like “What surprised you about how your partner solved the problem?” Having students share their partner’s thinking or responding to a prompt forces them to think even more deeply. 

Group/Partner Problem Solving  

I absolutely love this structure to introduce new math topics. I know, I know, having them solve problems about a new math topic? Yup, problem-based instruction is challenging and it really gets kids grappling with new ideas. To support their growth, I have students work with a partner or small group. I then assign them a problem that relates to and builds on previous content.

For example, if my students know how to subtract two-digit numbers without regrouping and we’re moving on to regrouping, I may pose the problem 56 – 29 and have students try to solve using the strategies they’ve already learned or using any strategy they think may work. I emphasize that all students need to be able to explain what their group did and that I should be able to ask any member of the group to share.

My classes have always loved these activities and it’s incredibly rewarding to see their excitement when they crack the code and master a new idea!

Important Considerations for Math Discourse

Good ol’ wait time! It’s one of the simplest but most effective strategies to get kids talking. Whether as a student ourselves or as a teacher, we’ve all had the experience of having the same person answer question after question while everyone else watches and listens on.

As teachers, we want all of our students to be engaged in the thinking required to engage in math discourse, so how do we do that? Well, people will often fill silence and I use that to my advantage when having whole class discussions!

I’ll pose a question to get us started and then wait. Some kids need time to process the question. Other kids need time to formulate a response, and even others just need time to get up the courage to share with the whole class.

Regardless of why, pausing, sometimes for longer than feels comfortable, encourages more students to join the discussion. I even let my students in on my “secret” and encourage them to give their partners or groups wait time when having discussions.

Questioning

Consider these two questions: What is 25 – 18? and what do you notice about 25 – 18? Both questions are about the same problem but one is asking for a very brief answer and the other is asking a more opened ended question that requires explanation.

The kinds of questions you ask your students can either encourage or discourage conversation. Open-ended questions work wonders for encouraging math discourse. The open-ended question I probably use most often is “How do you know?”

If you are making the shift to more open-ended questions, start with just that one and see how kids respond. You may get some students who say they “just know” at first but don’t stop there. Really challenge students to expand on their thinking – it’s Math Practice Standard 3 of the Common Core State Standards, so get those kids explaining!

Supportive Tools for Math Discourse

Anchor charts and word walls .

Anchor charts and math word walls can be very helpful when encouraging kids to engage in math discourse. When discussing, we want students to be able to explain their ideas clearly and specifically but since they are often discussing content that is new to them, they may be less comfortable with the vocabulary or may need a reference to support them as they speak.

Enter anchor charts and math word walls ! Students can refer to word walls to find the math vocabulary word to describe what they are thinking or refer to the anchor chart to help them express their mathematical ideas more clearly and confidently. They are truly game changers for encouraging math discourse!

Math Vocabulary Word Walls

If you’re looking for more ways to improve your student’s math vocabulary, you can check out 6 ways to build math vocabulary right here!

Low Entry Warm Ups 

Low-entry warm-ups are wonderful for getting all students engaged and talking about math because they are accessible to most, if not all, students. Warm-ups like this include Notice and Wonder, How Many, and What Do You Know About.

Notice and Wonder

Display a photo, image, or problem and ask students what they notice and what they wonder about what they see. This is a low-entry activity because some students may notice things like the color of a shape, how many 3s are in a problem, or the symmetry in the letters written in the image. The idea is that kids can enter this warm-up at the level that’s right for them and feel safe engaging in math discourse. 

Show students an image and ask how many they see. For example, you may display an image of a group of coins and ask how many. Students may say that they see 4 coins or they may say that they see 26 cents or even 1 copper coin. Again, this provides a safe environment for students to engage in math discourse because they are able to share various interpretations of the question and multiple correct answers. 

What Do You Know About

Present students with a number, image, shape, or really anything mathematical and ask what they know about it. If you shared the picture of a green triangle, students could share things as simple as knowing that the shape is green or as complex as knowing that this particular triangle has three lines of symmetry.

These warm-up routines are such a great way to get all students engaged and talking about math. They spark rich discussions and allow students to share their prior knowledge.

Sentence Starters

For students who are reluctant to participate in math discourse, sentence starters can be a game changer. By providing students with a starting point, sentence starters take off the pressure and make it easier for students to articulate their ideas. Post sentence starters on an anchor chart or on smaller posters around the classroom so students can reference them anytime they are discussing math. Here are the sentence starters we use:

• My strategy is the same/different than yours because…
• I think that makes sense/doesn’t make sense because…
• The first thing I did to solve the problem was…
• I agree/disagree because… 
• To add on to what ___ said,…
• I know my answer makes sense because…

I hope you’ll give some of these ideas to encourage math discourse! I can’t wait to hear all about the wonderful discussions your students are having! Not only is math enjoyable when discussing it with others, but it also helps students to grow their mathematical thinking and skills. 

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JOIN MEANINGFUL MATH

hello I'm Jillian

I’m so happy you’re here. I want every child to feel confident in their math abilities, and that happens when every teacher feels confident in their ability to teach math.

In my fifteen years of teaching, I sought every opportunity to learn more about teaching math. I wanted to know HOW students develop math concepts, just like I had been taught how students learn to read. I want every teacher to experience the same math transformation I did, and have the confidence to teach any student that steps foot in their classroom. I’m excited to be alongside you in your math journey!

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• January 22, 2024

10 Sentence Starters for Elementary Math Explorations

Greetings, fellow educators! Today, we’re delving into the realm of elementary mathematics and unveiling ten powerful sentence starters to spark curiosity, engagement, and deep mathematical thinking in your students. These versatile prompts can be adapted for various math topics, fostering a positive and interactive learning environment. Let’s explore how to use these sentence starters effectively!

Sentence Starter Usage

• “I notice that…” Usage: Encourage students to observe and articulate patterns or relationships within a set of numbers, shapes, or mathematical concepts. Use Sentence Starters to promote keen observation skills and lays the foundation for mathematical analysis.
• “Can you explain your thinking when…” Usage: Prompt students to express their thought processes when solving a math problem or tackling a mathematical challenge. This fosters a culture of sharing ideas and allows for a deeper understanding of different problem-solving approaches.
• “What would happen if…” Usage: Inspire creativity by asking students to explore hypothetical scenarios related to a math concept. This sentence starter encourages critical thinking and helps students anticipate outcomes, enhancing their problem-solving skills.
• “I can solve this problem by…” Usage: Empower students to take ownership of their problem-solving strategies. Encourage them to articulate the methods they plan to use, promoting a sense of confidence and independence in approaching mathematical challenges.

More uses For Sentence Starters

• “Let’s investigate why…” Usage: Spark curiosity and a love for exploration by inviting students to investigate the reasons behind mathematical phenomena. This sentence starter encourages a hands-on, inquiry-based approach to learning.
• “In what ways are these two concepts similar or different?” Usage: Foster connections between different mathematical ideas by prompting students to compare and contrast concepts. These sentence starters encourages students to identify similarities and differences, promoting a deeper understanding of mathematical relationships.
• “What strategy would you use to…” Usage: Encourage students to consider various problem-solving strategies when tackling mathematical challenges. This sentence starter promotes metacognition and allows students to reflect on the most effective approach for a given task.
• “Let’s explore real-world situations where…” Usage: Connect math to the real world by prompting students to explore how mathematical concepts apply to everyday scenarios. This sentence starter encourages students to see the relevance of math in their lives.
• “How can we represent this mathematically?” Usage: Encourage students to translate real-world problems into mathematical expressions, equations, or models. This sentence starter reinforces the importance of mathematical representation and abstraction.
• “What questions do you have about…” Usage: Cultivate a culture of inquiry by inviting students to generate questions related to a specific math concept. Sentence starters encourages curiosity and sets the stage for collaborative exploration and discussion.

Sentence Starter Wrap Up

Incorporating these sentence starters into your elementary math lessons can transform the learning experience, making it more interactive, engaging, and reflective. Encourage a supportive classroom environment where students feel empowered to express their mathematical thinking, fostering a love for learning that extends beyond the textbook.

Happy teaching!

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Maths Thinking Sentence Starter Posters

Updated:  08 Oct 2019

Forty-two posters with maths reflective sentence starters.

Non-Editable:  PDF

Pages:  42 Pages

Years:  F - 7

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• My strategy was successful because…
• The steps I followed were…
• The maths words I used were…
• I solved the problem by…
• The maths words that help someone understand what I did are…
• I could make this clearer by using a…
• A graph (table, T-chart, picture) shows this the best because…
• I decided to use a…
• The most important thing I learnt in maths today is…
• I found challenging… because…
• I was feeling really…
• A question I had was…
• We do this at home when we…
• I did something like this before when…
• I thought of…
• This new maths idea is like…
• Today, I felt…
• I need help with… because…
• The hardest part of this unit on… is…
• The thing I like best about mathematics is…
• We found out by…
• I knew it couldn’t be that because…
• I got the same answer but…
• I got the same answer by…
• I found the answer by…
• How did you…
• I knew that…
• The best way to solve this problem would be to…
• I need to work on…
• I learnt that…
• I discovered that…
• I know this because…
• Another strategy I could use would be…
• The strategy I used was…
• I know my answer is correct because…
• I can prove my thinking by…
• I can check my answer by…
• I know the answer is reasonable because…
• The first thing I did to solve the problem was…

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These sentences starters are great for getting students to reflect in different ways.

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Constructing in three dimensions: sentence starters and frames.

Some ideas for sentence frames/starters that could be incorporated into your lesson are listed below. If you think a sentence frame/starter will be helpful, consider how will it support students’ mathematical learning and/or development of academic language, and decide which sentence frame/starter (from the list below or that you create) would best support students’ learning.

One relationship I noticed between the number of faces on a pyramid and the number of toothpicks I needed was 

____________________________________________________________________________________________________________

One relationship I noticed between the number of faces on a pyramid and the number of marshmallows I needed was 

For every ____________ that I added to a pyramid, I needed 

The cube is a ______________________ with 

____________________________________________________________________________________________________________  

Academic Language

Students should have opportunities to see, hear, and write key mathematical ideas during this activity. There are some specific terms that students need to understand in order to engage in this task, and there are some additional terms and phrases that may surface as the students engage with the task. You may think of additional words or phrases that are key to this activity.  As the task is introduced, solved by the students, and discussed, ensure that students have opportunities to experience (i.e., through discussion, pictures, and the use of gestures) and to build understanding for key words and phrases. Examples of words and phrases that may be involved in work on this problem include:

·      3-dimensional; Polyhedron; Prism

·      Pyramid; Cube

·      Base; Faces

·      Pentagon

·      Construct

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20 MASTERY STEM SENTENCE STARTERS

Subject: Mathematics

Age range: 7-11

Resource type: Visual aid/Display

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4 December 2019

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Maths STEM sentences help support all abilities in KS1 and KS2 to explain their reasoning and problem solving strategies.

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