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Math Essay | Essay on Math for Students and Children in English

February 13, 2024 by Prasanna

Math Essay: Mathematics is generally defined as the science that deals with numbers. It involves operations among numbers, and it also helps you to calculate the product price, how many discounted prizes here, and If you good in maths so you can calculate very fast. Mathematicians and scientists rely on mathematics principles in their real-life to experiments with new things every day. Many students say that ” I hate mathematics ” and maths is a useless subject, but it is wrong because without mathematics your life is tough to survive. Math has its applications in every field.

You can also find more  Essay Writing  articles on events, persons, sports, technology and many more.

Long and Short Essays on Math for Students and Kids in English

We are presenting students with essay samples on an extended essay of 500 words and a short of 150 words on the topic of math for reference.

Long Essay on Math 500 Words in English

Long Essay on Math is usually given to classes 7, 8, 9, and 10.

Mathematics is one of the common subjects that we study since our childhood. It is generally used in our daily life. Every person needs to learn some basics of it. Even counting money also includes math. Every work is linked with math in some way or the other. A person who does math is called a Mathematician.

Mathematics can be divided into two parts. The first is Pure mathematics, and the second is Applied mathematics. In Pure mathematics, we need to study the basic concept and structures of mathematics. But, on the other side, Applied mathematics involves the application of mathematics to solve problems that arise in various areas,(e.g.), science, engineering, and so on.

One couldn’t imagine the world without math. Math makes our life systematic, and every invention involves math. No matter what action a person is doing, he should know some basic maths. Every profession involves maths. Our present-day world runs on computers, and even computer runs with the help of maths. Every development that happens requires math.

Mathematics has a wide range of applications in our daily life. Maths generally deals with numbers. There are various topics in math, such as trigonometry; integration; differentiation, etc. All the subjects such as physics; chemistry; economy; commerce involve maths in some way or the other. Math is also used to find the relation between two numbers, and math is considered to be one of the most challenging subjects to learn. Math includes various numbers, and many symbols are used to show the relation between two different numbers.

Math is complicated to learn, and one needs to focus and concentrate more. Math is logical sometimes, and the logic needs to be derived out. Maths make our life easier and more straightforward. Math is considered to be challenging because it consists of many formulas that have to be learned, and many symbols and each symbol generally has its significance.

Some of the advantages of Math in our daily life

• Managing Money: Counting money and calculating simple interest, compound interest includes the usage of mathematics. Profit and loss are also computed using maths. Anything related to maths contains maths.
• Cooking: Maths is even used in cooking as estimating the number of ingredients that have to be used is calculated in numbers. Proportions also include maths.
• Home modelling: Calculating the area is essential in the construction of the home or home modelling. The size is also measured using maths. Even heights are also measured using maths.
• Travelling: Distance between two places and time taken to travel also includes maths. The amount of time taken revolves around maths. Almost every work is related to maths in some way or another. Maths contains some conditions that need to be followed, and maths has several formulas that have to be learned to become a mathematician.

Short Essay on Math 150 Words in English

Short Essay on Math is usually given to classes 1, 2, 3, 4, 5, and 6.

Maths is generally defined as the science of numbers and the operations performed among them. It deals with both alphabets along with numbers and involves addition, subtraction, multiplication, division, comparison, etc. It is used in every field. Maths consists of finding a relation between numbers, calculating the distance between two places, counting money, calculating profit and loss.

It is of two types pure and applied. Pure math deals with the basic structure and concept of maths, whereas applied mathematics deals with how maths is used it involves the application of maths in our daily life. All the subjects include maths, and hence maths is considered to be one of the primary and joint issues which need to be learned by everyone. One couldn’t imagine their life using maths. It has made our experience easy and straightforward. It has prevented chaos in our daily life. Hence learning maths is mandatory for everyone.

10 Lines on Math in English

• Father of Mathematics was Archimedes.
• Hypatia is the first woman know to know to have taught mathematics.
• From 0-1000 ,letter “A” only appears first in 1,000 ( “one thousand “).
• Zero (0) is the only number that can not be represented by Roman numerals.
• The Sign plus (+) and Minus(-) were discovered in 1489 A.D.
• Do you know that a Baseball field is of the perfect shape of a Rhombus.
• Jiffy is considered to be a unit of time for 1/100th of a second.
• 14th March International Day of Mathematics.
• Most mathematics symbols weren’t invented until the 16th century.
• The symbols for the division is called an Obelus.

FAQ’s on Math Essay

Question 1. What is Mathematics in simple words?

Answer: Mathematics is the study of shapes, patterns, numbers, and more. It involves a comparison between two numbers and calculating the distance between two places.

Question 2. Do we need mathematics every day?

Answer: Yes, we need mathematics every day, from buying a product to sell anything you want. Maths is present in our daily life, and no matter what work we do, maths is involved, and the application of maths is current in our everyday life.

Question 3. Who was the No.1 Mathematicians in the world?

Answer: Isaac Newton, who was a profound mathematician, is considered to be one of the best mathematicians in the world.

Question 4. What are the applications of maths?

Answer: Maths have various applications in our daily life. Maths is present everywhere from counting money to the calculating distance between two places. We could find math applications around.

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Essay on Importance of Mathematics in our Daily Life in 100, 200, and 350 words.

• Updated on  
• Dec 22, 2023

Mathematics is one of the core aspects of education. Without mathematics, several subjects would cease to exist. It’s applied in the science fields of physics, chemistry, and even biology as well. In commerce accountancy, business statistics and analytics all revolve around mathematics. But what we fail to see is that not only in the field of education but our lives also revolve around it. There is a major role that mathematics plays in our lives. Regardless of where we are, or what we are doing, mathematics is forever persistent. Let’s see how maths is there in our lives via our blog essay on importance of mathematics in our daily life. 

Table of Contents

• 1 Essay on Importance of Mathematics in our Daily life in 100 words 
• 2 Essay on Importance of Mathematics in our Daily life in 200 words
• 3 Essay on Importance of Mathematics in our Daily Life in 350 words

Essay on Importance of Mathematics in our Daily life in 100 words 

Mathematics is a powerful aspect even in our day-to-day life. If you are a cook, the measurements of spices have mathematics in them. If you are a doctor, the composition of medicines that make you provide prescription is made by mathematics. Even if you are going out for just some groceries, the scale that is used for weighing them has maths, and the quantity like ‘dozen apples’ has maths in it. No matter the task, one way or another it revolves around mathematics. Everywhere we go, whatever we do, has maths in it. We just don’t realize that. Maybe from now on, we will, as mathematics is an important aspect of our daily life.

Also Read:- Importance of Internet

Essay on Importance of Mathematics in our Daily life in 200 words

Mathematics, as a subject, is one of the most important subjects in our lives. Irrespective of the field, mathematics is essential in it. Be it physics, chemistry, accounts, etc. mathematics is there. The use of mathematics proceeds in our daily life to a major extent. It will be correct to say that it has become a vital part of us. Imagining our lives without it would be like a boat without a sail. It will be a shock to know that we constantly use mathematics even without realising the same. 

From making instalments to dialling basic phone numbers it all revolves around mathematics. 

Let’s take an example from our daily life. In the scenario of going out shopping, we take an estimate of hours. Even while buying just simple groceries, we take into account the weight of vegetables for scaling, weighing them on the scale and then counting the cash to give to the cashier. We don’t even realise it and we are already counting numbers and doing calculations. 

Without mathematics and numbers, none of this would be possible.

Hence we can say that mathematics helps us make better choices, more calculated ones throughout our day and hence make our lives simpler. 

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Also Read: How to Prepare for UPSC in 6 Months?

Essay on Importance of Mathematics in our Daily Life in 350 words

Mathematics is what we call a backbone, a backbone of science. Without it, human life would be extremely difficult to imagine. We cannot live even a single day without making use of mathematics in our daily lives. Without mathematics, human progress would come to a halt. 

Maths helps us with our finances. It helps us calculate our daily, monthly as well as yearly expenses. It teaches us how to divide and prioritise our expenses. Its knowledge is essential for investing money too. We can only invest money in property, bank schemes, the stock market, mutual funds, etc. only when we calculate the figures. Let’s take an example from the basic routine of a day. Let’s assume we have to make tea for ourselves. Without mathematics, we wouldn’t be able to calculate how many teaspoons of sugar we need, how many cups of milk and water we have to put in, etc. and if these mentioned calculations aren’t made, how would one be able to prepare tea? 

In such a way, mathematics is used to decide the portions of food, ingredients, etc. Mathematics teaches us logical reasoning and helps us develop problem-solving skills. It also improves our analytical thinking and reasoning ability. To stay in shape, mathematics helps by calculating the number of calories and keeping the account of the same. It helps us in deciding the portion of our meals. It will be impossible to think of sports without mathematics. For instance, in cricket, run economy, run rate, strike rate, overs bowled, overs left, number of wickets, bowling average, etc. are calculated. It also helps in predicting the result of the match. When we are on the road and driving, mathetics help us keep account of our speeds, the distance we have travelled, the amount of fuel left, when should we refuel our vehicles, etc. 

We can go on and on about how mathematics is involved in our daily lives. In conclusion, we can say that the universe revolves around mathematics. It encompasses everything and without it, we cannot imagine our lives. 

Also Read:- Essay on Pollution

Ans: Mathematics is a powerful aspect even in our day-to-day life. If you are a cook, the measurements of spices have mathematics in them. If you are a doctor, the composition of medicines that make you provide prescription is made by mathematics. Even if you are going out for just some groceries, the scale that is used for weighing them has maths, and the quantity like ‘dozen apples’ has maths in it. No matter the task, one way or another it revolves around mathematics. Everywhere we go, whatever we do, has maths in it. We just don’t realize that. Maybe from now on, we will, as mathematics is an important aspect of our daily life.

Ans: Mathematics, as a subject, is one of the most important subjects in our lives. Irrespective of the field, mathematics is essential in it. Be it physics, chemistry, accounts, etc. mathematics is there. The use of mathematics proceeds in our daily life to a major extent. It will be correct to say that it has become a vital part of us. Imagining our lives without it would be like a boat without a sail. It will be a shock to know that we constantly use mathematics even without realising the same.  From making instalments to dialling basic phone numbers it all revolves around mathematics. Let’s take an example from our daily life. In the scenario of going out shopping, we take an estimate of hours. Even while buying just simple groceries, we take into account the weight of vegetables for scaling, weighing them on the scale and then counting the cash to give to the cashier. We don’t even realise it and we are already counting numbers and doing calculations. Without mathematics and numbers, none of this would be possible. Hence we can say that mathematics helps us make better choices, more calculated ones throughout our day and hence make our lives simpler.  

Ans: Archimedes is considered the father of mathematics.

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Home — Essay Samples — Science — Mathematics in Everyday Life — Mathematics In Everyday Life: Most Vital Discipline

Mathematics in Everyday Life: Most Vital Discipline

• Categories: Mathematics in Everyday Life

About this sample

Words: 795 |

Published: Mar 14, 2019

Words: 795 | Pages: 2 | 4 min read

Works Cited

• Benacerraf, P. (1991). Mathematics as an object of knowledge. In P. Benacerraf & H. Putnam (Eds.), Philosophy of mathematics: Selected readings (pp. 1-13). Cambridge University Press.
• EdReady. (n.d.). Home. Retrieved from https://www.edready.org/
• Puttaswamy, T. K. (2012). Engineering mathematics. Dorling Kindersley (India) Pvt. Ltd.
• Steen, L. A. (Ed.). (2001). Mathematics today: Twelve informal essays. Springer Science & Business Media.
• Suter, B. W. (2012). Mathematics education: A critical introduction. Bloomsbury Academic.
• Tucker, A. W. (2006). Applied combinatorics. John Wiley & Sons.
• Vakil, R. (2017). A mathematical mosaic: Patterns & problem solving. Princeton University Press.
• Wolfram MathWorld. (n.d.). MathWorld--The web's most extensive mathematics resource. Retrieved from http://mathworld.wolfram.com/
• Wu, H. H. (2011). The mis-education of mathematics teachers. Educational Studies in Mathematics, 77(1), 1-20.
• Ziegler, G. M., & Aigner, M. (2012). Proofs from THE BOOK. Springer Science & Business Media.

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Essay on Importance of Mathematics in Our Daily Life

Students are often asked to write an essay on Importance of Mathematics in Our Daily Life in their schools and colleges. And if you’re also looking for the same, we have created 100-word, 250-word, and 500-word essays on the topic.

Let’s take a look…

100 Words Essay on Importance of Mathematics in Our Daily Life

Introduction.

Mathematics is a crucial part of everyday life. It helps us make sense of the world around us and solve practical problems.

Mathematics in Daily Tasks

From shopping to cooking, we use math. It helps us calculate costs, quantities, and time.

Mathematics in Professions

In professions like engineering, computer science, and finance, math is indispensable.

Mathematics in Decision Making

Math helps us make informed decisions by analyzing data and predicting outcomes.

250 Words Essay on Importance of Mathematics in Our Daily Life

The pervasive presence of mathematics.

Mathematics, often perceived as a complex and abstract discipline, is in fact an integral part of our everyday lives. It forms the foundation for many of the decisions we make and the actions we perform daily, from managing finances to navigating directions.

A Tool for Logical Reasoning

Mathematics fosters logical reasoning and problem-solving skills. It cultivates an analytical mindset, enabling us to break down complex problems into simpler, manageable parts. This approach is not just confined to mathematical problems but extends to various real-life situations, thereby honing our decision-making abilities.

Mathematics in Technological Advancements

The rapid progress in technology, which has become an inseparable part of our lives, is deeply rooted in mathematical principles. Algorithms, which form the basis of computing, are mathematical models. The internet, smartphones, GPS, and even AI owe their existence to mathematical concepts.

Financial Management and Mathematics

Managing personal finances, a critical life skill, is essentially a mathematical exercise. Budgeting, calculating interest, understanding the implications of loans and mortgages, or even evaluating investment options, all require a good grasp of mathematics.

Mathematics and Scientific Understanding

Mathematics is the language of science. It helps us quantitatively understand and describe the physical world around us, from the trajectory of planets to the behavior of subatomic particles.

500 Words Essay on Importance of Mathematics in Our Daily Life

Mathematics, often perceived as a complex and abstract subject, is in fact deeply intertwined with our daily lives. It is the foundation of numerous activities we engage in, from basic tasks such as shopping and cooking to more complex ones like planning finances or solving problems.

The Ubiquity of Mathematics

Mathematics is everywhere. It is used in our everyday activities, often without our conscious realization. When we shop, we use mathematics to calculate prices, discounts, and taxes. When we cook, we use it to measure ingredients. When we travel, we use it to calculate distances, time, and fuel consumption. Even in our leisure activities such as playing games or music, mathematics plays a crucial role in understanding patterns, probabilities, and rhythms.

Mathematics in the Professional Sphere

Mathematics and problem-solving.

Mathematics also enhances our problem-solving skills. It teaches us to approach problems logically and systematically. It encourages us to break down complex problems into simpler parts, solve them individually, and combine the solutions to solve the original problem. This skill is not just applicable to mathematical problems but to any problem we encounter in life.

Mathematics and Critical Thinking

Furthermore, mathematics fosters critical thinking. It trains us to question assumptions, identify patterns, and draw conclusions based on evidence. It also teaches us to understand the limitations of our solutions and consider alternative approaches. These are valuable skills that can be applied in various aspects of life, from making informed decisions to evaluating the credibility of information.

Mathematics and the Digital Age

In conclusion, mathematics is not just a subject we learn in school. It is a powerful tool that helps us understand and navigate the world around us. It enhances our problem-solving and critical thinking skills, and it opens up a world of opportunities in the professional sphere. Therefore, it is essential that we appreciate the importance of mathematics in our daily lives, and strive to improve our mathematical literacy.

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The Best Writing on Mathematics 12

Mircea pitici,  series editor.

This annual anthology brings together the year’s finest mathematics writing from around the world. Featuring promising new voices alongside some of the foremost names in the field, The Best Writing on Mathematics makes mathematical writing available to a wide audience.

The year’s finest mathematical writing from around the world

The year's finest mathematical writing from around the world

The year's finest mathematics writing from around the world

The year's finest writing on mathematics from around the world

The year's finest writing on mathematics from around the world, with a foreword by Nobel Prize – winning physicist Roger Penrose

The year’s most memorable writing on mathematics

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25 Interesting Math Topics: How to Write a Good Math Essay

writing good math essay

Mathematics is a fascinating world of numbers, shapes, and patterns. 

Whether you are a student looking to grasp math concepts or someone who finds math intriguing, these topics will spark your curiosity and help you discover the beauty of mathematics straightforwardly and engagingly.

In this article, I will explore interesting math topics that make this subject not only understandable but also enjoyable.

Why Write About Mathematics

First, it helps demystify a subject that many find intimidating. By breaking down complex mathematical concepts into simple, understandable language, we can make math accessible to a wider audience, fostering greater understanding and appreciation.

Second, writing about mathematics allows us to showcase the practical applications of math in everyday life, from managing personal finances to solving real-world problems.

This helps readers recognize the relevance of math and its role in various fields and industries.

Additionally, writing about mathematics can inspire curiosity and a love for learning.

It encourages critical thinking and problem-solving skills, promoting intellectual growth and academic success.

Finally, mathematics is a universal language that transcends cultural and linguistic barriers.

After discussing math topics, we can connect with a global audience, fostering a sense of unity and collaboration in the pursuit of knowledge

 25 Interesting Math Topics to Write On

 Mathematics is a vast and intriguing field, offering a multitude of interesting topics to explore and write about.

Here are 25 such topics that promise to engage both math enthusiasts and those seeking a deeper understanding of this fascinating subject.

1. Fibonacci Sequence: Delve into the mesmerizing world of numbers with this sequence, where each number is the sum of the two preceding ones.

2. Golden Ratio: Explore the ubiquity of the golden ratio in art, architecture, and nature.

3. Prime Numbers: Investigate the mysterious properties of prime numbers and their role in cryptography.

4. Chaos Theory: Understand the unpredictability of chaotic systems and how small changes can lead to drastically different outcomes.

5. Game Theory: Examine the strategies and decision-making processes behind games and real-world situations.

6. Cryptography: Uncover the mathematical principles behind secure communication and encryption.

7. Fractals: Discover the self-replicating geometric patterns that occur in nature and mathematics.

8. Probability Theory: Dive into the world of uncertainty and randomness, where math helps us make informed predictions.

9. Number Theory: Explore the properties and relationships of integers, including divisibility and congruence.

10. Geometry of Art: Analyze how geometry and math principles influence art and design.

11. Topology: Study the properties of space that remain unchanged under continuous transformations, leading to the concept of “rubber-sheet geometry.”

12. Knot Theory: Investigate the mathematical study of knots and their applications in various fields.

13. Number Systems: Learn about different number bases, such as binary and hexadecimal, and their significance in computer science.

14. Graph Theory: Explore networks, relationships, and the mathematics of connections.

15. The Monty Hall Problem: Delight in this famous probability puzzle based on a game show scenario.

16. Calculus: Examine the principles of differentiation and integration that underlie a wide range of scientific and engineering applications.

17. The Riemann Hypothesis: Consider one of the most famous unsolved problems in mathematics involving the distribution of prime numbers.

18. Euler’s Identity: Marvel at the beauty of Euler’s equation, often described as the most elegant mathematical formula.

19. The Four-Color Theorem: Uncover the fascinating problem of coloring maps with only four colors without adjacent regions sharing the same color.

20. P vs. NP Problem: Delve into one of the most critical unsolved problems in computer science, addressing the efficiency of algorithms.

21. The Bridges of Konigsberg: Explore a classic problem in graph theory that inspired the development of topology.

22. The Birthday Paradox: Understand the surprising likelihood of shared birthdays in a group.

23. Non-Euclidean Geometry: Step into the world of geometries where Euclid’s parallel postulate doesn’t hold, leading to intriguing alternatives like hyperbolic and elliptic geometry.

24. Perfect Numbers: Learn about the properties of numbers that are the sum of their proper divisors.

25. Zero: The History of Nothing: Trace the historical and mathematical significance of the number zero and its role in the development of mathematics.

How to Write a Good Math Essay

Mathematics essays , though often perceived as daunting, can be a rewarding way to delve into the world of mathematical concepts, problem-solving, and critical thinking.

Whether you are a student assigned to write a math essay or someone who wants to explore math topics in-depth, this guide will provide you with the key steps to write a good math essay that is clear, concise, and engaging.

1. Understanding the Essay Prompt

Before you begin writing, it’s crucial to understand the essay prompt or question.

Analyze the specific topic, the scope of the essay, and any guidelines or requirements provided by your instructor.

Mostly, this initial step sets the direction for your essay and ensures you stay on topic.

2. Research and Gather Information

You need to gather relevant information and resources to write a strong math essay. This includes textbooks, academic papers, and reputable websites.

Make sure to cite your sources properly using a recognized citation style such as APA, MLA, or Chicago.

3. Structuring Your Math Essay

Start with a clear introduction that provides an overview of the topic and the main thesis or argument of your essay. This section should capture the reader’s attention and present a roadmap for what to expect.

The body of your essay is where you present your arguments, explanations, and evidence. Use clear subheadings to organize your ideas. Ensure that your arguments are logical and well-structured.

Begin by defining any important mathematical concepts or terms necessary to understand your topic.

Clearly state your main arguments or theorems. Please support them with evidence, equations, diagrams, or examples.

Explain the logical steps or mathematical reasoning behind your arguments. This can include proofs, derivations, or calculations.

Ensure your writing is clear and free from jargon that might confuse the reader. Explain complex ideas in a way that’s accessible to a broader audience.

Whenever applicable, include diagrams, graphs, or visual aids to illustrate your points. Visual representations can enhance the clarity of your essay.

Summarize your main arguments, restate your thesis, and offer a concise conclusion. Address the significance of your findings and the implications of your research or discussion.

4. Proofreading and Editing

Once you’ve written your math essay, take the time to proofread and edit it. Pay attention to grammar, spelling, punctuation, and the overall flow of your writing.

Ensure that your essay is well-organized and free from errors.

Consider seeking feedback from peers or an instructor to gain a fresh perspective.

5. Presentation and Formatting

A well-presented essay is more likely to engage the reader. Follow these formatting guidelines:

• Use a legible font (e.g., Times New Roman or Arial) in a standard size (12-point).
• Double-space your essay and include page numbers if required.
• Create a title page with your name, essay title, course information, and date.
• Use section headings and subheadings for clarity.
• Include a reference page to cite your sources appropriately.

6. Mathematical Notation and Symbols

Mathematics relies heavily on notation and symbols. Ensure that you use mathematical notation correctly and consistently.

If you introduce new symbols or terminology, define them clearly for the reader’s understanding.

7. Seek Clarification

If you encounter difficulties or ambiguities in your math essay, don’t hesitate to seek clarification from your instructor or peers.

Discussing complex mathematical concepts with others can help you refine your understanding and improve your essay.

8. Practice and Feedback

Writing math essays, like any skill, improves with practice. The more you write and receive feedback, the better you’ll become.

Take your time with initial challenges. Instead, view them as opportunities for growth and learning.

With dedication and attention to detail, you can craft a math essay that not only conveys your mathematical knowledge but also engages and informs your readers.

Josh Jasen or JJ as we fondly call him, is a senior academic editor at Grade Bees in charge of the writing department. When not managing complex essays and academic writing tasks, Josh is busy advising students on how to pass assignments. In his spare time, he loves playing football or walking with his dog around the park.

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Math Essay Writing Guide

It is often met that students feel wondered when they are asked to write essays in math classes. Actually, the tasks of math essay writing want to make students demonstrate their knowledge and understanding of mathematical concepts and ideas.

This kind of essay is what students of both college and high school students can be asked to create. Yes, this type of writing is quite special, and having its own tricks and demands. Still, guides for writing a math essay is mostly the same as for those of other subjects.

If you think you do not have enough time or skill to complete a math essay on your own, remember about the possibility to ask for essay help online .

Set Up Your Topic

Just like any other essay, math writing is to be started from choosing a topic. Here are several possible ways to go. First one wants you to choose any mathematical concept that seems to be interesting for you, like one of those you discussed with a teacher and classmates and want to investigate it a bit deeper. Another way is, you can choose any math problem you have solved in the past.

For this type of writing, you show up a problem, and then show your way towards solving it and getting the right answer. Whatever the type of essay is, you need to provide a brainstorm and find the topic worrying your mind the most, as to write about something you need to research it seriously. For instance think about any particular concept or equation of mathematics you would like to spend a bit more time to investigate, and then note your thoughts on a paper.

Consider the Audience

Thinking about the audience that is going to read your essay is a must for any essay, same thing goes for math paper writing. Mathematician P. R. Halmos offers the way to think about the particular person while writing an essay, in the text of his article “How to Write Mathematics”.

Halmos says it is good to think about someone who has math ways that “can stand mending”. To say in other words, when writing an essay, do not try jumping above your head and write the text for the audience that has the same skill in math as you do. Yes, you write a math essay in order to present the idea or to explain a problem solution. But still, you want to prove your method to be the best one. Try convincing the reader in that, and the essay is guaranteed to be interesting.

Concept Essay in Math

In case of math, concept essays look similar to those for other classes. In fact, you need to write a regular expository essay to complete your task. To do that, you research a certain math concept, analyze it, then form and develop your upcoming theoretical ideas basing on the experience and knowledge you could get when providing the investigation, and then claim it as a usual thesis statement.

Start writing your essay with the intro, importing the topic through it. include your claim about the theory there. The, you need to develop your claim in the further text, and to present reliable evidences you found during the research to prove your viewpoint. Write a conclusion, tie up any loose ends and readdress your theoretical info according to the way how it was provided before.

Math Equation Essay

To complete an equation essay successfully, you should show up the problem and solution at once, in the essay intro. Then, explain the problem significance and factors that made you choose your certain way towards the solution. Both significance and rationale are the same with a thesis statement, they serve as the base ground for your argumentation here.

Compose a paragraph that clearly shows the reader how to solve the problem according to your vision, make a “how-to” user guide for the chosen problem. If the problem is complex, set up a helpful graph that could demonstrate your equation result. Explain what can be seen on that graph. Same thing: define variables carefully and precisely with sentences like “Let’s think n is any real number.” Show up your problem solving methodical, guide the reader through the used formulas and explain why you used exactly those ones.

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How mathematical practices can improve your writing

Writing is similar to three specific mathematical practices: modelling, problem-solving and proving, writes Caroline Yoon. Here, she gives some tips on how to use these to improve academic writing

Caroline Yoon

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I feel for my students when I hand them their first essay assignment. Many are mathematicians, students and teachers who chose to study mathematics partly to avoid writing. But in my mathematics education courses, and in the discipline more generally, academic writing is part of our routine practice.

Mathematicians face some challenging stereotypes when it comes to writing. Writing is seen as ephemeral, subjective and context-dependent, whereas mathematics is seen as enduring, universal and context-free. Writing reflects self, but mathematics transcends it: they are distinct from each other.

This is a false dichotomy that can discourage mathematicians from writing. It suggests writing is outside the natural skill set of the mathematician, and that one’s mathematics training not only neglects one’s development as a writer but actively prevents it. Rather than capitulate to this false dichotomy, I propose we turn it around to examine how writing is similar to three specific mathematical practices: modelling, problem-solving and proving.

Three mathematical practices that can improve your writing

Mathematical modelling.

Let us consider a hypothetical mathematics education student who has spent weeks thinking, reading and talking about her essay topic, but only starts writing it the night before it is due. She writes one draft only – the one she hands in – and is disappointed with the low grade her essay receives.

She wishes she had started earlier but she was still trying to figure out what she wanted to say up until the moment she started writing. It was only the pressure of the deadline that forced her to start; without it, she would have spent even more time thinking and reading to develop her ideas. After all, she reasons, there is no point writing when you do not know what to write about!

This “think first, write after” approach, sometimes known as the “writing up” model is a dangerous trap many students fall into, and is at odds with the way writing works. The approach allows no room for imperfect drafts that are a necessary part of the writing process . Writing experts trade on the generative power of imperfect writing; they encourage writers to turn off their internal critics and allow themselves to write badly as a way of overcoming writing inertia and discovering new ideas. The “shitty first draft” is an ideal (and achievable) first goal in the writing process. Anyone can produce a sketchy first draft that generates material that can be worked on, improved and eventually rewritten into a more sharable form.

Mathematical modelling offers a compelling metaphor for the generative power of imperfect writing. Like polished writing, polished mathematical models are seldom produced in the first attempt. A modeller typically begins with some understanding of the real situation to be modelled. The modeller considers variables and relationships from his or her understanding of the real situation and writes them into an initial mathematical model.

The model is his or her mathematical description of the situation, written in mathematical notation, and the modeller who publishes a mathematical model has typically created and discarded multiple drafts along the way, just as the writer who publishes a piece of writing has typically written and discarded multiple drafts along the way.

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Problem-solving

Writing an original essay is like trying to solve a mathematics problem. There is no script to follow; it must be created by simultaneously determining one’s goals and figuring out how to achieve them. In both essay writing and mathematical problem-solving, getting stuck is natural and expected. It is even a special kind of thrill.

This observation might come as a surprise to mathematicians who do not think of their problem-solving activity as writing. But doing mathematics, the ordinary everyday act of manipulating mathematical relationships and objects to notice new levels of structure and pattern, involves scratching out symbols and marks, and moving ideas around the page or board.

Why do I care that mathematicians acknowledge their natural language of symbols and signs as writing? Quite frankly because they are good at it. They have spent years honing their ability to use writing to restructure their thoughts, to dissect their ideas, identify new arguments. They possess an analytic discipline that most writers struggle with.

Yet few of my mathematics education students take advantage of this in their academic writing. They want their writing to come out in consecutive, polished sentences and become discouraged when it does not. They do not use their writing to analyse and probe their arguments as they do when they are stuck on mathematical problems. By viewing writing only as a medium for communicating perfectly formed thoughts, they deny themselves their own laboratories, their own thinking tools.

I am not suggesting that one’s success in solving mathematical problems automatically translates into successful essay writing. But the metaphor of writing as problem-solving might encourage a mathematics education student not to give up too easily when she finds herself stuck in her writing.

Our hypothetical student now has a good draft that she is happy with. She is satisfied it represents her knowledge of the subject matter and has read extensively to check the accuracy of its content. A friend reads the draft and remarks that it is difficult to understand. Our student is unperturbed. She puts it down to her friend’s limited knowledge of the subject and is confident her more knowledgeable teacher will understand her essay.

But the essay is not an inert record judged on the number of correct facts it contains. It is also a rhetorical act that seeks to engage the public. It addresses an audience, it tries to persuade, to inspire some response or action.

Mathematical proofs are like expository essays in this regard; they must convince an audience. When undergraduate mathematics students learn to construct proofs of their own, a common piece of advice is to test them on different audiences. The phrase “Convince yourself, convince a friend, convince an enemy” becomes relevant in this respect.

Mathematicians do not have to see themselves as starting from nothing when they engage in academic writing. Rather, they can use mathematical principles they have already honed in their training, but which they might not have formerly recognised as tools for improving their academic writing.

Practical tips for productive writing beliefs and behaviours

• Writing can generate ideas. Free writing is a good way to start. Set a timer and write continuously for 10 minutes without editing. These early drafts will be clumsy, but there will also be some gold that can be mined and developed.
• Writing can be used to analyse and organise ideas. When stuck, try to restructure your ideas. Identify the main point in each paragraph and play around with organising their flow. 
• Writing is a dialogue with the public. Seek out readers’ interpretations of your writing and listen to their impressions. Read your writing out loud to yourself: you will hear it differently!

Caroline Yoon is an associate professor of mathematics at the University of Auckland.

This is an edited version of the journal article “The writing mathematician” by Caroline Yoon, published in For the Learning of Mathematics  and collected in The Best Writing on Mathematics , edited by  Mircea Pitici  (Princeton University Press).

If you would like advice and insight from academics and university staff delivered direct to your inbox each week,  sign up for the Campus newsletter .

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Math Essay Examples and Topics

Mathematics: discovered or created, the importance of geometry in our daily life.

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Leonardo Da Vinci and His Contribution to the Development of Mathematics

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Debate on Mathematics: An Art or a Science

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History of Algebra Brief Overview

Statistics abuse: how, why, and when.

• Words: 2836

Statistics: Chi-Square Test and Regression Analysis

• Words: 1989

Parabolas and Their Application in the Real Life

Spatial modeling: types, pros and cons, measurements’ standarts, mathematical analysis of the pyramid of the louvre.

• Words: 1523

Pythagorean Theorem: History, Formula, and Proof

• Words: 1524

The Life and Works of Archimedes

• Words: 2513

Arthur Cayley: Life, Career, and Achievements

Order of operations: connecting to real life, the value of mathematics in antonsen’s ted talk, mathematics: the language of nature, leonardo pisano fibonacci’s life and contributions, oblique triangles in everyday life, sofia kovalevskaya’s contributions to math, correlation.

• Words: 1036

Mathematics – Concept of Multiplication

• Words: 1161

The Use of Polynomials in the Real World

Pythagoras theories.

• Words: 1918

Math Functions in Economics

• Words: 2443

Algebra in the Real World and Everyday Life

Linear equations comprehensive study, construction of regular polygons: octagon, bouncing ball as an example of a conic section, exponential and logarithmic functions, applications of algebraic functions in an environmental agency, fundamental theorem of calculus in modern world, optimizing the cross-section of a gutter, fibonacci sequence and related mathematical concepts.

• Words: 2144

Quantitative Approach to Research

Mathematical and statistical investigation.

• Words: 1798

Fourier Transform: The Behavior of the Image in the Frequency Domain

• Words: 2889

Prime Numbers Role in People’s Life

The formal mathematical language and its importance, the use of mathematics in advertisements, history of calculus: brief review one of the branches of mathematics.

• Words: 1169

Reflection on Statistics Learning Goals

Qualitative research method analysis.

• Words: 1766

Importance of Math During Trip from US to Japan

Implicit differentiation in the business sector, number theory and major contributors to the field.

• Words: 1136

Historical Data Analysis: Various Variables Trends

• Words: 2828

Discrete Probability Distribution

• Words: 1111

Problem Solving Process in Mathematics

Quantitative data analysis, a-level math aqa : specification.

• Words: 4304

Practical Usages of Scientific Notation

The discipline of criminal justice: the use of mathematics, data results of statistics, hamilton-jacobi-bellman equation and linear pearson coefficient, rational functions and their real-world applications, deduction in ancient greece and egypt, mathematical explorations: quantitative reasoning, using the weibull distribution to study failure intensity, the perfect square trinomial and the sum of cubes, compound interest as mathematical fact.

• Words: 3827

Math: Compound Interest as a Future Problem

Sir isaac newton mathematical theory.

• Words: 1051

Pierre de Fermat: One of the Most Prominent Mathematicians

The scientific method isn’t what it used to be.

• Words: 1100

Qualitative research design and methods

A comparison of observations to measurement instruments, t-test discussion, the exponential function in analytic algebra, teaching math: number sense instruction.

• Words: 1191

Algebraic Equations and Graphical Representations

History of pythagoras theorem.

• Words: 1370

Investigating Number Systems

• Words: 1117

Roller Coasters: Mathematical Simulation

Real and complex numbers, big o notation: extended definition.

• Words: 1107

Statistical Process in Data Analysis

Measures of central tendency and dispersion, probability: theory and experiment.

• Words: 1138

Calculus-Integration

• Words: 1074

Misconceptions and Errors in Math

Positive and negative association between variables, carl friedrich gauss: mathematician and innovator, charting a career in mathematics: from teaching to actuarial practice.

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Navigating the Math Maze: A Strategic Policy Framework

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Aspects of the Mathematics Problem Solving

• Words: 1154

The Life Accomplishments of John von Neumann

Report: tow tank statistical analysis.

• Words: 1409

Determining the Area of the Isosceles Triangles

Mathematical operations with positive and negative numbers.

• Words: 1460

A Random Variable and Binomial Experiment

Evaluating the effectiveness of an instructional design.

• Words: 1210

Determining the Strongest Predictors of Kappa Number in Kraft Pulp

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Mathematician John Wilder Tukey’s Biography

Dangers of false representation in mathematics.

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Slope Desciption and Necessity

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• Words: 1666

Probability Theory: Descriptive Statistics

Math assignment: graph visualization.

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Extended Essay: Group 5: Mathematics

• General Timeline
• Group 1: English Language and Literature
• Group 2: Language Acquisition
• Group 3: Individuals and Societies
• Group 4: Sciences
• Group 5: Mathematics
• Group 6: The Arts
• Interdisciplinary essays
• Six sub-categories for WSEE
• IB Interdisciplinary EE Assessment Guide
• Brainstorming
• Pre-Writing
• Research Techniques
• The Research Question
• Paraphrasing, Summarising and Quotations
• Writing an EE Introduction
• Writing the main body of your EE
• Writing your EE Conclusion
• Sources: Finding, Organising and Evaluating Them
• Conducting Interviews and Surveys
• Citing and Referencing
• Check-in Sessions
• First Formal Reflection
• Second Formal Reflection
• Final Reflection (Viva Voce)
• Researcher's Reflection Space (RRS) Examples
• Information for Supervisors
• How is the EE Graded?
• EE Online Resources
• Stavanger Public Library
• Exemplar Essays
• Extended Essay Presentations
• ISS High School Academic Honesty Policy

Mathematics

An extended essay (EE) in mathematics is intended for students who are writing on any topic that has a mathematical focus and it need not be confined to the theory of mathematics itself.

Essays in this group are divided into six categories:

• the applicability of mathematics to solve both real and abstract problems
• the beauty of mathematics—eg geometry or fractal theory
• the elegance of mathematics in the proving of theorems—eg number theory
• the history of mathematics: the origin and subsequent development of a branch of mathematics over a period of time, measured in tens, hundreds or thousands of years
• the effect of technology on mathematics:
• in forging links between different branches of mathematics,
• or in bringing about a new branch of mathematics, or causing a particular branch to flourish.

These are just some of the many different ways that mathematics can be enjoyable or useful, or, as in many cases, both.

For an Introduction in a Mathematics EE look HERE . 

Choice of topic

The EE may be written on any topic that has a mathematical focus and it need not be confined to the theory of mathematics itself.

Students may choose mathematical topics from fields such as engineering, the sciences or the social sciences, as well as from mathematics itself.

Statistical analyses of experimental results taken from other subject areas are also acceptable, provided that they focus on the modeling process and discuss the limitations of the results; such essays should not include extensive non-mathematical detail.

A topic selected from the history of mathematics may also be appropriate, provided that a clear line of mathematical development is demonstrated. Concentration on the lives of, or personal rivalries between, mathematicians would be irrelevant and would not score highly on the assessment criteria.

It should be noted that the assessment criteria give credit for the nature of the investigation and for the extent that reasoned arguments are applied to an appropriate research question.

Students should avoid choosing a topic that gives rise to a trivial research question or one that is not sufficiently focused to allow appropriate treatment within the requirements of the EE.

Students will normally be expected either to extend their knowledge beyond that encountered in the Diploma Programme mathematics course they are studying or to apply techniques used in their mathematics course to modeling in an appropriately chosen topic.

However, it is very important to remember that it is an essay that is being written, not a research paper for a journal of advanced mathematics, and no result, however impressive, should be quoted without evidence of the student’s real understanding of it.

Example and Treatment of Topic

Examples of topics

These examples are just for guidance. Students must ensure their choice of topic is focused (left-hand column) rather than broad (right-hand column

Treatment of the topic

Whatever the title of the EE, students must apply good mathematical practice that is relevant to the

chosen topic, including:

• data analysed using appropriate techniques

• arguments correctly reasoned

• situations modeled using correct methodology

• problems clearly stated and techniques at the correct level of sophistication applied to their solution.

Research methods

Students must be advised that mathematical research is a long-term and open-ended exploration of a set of related mathematical problems that are based on personal observations. 

The answers to these problems connect to and build upon each other over time.

Students’ research should be guided by analysis of primary and secondary sources.

A primary source for research in mathematics involves:

• data-gathering

• visualization

• abstraction

• conjecturing

• proof.

A secondary source of research refers to a comprehensive review of scholarly work, including books, journal articles or essays in an edited collection.

A literature review for mathematics might not be as extensive as in other subjects, but students are expected to demonstrate their knowledge and understanding of the mathematics they are using in the context of the broader discipline, for example how the mathematics they are using has been applied before, or in a different area to the one they are investigating.

Writing the essay

Throughout the EE students should communicate mathematically:

• describing their way of thinking

• writing definitions and conjectures

• using symbols, theorems, graphs and diagrams

• justifying their conclusions.

There must be sufficient explanation and commentary throughout the essay to ensure that the reader does not lose sight of its purpose in a mass of mathematical symbols, formulae and analysis.

The unique disciplines of mathematics must be respected throughout. Relevant graphs and diagrams are often important and should be incorporated in the body of the essay, not relegated to an appendix.

However, lengthy printouts, tables of results and computer programs should not be allowed to interrupt the development of the essay, and should appear separately as footnotes or in an appendix. Proofs of key results may be included, but proofs of standard results should be either omitted or, if they illustrate an important point, included in an appendix.

Examples of topics, research questions and suggested approaches

Once students have identified their topic and written their research question, they can decide how to

research their answer. They may find it helpful to write a statement outlining their broad approach. These

examples are for guidance only.

An important note on “double-dipping”

Students must ensure that their EE does not duplicate other work they are submitting for the Diploma Programme. For example, students are not permitted to repeat any of the mathematics in their IA in their EE, or vice versa.

The mathematics EE and internal assessment

An EE in mathematics is not an extension of the internal assessment (IA) task. Students must ensure that they understand the differences between the two.

• The EE is a more substantial piece of work that requires formal research
• The IA is an exploration of an idea in mathematics.

It is not appropriate for a student to choose the same topic for an EE as the IA. There would be too much danger of duplication and it must therefore be discouraged.

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What Students Are Saying About the Value of Math

We asked teenagers: Do you see the point in learning math? The answer from many was “yes.”

By The Learning Network

“Mathematics, I now see, is important because it expands the world,” Alec Wilkinson writes in a recent guest essay . “It is a point of entry into larger concerns. It teaches reverence. It insists one be receptive to wonder. It requires that a person pay close attention.”

In our writing prompt “ Do You See the Point in Learning Math? ” we wanted to know if students agreed. Basic arithmetic, sure, but is there value in learning higher-level math, such as algebra, geometry and calculus? Do we appreciate math enough?

The answer from many students — those who love and those who “detest” the subject alike — was yes. Of course math helps us balance checkbooks and work up budgets, they said, but it also helps us learn how to follow a formula, appreciate music, draw, shoot three-pointers and even skateboard. It gives us different perspectives, helps us organize our chaotic thoughts, makes us more creative, and shows us how to think rationally.

Not all were convinced that young people should have to take higher-level math classes all through high school, but, as one student said, “I can see myself understanding even more how important it is and appreciating it more as I get older.”

Thank you to all the teenagers who joined the conversation on our writing prompts this week, including students from Bentonville West High School in Centerton, Ark, ; Harvard-Westlake School in Los Angeles ; and North High School in North St. Paul, Minn.

Please note: Student comments have been lightly edited for length, but otherwise appear as they were originally submitted.

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High School Mathematics at Work: Essays and Examples for the Education of All Students (1998)

Chapter: introduction, introduction.

Society's technological, economic, and cultural changes of the last 50 years have made many important mathematical ideas more relevant and accessible in work and in everyday life. As examples of mathematics proliferate, the mathematics education community is provided with both a responsibility and an opportunity. Educators have a responsibility to provide a high-quality mathematics education for all of our students. A recent report of the National Academy of Sciences (NAS) entitled Preparing for the 21st Century: The Education Imperative (National Research Council [NRC], 1997) neatly summarizes this point:

… today, an understanding of science, mathematics, and technology is very important in the workplace. As routine mechanical and clerical tasks become computerized, more and more jobs require high-level skills that involve critical thinking, problem solving, communicating ideas to others and collaborating effectively. Many of these jobs build on skills developed through high-quality science, mathematics, and technology education. Our nation is unlikely to remain a world leader without a better-educated workforce. (p. 1)

These economic and technological changes also present an opportunity for providing that high-quality education. Specifically, there is rich mathematics in workplace applications and in everyday life that can contribute to the school curriculum. Thus, today's world not only calls for increasing connection

between mathematics and its applications, but also provides compelling examples of mathematical ideas in everyday and workplace settings. These examples can serve to broaden the nation's mathematics education programs to encompass the dual objectives of preparing students for the worlds of work and of higher education. Furthermore, such programs can provide students with the flexibility to return to higher education whenever appropriate in their career paths. By illustrating the commonalities among the mathematical expectations for college, for work, and for everyday life, and by illustrating sophisticated uses of mathematics taught in high schools as well as in community colleges, this document aims to offer an expanded vision of mathematics. Mathematics based in the workplace and in everyday life can be good mathematics for everyone.

High School Mathematics at Work is a collection of essays and illustrative tasks from workplace and everyday contexts that suggest ways to strengthen the mathematical education of all students. The essays are written by a wide range of individuals who have thought deeply about mathematics education and about the futures of today's students, from mathematics educators to business leaders, from mathematicians to educational researchers, from curriculum developers to policy makers. The essays and tasks in High School Mathematics at Work not only underscore the points made in The Education Imperative (NRC, 1997), but also begin to explore connections between academic mathematics and mathematics for work and life.

As a step toward examining ways in which our schools and colleges can better serve the needs of both academic and vocational education, the National Research Council (NRC) of the National Academy of Sciences hosted a workshop in 1994 that resulted in a report entitled Mathematical Preparation of the Technical Work Force (NRC, 1995). Participants discussed questions such as

• How can mathematics content and technical applications of mathematics be integrated into educational programs?
• Should algebra continue to be the ''critical filter" used to determine whether or not students will be admitted into youth apprenticeship programs?
• Is the mathematics included in technical education programs consistent with emerging educational and occupational skills standards?
• Is it possible (or desirable) to design a core mathematics curriculum for the high school and community college levels that prepares students both for further formal education and for immediate employment in the technical work force? (p. 6)

High School Mathematics at Work continues discussion of these questions, and considers in particular how workplace and everyday mathematics can enrich mathematics teaching and learning.

Though the nominal mathematical content of this volume is high school mathematics, consideration of the above issues will lead to implications for colleges as well. For example, some two-year colleges have moved toward programs that include contextual learning and work-based experiences to enhance academic learning, often through articulated 2+2 partnerships that combine two years of course-work in high school with two years at a community college. The movement toward work-based learning has gained momentum in recent years through the School-to-Work Opportunities Act of 1994, administered jointly by the Departments of Education and Labor, and through the Advanced Technological Education program at the National Science Foundation. Both programs emphasize high academic expectations and require strong connections among schools, two-year colleges, businesses, and industry. By bringing these issues to the attention of the broader college and school communities, and by promoting higher mathematical expectations for all students, this document might provide an opportunity for schools and colleges to reconsider the mathematics courses before calculus, perhaps leading to new conceptualizations of their remedial, developmental, and "liberal arts" courses.

Fundamentally, High School Mathematics at Work is about mathematics. Its view of mathematics and mathematics learning recognizes a potential symbiotic relationship between concrete and abstract mathematics, each contributing to the other, enhancing their joint richness and power. This view is not new. Historically, much mathematics originated from attempts to solve problems from science and engineering. On the other hand, solutions to many problems from science and engineering have been based on creative ways of applying some mathematics that until then had no known applications. Mathematics can help solve problems, and complex workplace problems can help stimulate the creation of new mathematics.

Embracing this connected view of mathematics requires more than addressing content issues. In this document, the essays and tasks are organized according to four themes, each considering a different aspect of the many challenges involved in creating an enriched mathematics education for students. Each theme is introduced by an overview that provides a context for and a summary of the essays and tasks that follow. The first theme, Connecting Mathematics with Work and Life , sets the stage for the document as a whole, examining why and how "real world problems" can be used to enhance the learning of mathematics. With that premise, the remaining themes emphasize implications for various components of the educational system. The Roles of Standards and Assessments highlights the roles of standards and assessments in maintaining and also changing a vision of mathematics education. Curricular Considerations explores ways of designing curricula that attend to the needs of a diverse citizenry. Finally, Implications for Teaching and Teacher Education underscores the background and support teachers must have to respond to the needs of today's students.

Many of the issues raised by these essays are quite complex; no single essay provides a definitive resolution for any of these issues, and in fact, on some matters, some of the essayists disagree. Collectively, these essays point toward a vision of mathematics education that simultaneously considers the needs of all students. High School Mathematics at Work , however, unlike many documents produced by the National Research Council, is not a consensus document. The intent of this document is to point out some mathematical possibilities that are provided by today's world and to discuss some of the issues involved—not to resolve the issues, but to put forward some individual and personal perspectives that may contribute to the discussion.

Under each theme, the essays are accompanied by several tasks that illustrate some of the points raised in those essays, though many of the tasks could appropriately fit under several of the themes. The tasks serve as examples of where today's world can provide good contexts for good mathematics. They never were intended to represent, or even suggest, a full menu of high school mathematics. They provide possibilities for teaching. They exemplify central mathematical ideas and simultaneously convey the explanatory power of mathematics to help us make sense of the world around us. This book offers an existence proof: one can make connections between typical high school mathematics content and important problems from our everyday lives. And, it makes an important point: that the mathematics we learn in the classroom can and should help us to deal with the situations we encounter in our everyday lives. But High School Mathematics at Work is not only about relevance and utility. The mathematics involved is often generalizable; it often has aesthetic value, too. Mathematics can be beautiful, powerful, and useful. We hope you will discover all three of these virtues in some of the examples.

At a time when analysts of the Third International Mathematics and Science Study (TIMSS) have characterized the K-12 mathematics curriculum as "a mile wide and an inch deep" (Schmidt, McKnight & Raizen, 1996) this report does not advocate that tasks like the ones in this volume merely augment the curriculum. Rather, it suggests that tasks like these can provide meaningful contexts for important mathematics we already teach, including both well-established topics such as exponential growth and proportional reasoning, as well as more recent additions to the curriculum, such as data analysis and statistics.

Collectively, these essays and tasks explore how mathematics supports careers that are both high in stature and widely in demand. By suggesting ways that mathematics education can be structured to serve the needs of all students, the Mathematical Sciences Education Board (MSEB) hopes to initiate, inform, and invigorate discussions of how and what might be taught to whom. To this end, High School Mathematics at Work is appropriate for a broad audience, including teachers, teacher educators, college faculty, parents, mathematicians, curriculum designers, superintendents, school board members, and policy makers—in short, anyone interested in mathematics education.

For those who teach mathematics, the essays might provide new ways of thinking about teaching and learning; the tasks might provide ideas for the classroom. For parents, this book can give a sense of how mathematics can be powerful, useful, beautiful, meaningful, and relevant for students. And for those who influence educational policy, this book might motivate a search for curricula with these virtues.

As with all of the recent published work of the MSEB, High School Mathematics at Work is meant to be shared by all who care about the future of mathematics education, to serve as a stimulus for further discussion, planning, and action. All those who contributed to this report would be delighted if teachers gave copies to school board members, college faculty gave copies to deans, curriculum developers gave copies to publishers, employers gave copies to policy makers, and so on. Only through continued, broad-based discussion of curricular issues can we implement change and raise our expectations of what students know and are able to do.

National Research Council. (1995). Mathematical preparation of the technical work force . Washington, DC: National Academy Press.

National Research Council. (1997). Preparing for the 21st century: The education imperative . Washington, DC: National Academy Press.

Schmidt, W. H., McKnight, C. C., & Raizen, S. A. (1996) . A splintered vision: An investigation of U.S. science and mathematics education . Dordrecht, The Netherlands: Kluwer Academic Publishers.

Traditionally, vocational mathematics and precollege mathematics have been separate in schools. But the technological world in which today's students will work and live calls for increasing connection between mathematics and its applications. Workplace-based mathematics may be good mathematics for everyone.

High School Mathematics at Work illuminates the interplay between technical and academic mathematics. This collection of thought-provoking essays—by mathematicians, educators, and other experts—is enhanced with illustrative tasks from workplace and everyday contexts that suggest ways to strengthen high school mathematical education.

This important book addresses how to make mathematical education of all students meaningful—how to meet the practical needs of students entering the work force after high school as well as the needs of students going on to postsecondary education.

The short readable essays frame basic issues, provide background, and suggest alternatives to the traditional separation between technical and academic mathematics. They are accompanied by intriguing multipart problems that illustrate how deep mathematics functions in everyday settings—from analysis of ambulance response times to energy utilization, from buying a used car to "rounding off" to simplify problems.

The book addresses the role of standards in mathematics education, discussing issues such as finding common ground between science and mathematics education standards, improving the articulation from school to work, and comparing SAT results across settings.

Experts discuss how to develop curricula so that students learn to solve problems they are likely to encounter in life—while also providing them with approaches to unfamiliar problems. The book also addresses how teachers can help prepare students for postsecondary education.

For teacher education the book explores the changing nature of pedagogy and new approaches to teacher development. What kind of teaching will allow mathematics to be a guide rather than a gatekeeper to many career paths? Essays discuss pedagogical implication in problem-centered teaching, the role of complex mathematical tasks in teacher education, and the idea of making open-ended tasks—and the student work they elicit—central to professional discourse.

High School Mathematics at Work presents thoughtful views from experts. It identifies rich possibilities for teaching mathematics and preparing students for the technological challenges of the future. This book will inform and inspire teachers, teacher educators, curriculum developers, and others involved in improving mathematics education and the capabilities of tomorrow's work force.

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mathematics , the science of structure, order, and relation that has evolved from elemental practices of counting, measuring, and describing the shapes of objects. It deals with logical reasoning and quantitative calculation, and its development has involved an increasing degree of idealization and abstraction of its subject matter. Since the 17th century, mathematics has been an indispensable adjunct to the physical sciences and technology, and in more recent times it has assumed a similar role in the quantitative aspects of the life sciences.

In many cultures—under the stimulus of the needs of practical pursuits, such as commerce and agriculture—mathematics has developed far beyond basic counting. This growth has been greatest in societies complex enough to sustain these activities and to provide leisure for contemplation and the opportunity to build on the achievements of earlier mathematicians.

All mathematical systems (for example, Euclidean geometry ) are combinations of sets of axioms and of theorems that can be logically deduced from the axioms. Inquiries into the logical and philosophical basis of mathematics reduce to questions of whether the axioms of a given system ensure its completeness and its consistency. For full treatment of this aspect, see mathematics, foundations of .

This article offers a history of mathematics from ancient times to the present. As a consequence of the exponential growth of science, most mathematics has developed since the 15th century ce , and it is a historical fact that, from the 15th century to the late 20th century, new developments in mathematics were largely concentrated in Europe and North America . For these reasons, the bulk of this article is devoted to European developments since 1500.

This does not mean, however, that developments elsewhere have been unimportant. Indeed, to understand the history of mathematics in Europe, it is necessary to know its history at least in ancient Mesopotamia and Egypt, in ancient Greece, and in Islamic civilization from the 9th to the 15th century. The way in which these civilizations influenced one another and the important direct contributions Greece and Islam made to later developments are discussed in the first parts of this article.

India’s contributions to the development of contemporary mathematics were made through the considerable influence of Indian achievements on Islamic mathematics during its formative years. A separate article, South Asian mathematics , focuses on the early history of mathematics in the Indian subcontinent and the development there of the modern decimal place-value numeral system . The article East Asian mathematics covers the mostly independent development of mathematics in China, Japan, Korea, and Vietnam.

The substantive branches of mathematics are treated in several articles. See algebra ; analysis ; arithmetic ; combinatorics ; game theory ; geometry ; number theory ; numerical analysis ; optimization ; probability theory ; set theory ; statistics ; trigonometry .