critical thinking skills in mathematics

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How To Encourage Critical Thinking in Math

By Mary Montero

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Critical thinking is more than just a buzzword… It’s an essential skill that helps students develop problem-solving abilities and make logical connections between different concepts. By encouraging critical thinking in math, students learn to approach problems more thoughtfully, they learn to analyze and evaluate math concepts, identify patterns and relationships, and explore different strategies for finding the solution. Critical thinking also involves a great deal of persistence. Those are critical life skills!

When you think about it, students are typically asked to solve math problems and find the answer. Showing their work is frequently stressed too, which is important, but not the end. Instead, students need to be able to look at math in different ways in order to truly grasp a complete understanding of math concepts. Mathematics requires logical reasoning, problem-solving, and abstract thinking.

What Does Critical Thinking in Math Look Like?

When I think about critical thinking in math, I focus on:

• Solving problems through logical thinking . Students learn how to break down complex problems, analyze the different parts, and understand how they fit together logically.
• Identifying patterns and making connections. Students learn how to identify patterns across different math concepts, make connections between seemingly unrelated topics, and develop a more in-depth understanding of how math works.
• Evaluating and comparing solutions. Students learn to evaluate which solution is best for a given problem and identify any flaws in their reasoning or others’ reasoning when looking at different solutions

Mathematician Posters

These FREE Marvelous Mathematician posters have been a staple in my classroom for the last 8+ years! I first started using a version from MissMathDork and adapted them for my classroom over the years. 

I print, laminate, and add magnetic stickers on the back. At the beginning of the year, I only put one or two up at a time depending on our area of focus. Now, they are all hanging on my board, and I’ll pull out different ones depending on our area of focus. They are so empowering to my mathematicians and help them stay on track!

A Marvelous Mathematician:

• knows that quicker doesn’t mean better
• looks for patterns
• knows mistakes happen and keeps going
• makes sense of the most important details
• embraces challenges and works through frustrations
• uses proper math vocabulary to explain their thinking
• shows their work and models their thinking
• discusses solutions and evaluates reasonableness
• gives context by labeling answers
• applies mathematical knowledge to similar situations
• checks for errors (computational and conceptual)

Critical Thinking Math Activities

Here are a few of my favorite critical thinking activities. 

Square Of Numbers

I love to incorporate challenge problems (use Nrich and Openmiddle to get started) because they teach my students so much more than how to solve a math problem. They learn important lessons in teamwork, persistence, resiliency, and growth mindset. We talk about strategies for tackling difficult problems and the importance of not giving up when things get hard.

This square of numbers challenge was a hit!

ALL kids need to feel and learn to embrace challenge. Oftentimes, kids I see have rarely faced an academic challenge. Things have just come easy to them, so when it doesn’t, they can lack strategies that will help them. In fact, they will often give up before they even get started.

I tell them it’s my job to make sure I’m helping them stretch and grow their brain by giving them challenges. They don’t love it at first, but they eventually do! 

This domino challenge was another one from Nrich . I’m always on the hunt for problems like this!!  How would you guide students toward an answer??

Fifteen Cards

This is a well-loved math puzzle with my students, and it’s amazing for encouraging students to consider all options when solving a math problem.

We have number cards 1-15 (one of each number) and only seven are laid out. With the given clues, students need to figure out which seven cards should be put out and in what order. My students love these, and after they’ve done a few, they enjoy creating their own, too! Use products, differences, and quotients to increase the challenge.

This is also adapted from Nrich, which is an AMAZING resource for math enrichment!

This is one of my favorite fraction lessons that I’ve done for years! Huge shout out to Meg from The Teacher Studio for this one. I give each child a slip of paper with this figure and they have to silently write their answer and justification. Then I tally up the answers and have students take a side and DEBATE with their reasoning! It’s an AMAZING conversation, and I highly recommend trying it with your students. 

Sometimes we leave it hanging overnight and work on visual models to make some proofs. 

Logic Puzzles

Logic puzzles are always a hit too! You can enrich and extend your math lessons with these ‘Math Mystery’ logic puzzles that are the perfect challenge for 4th, 5th, and 6th grades. The puzzles are skills-based, so they integrate well with almost ANY math lesson. You can use them to supplement instruction or challenge your fast-finishers and gifted students… all while encouraging critical thinking about important math skills!

Three levels are included, so they’re perfect to use for differentiation.

• Introductory logic puzzles are great for beginners (4th grade and up!)
• Advanced logic puzzles are great for students needing an extra challenge
• Extra Advanced logic puzzles are perfect for expert solvers… we dare you to figure these puzzles out! 

Do you have a group of students who are ready for more of a fraction challenge? My well-loved fraction puzzlers are absolutely perfect for fraction enrichment. They’ll motivate your students to excel at even the most challenging tasks! 

Math Projects

Math projects are another way to differentiation while building critical thinking skills. Math projects hold so much learning power with their real-world connections, differentiation options, collaborative learning opportunities, and numerous avenues for cross curricular learning too. 

If you’re new to math projects, I shared my best tips and tricks for using math projects in this blog post . They’re perfect for cumulative review, seasonal practice, centers, early finisher work, and more.

I use both concept-based math projects to focus on specific standards and seasonal math projects that integrate several skills.

Error Analysis

Finally, error analysis is always a challenging way to encourage critical thinking. When we use error analysis, we encourage students to analyze their own mistakes to prevent making the same mistakes in the future.

For my gifted students, I use error analysis tasks as an assessment when they have shown mastery of a unit during other tasks. For students in the regular classroom needing enrichment, I usually have them complete the tasks in a center or with a partner.

For students needing extra support, we complete error analysis in small groups.  We go step-by-step through the concept and they are always able to eventually identify what the error is. It is so empowering to students when they finally figure out the error AND it helps prevent them from making the same error in the future!

My FREE addition error analysis is a good place to start, no matter the grade level. I show them the process of walking through the problem and how best to complete an error analysis task.

When you’re ready for more, this bundle of error analysis tasks contains more than 240 tasks to engage and enrich your students in critical thinking practice.

If you want to dig even deeper, visit this conceptual vs computational error analysis post to learn more about using error analysis in the classroom. 

Related Critical Thinking Posts

• How to Increase Critical Thinking and Creativity in Your “Spare” Time
• More Tips to Increase Critical Thinking

Critical thinking is essential for students to develop a deeper understanding of math concepts, problem-solving skills, and a stronger ability to reason logically. When you learn how to encourage critical thinking in math, you’re setting your students up for success not only in more advanced math subjects they’ll encounter, but also in life. 

How do you integrate critical thinking in your classroom? Come share your ideas with us in our FREE Inspired In Upper Elementary Facebook group .

Mary Montero

I’m so glad you are here. I’m a current gifted and talented teacher in a small town in Colorado, and I’ve been in education since 2009. My passion (other than my family and cookies) is for making teachers’ lives easier and classrooms more engaging.

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Mary Thankyou for your inspirational activities. I have just read and loved the morning talk activities. I do have meetings with my students but usually at end of day. What time do you

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Engaging Maths

Dr catherine attard, promoting creative and critical thinking in mathematics and numeracy.

• by cattard2017
• Posted on June 25, 2017

What is critical and creative thinking, and why is it so important in mathematics and numeracy education?

Numeracy is often defined as the ability to apply mathematics in the context of day to day life. However, the term ‘critical numeracy’ implies much more. One of the most basic reasons for learning mathematics is to be able to apply mathematical skills and knowledge to solve both simple and complex problems, and, more than just allowing us to navigate our lives through a mathematical lens, being numerate allows us to make our world a better place.

The mathematics curriculum in Australia provides teachers with the perfect opportunity to teach mathematics through critical and creative thinking. In fact, it’s mandated. Consider the core processes of the curriculum. The Australian Curriculum (ACARA, 2017), requires teachers to address four proficiencies : Problem Solving, Reasoning, Fluency, and Understanding. Problem solving and reasoning require critical and creative thinking (). This requirement is emphasised more heavily in New South wales, through the graphical representation of the mathematics syllabus content , which strategically places Working Mathematically (the proficiencies in NSW) and problem solving, at its core. Alongside the mathematics curriculum, we also have the General Capabilities , one of which is Critical and Creative Thinking – there’s no excuse!

Critical and creative thinking need to be embedded in every mathematics lesson . Why? When we embed critical and creative thinking, we transform learning from disjointed, memorisation of facts, to sense-making mathematics. Learning becomes more meaningful and purposeful for students.

How and when do we embed critical and creative thinking?

There are many tools and many methods of promoting thinking. Using a range of problem solving activities is a good place to start, but you might want to also use some shorter activities and some extended activities. Open-ended tasks are easy to implement, allow all learners the opportunity to achieve success, and allow for critical thinking and creativity. Tools such as Bloom’s Taxonomy and Thinkers Keys  are also very worthwhile tasks. For good mathematical problems go to the nrich website . For more extended mathematical investigations and a wonderful array of rich tasks, my favourite resource is Maths300   (this is subscription based, but well worth the money). All of the above activities can be used in class and/or for homework, as lesson starters or within the body of a lesson.

Will critical and creative thinking take time away from teaching basic concepts?

No, we need to teach mathematics in a way that has meaning and relevance, rather than through isolated topics. Therefore, teaching through problem-solving rather than for problem-solving. A classroom that promotes and critical and creative thinking provides opportunities for:

• higher-level thinking within authentic and meaningful contexts;
• complex problem solving;
• open-ended responses; and
• substantive dialogue and interaction.

Who should be engaging in critical and creative thinking?

Is it just for students? No! There are lots of reasons that teachers should be engaged with critical and creative thinking. First, it’s important that we model this type of thinking for our students. Often students see mathematics as black or white, right or wrong. They need to learn to question, to be critical, and to be creative. They need to feel they have permission to engage in exploration and investigation. They need to move from consumers to producers of mathematics.

Secondly, teachers need to think critically and creatively about their practice as teachers of mathematics. We need to be reflective practitioners who constantly evaluate our work, questioning curriculum and practice, including assessment, student grouping, the use of technology, and our beliefs of how children best learn mathematics.

Critical and creative thinking is something we cannot ignore if we want our students to be prepared for a workforce and world that is constantly changing. Not only does it equip then for the future, it promotes higher levels of student engagement, and makes mathematics more relevant and meaningful.

How will you and your students engage in critical and creative thinking?

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20 Math Critical Thinking Questions to Ask in Class Tomorrow

• November 20, 2023

The level of apathy towards math is only increasing as each year passes and it’s up to us as teachers to make math class more meaningful . This list of math critical thinking questions will give you a quick starting point for getting your students to think deeper about any concept or problem. 

Since artificial intelligence has basically changed schooling as we once knew it, I’ve seen a lot of districts and teachers looking for ways to lean into AI rather than run from it.

The idea of memorizing formulas and regurgitating information for a test is becoming more obsolete. We can now teach our students how to use their resources to make educated decisions and solve more complex problems.

With that in mind, teachers have more opportunities to get their students thinking about the why rather than the how.

Table of Contents

Looking for more about critical thinking skills? Check out these blog posts:

• Why You Need to Be Teaching Writing in Math Class Today
• How to Teach Problem Solving for Mathematics
• Turn the Bloom’s Taxonomy Verbs into Engaging Math Activities

What skills do we actually want to teach our students?

As professionals, we talk a lot about transferable skills that can be valuable in multiple jobs, such as leadership, event planning, or effective communication. The same can be said for high school students. 

It’s important to think about the skills that we want them to have before they are catapulted into the adult world. 

Do you want them to be able to collaborate and communicate effectively with their peers? Maybe you would prefer that they can articulate their thoughts in a way that makes sense to someone who knows nothing about the topic.

Whatever you decide are the most essential skills your students should learn, make sure to add them into your lesson objectives.

When should I ask these math critical thinking questions?

Critical thinking doesn’t have to be complex or fill an entire lesson. There are simple ways that you can start adding these types of questions into your lessons daily!

Start small

Add specific math critical thinking questions to your warm up or exit ticket routine. This is a great way to start or end your class because your students will be able to quickly show you what they understand. 

Asking deeper questions at the beginning of your class can end up leading to really great discussions and get your students talking about math.

Add critical thinking questions to word problems

Word problems and real-life applications are the perfect place to add in critical thinking questions. Real-world applications offer a more choose-your-own-adventure style assignment where your students can expand on their thought processes. 

They also allow your students to get creative and think outside of the box. These problem-solving skills play a critical role in helping your students develop critical thinking abilities.

Keep reading for math critical thinking questions that can be applied to any subject or topic!

When you want your students to defend their answers.

• Explain the steps you took to solve this problem
• How do you know that your answer is correct?
• Draw a diagram to prove your solution.
• Is there a different way to solve this problem besides the one you used?
• How would you explain _______________ to a student in the grade below you?
• Why does this strategy work?
• Use evidence from the problem/data to defend your answer in complete sentences.

When you want your students to justify their opinions

• What do you think will happen when ______?
• Do you agree/disagree with _______?
• What are the similarities and differences between ________ and __________?
• What suggestions would you give to this student?
• What is the most efficient way to solve this problem?
• How did you decide on your first step for solving this problem?

When you want your students to think outside of the box

• How can ______________ be used in the real world?
• What might be a common error that a student could make when solving this problem?
• How is _____________ topic similar to _______________ (previous topic)?
• What examples can you think of that would not work with this problem solving method?
• What would happen if __________ changed?
• Create your own problem that would give a solution of ______________.
• What other math skills did you need to use to solve this problem?

Let’s Recap:

• Rather than running from AI, help your students use it as a tool to expand their thinking.
• Identify a few transferable skills that you want your students to learn and make a goal for how you can help them develop these skills.
• Add critical thinking questions to your daily warm ups or exit tickets.
• Ask your students to explain their thinking when solving a word problem.
• Get a free sample of my Algebra 1 critical thinking questions ↓

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I would love to see your free math writing prompts, but there is no place for me to sign up. thank you

Ahh sorry about that! I just updated the button link!

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• Our Mission

A Powerful Rethinking of Your Math Classroom

We look at strategies you can reset this year—adjusting your testing regimen, tackling math anxiety, encouraging critical thinking, and fostering a mistake-friendly environment.

The beginning of school is a great time for teachers—both veteran and early career—to consider ways they can improve upon their classroom practices over the next year. This may be especially important for math teachers, who often spend the early days of the school year confronting math anxiety , convincing students that they are indeed “math people,” and coming up with engaging practices to guide students to find pleasure in math challenges. Innovating in these areas has the potential to yield big benefits for students all year long.

To help you re-imagine some of your teaching practices this year, we’ve pulled together a collection of big and small strategies aimed at:

• helping students adopt a more productive, curious mindset when they approach math,
• engaging students as soon as they walk through the door,
• rethinking how you handle testing,
• fostering a mistake-friendly environment,
• incorporating humanities-style discussions into math, and
• building what Peter Liljedahl calls a “ thinking classroom .”

Tackle Negative Math Mindsets

“Most of my work as a math teacher isn’t even math ,” former middle school math teacher José Vilson has said. “It’s helping students believe that they can also do math.”

Striking a similar note, middle school math coordinator Alessandra King writes that supporting students—particularly students from marginalized backgrounds—to develop a “ positive mathematical identity ” is crucial to fostering a sense of belonging in a larger math community, boosting “their willingness and ability to engage” in challenging work.

King recommends spending the first few days of the school year spotlighting mathematicians from the past who reflect the makeup of your classroom. In her all-girls school, for example, she has students read and respond to a play about the achievements and struggles of Maria Agnesi, Sofya Kovalevskaya, and Emmy Noether, three historical female mathematicians. You can also hang up posters of famous Black or Latino mathematicians—such as Euphemia Haynes, the first African American woman to earn a PhD in math, or Robert Luis Santos, a Latino statistician and director of the U.S. Census Bureau—and devote lessons to discussing their achievements and backgrounds.

To get students thinking about—and challenging—their own math identity, educator Rolanda Baldwin suggests asking students early in the year to write a “ math autobiography .” They might respond to questions like: “How do you feel about math? How did your relationship with math change over time?” To draw students closer together—and make them realize that many students, of all backgrounds, struggle—have them share their responses in groups, or with the entire class.

Sometimes, our best intentions can go awry. Rachel Fuhrman, a former special education math teacher, notes that teachers can sometimes dampen a student’s math identity by wheeling out phrases that might seem helpful but can actually demotivate students , like: “This is so easy.” Framing something as “easy,” she writes, can leave students feeling uncomfortable or afraid of asking crucial, clarifying questions.

Engage Students the Moment They Enter the Classroom

To set a playful tone and lower the stakes of the work so students can effectively experiment and collaborate, high school math teacher Lorenzo Robinson suggests starting off class with fun, challenging brain teasers .

For example, ask students to draw a cross on a sheet of paper (you should draw one on the board as a point of reference). Ask students to draw two straight lines that will segment or cut the cross into pieces. The goal is to cut the cross in a way that produces the most pieces .

You could also try math riddles: Ask students to imagine they have two coins that total 30 cents. Tell them that one of the coins is not a nickel, and ask them to figure out what the two coins are.

Robinson finds that brain teasers like these can get students primed for problem solving and critical thinking, without even realizing it.

Lower the Stakes of Testing

Big tests—centered around units or near the end of a grading period—are staples of many math classrooms. But that doesn’t mean they have to be the only opportunity for students to show what they know. One way to lower the stakes for students and give them more opportunities to practice, while providing yourself more of an opportunity to both teach content and check for understanding is to give short assessments on a regular schedule. 

Math coordinator Steven Goldman’s school switched from tests to checkpoints . These short assessments include a mix of current and past topics—retrieval practice is a research-backed way to support greater learning , after all—with some repetition for the most important skills students need to know. The checkpoints are given every two weeks and are not formally graded, but mistakes are noted and teachers leave feedback to guide student revisions. The change, Goldman writes, resulted in a big reduction in student stress levels—something research shows is a benefit of frequent practice tests, alongside a boost in long-term retention. Because the checkpoints happen all the time, Goldman and his colleagues don’t have to “go through all kinds of contortions to finish a unit before a break or on a Thursday so that we could give the test at the right time.”

Fresno State math instructor Howie Hua suggests lowering the stake in your classroom by allowing students to discuss a test before starting to work on it . Hua recommends having students put their pencils on the floor so they can focus on their discussion. Hand out the test and give students five minutes to discuss strategies they can use to solve the problems. 

Good Mistakes, Better Mistakes

Mistakes are bound to happen in any math classroom, and how you respond to them throughout the year can make a world of difference. Making light of your own mistakes is a good first gambit, but research suggests a more advanced approach: Giving students space to make mistakes—and opportunities to analyze and discuss them with peers—can better encode information in their brains than simply providing them with the correct answer.

To use mistakes as building blocks to better solutions, math teacher Emma Chiapetta uses an ingenious, small-group activity that asks students to identify and reflect on common mistakes , and then explain the rationale behind them to their peers. Here’s how it works: Randomly separate students into groups and assign each group to a board to generate a problem and solve it incorrectly. Groups rotate so they’re looking at a problem and an incorrect solution, and have to identify the error and solve the problem correctly. After another rotation—so students are looking at a problem and both the incorrect and correct solutions—they explain to the class the mistake made by the first group and the correct solution provided by the second. The activity, Chiapetta writes, helps students think about the same content from various perspectives, which can lead to deeper understanding.

Not all mistakes are created equal, and they often conceal thoughtful, underlying work. Former math teacher Colin Seale asks students to reflect on which wrong answer to a problem is “ more right .” He suggests offering students two equations that are both incorrect—perhaps one is wrong conceptually and the other computationally. Seale notes that this exercise gets students to tease out nuances around the skills and concepts they’re learning, while also correcting their approach to similar problems moving forward.

Bring Humanities Strategies to Math Class

The discussion, analysis of reasoning, and argumentation that happen in humanities classrooms can be extremely useful in math classrooms to help students slow down and think through the work they’re doing , says middle school math teacher Connell Cloyd. 

He does this in his classroom by posting four incorrectly solved math problems around the room and having students rotate around each problem in groups to discuss the error and write down (in complete sentences) a claim and supporting evidence to show why they believe the error occurred. As they rotate around, students read the arguments of peers and either support an argument or refute it with new evidence. This is like adding techniques from debate to Chiappetta’s strategy.

Math journals can also inject more writing and reasoning into your classroom. Former math teacher Nell McAnelly prompts students to reflect on concepts they’re having trouble with : They work through a problem and then write about the strategy they used to solve it, or informally journal about other approaches they could have used. Doing so, she writes, gives students a chance to “synthesize learning and address unanswered questions.”

Driving Deep, Critical Thinking

A traditional math classroom, where the teacher demonstrates a skill numerous times before students take the reins, can inhibit higher order thinking and result in students who “mimic” teachers rather than develop their own strategies to solve complex problems , says Peter Liljedahl, a researcher and professor of mathematics at Simon Fraser University. 

Instead of starting lessons with direct instruction, Liljedahl says, give students novel “ thinking tasks ” to work on in groups. These are problem-solving activities and mental puzzles that should get students in the mindset of challenging themselves. Work groups should not be chosen based on ability or students’ preferences—Liljedahl’s research shows that students are more likely to contribute in randomized groups. Having students stand while they engage in this collaborative, messy thinking—as Chiappetta does in her mistake-analysis exercise—is another way to engage them.

Instead of using notebooks to compute, Liljedahl calls for groups to work at vertical, non-permanent surfaces, such as whiteboards, blackboards, or windows—surfaces that he says promote more risk-taking because students have the freedom to quickly erase false starts without feeling committed. As students work in groups, teachers bounce around the room and avoid directly answering questions such as “Is this right?” that circumvent student thinking and instead make suggestions that lead to further independent thinking. 

Because the goal of this approach is to get students to develop perseverance, curiosity, and collaboration, Liljedahl suggests evaluating them in a way that prioritizes these competencies. He developed formative assessments that focus on informing students “about where they are and where they’re going in their learning.” These include observations, check-for-understanding questions, and unmarked quizzes. Summative assessments, meanwhile, should focus less on end products and more on the process of learning through both group and individual work.

Shifting to this thinking classroom model requires a fundamental shift in how you run your classroom, but it could result in large rewards throughout the year.

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Spirit of Mathematics Critical Thinking Skills (CTS)

S Syafril 1 , N R Aini 1 , Netriwati 1 , A Pahrudin 1 , N E Yaumas 1 and Engkizar 2

Published under licence by IOP Publishing Ltd Journal of Physics: Conference Series , Volume 1467 , Young Scholar Symposium on Science Education and Environment 2019 4-5 November 2019, Lampung, Indonesia Citation S Syafril et al 2020 J. Phys.: Conf. Ser. 1467 012069 DOI 10.1088/1742-6596/1467/1/012069

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1 Universitas Islam Negeri Raden Intan Lampung, Indonesia

2 Universitas Negeri Padang, Indonesia

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The mathematical critical-thinking skill is a process of thinking systematically to develop logical and critical thinking on mathematical problems, which characterize and demand to learn in the 21st century. This conceptual paper aims to analyze the spirit of critical thinking skill, and various approaches that can be applied in mathematics learning. Based on the analysis of several theories and research findings from various countries in the world, it can be concluded that the mathematical critical-thinking skill is very important for students, too; (i) help rational thinking in making decisions to express an idea, (ii) dare to make conclusions with alternative logical thinking, and (iii) able to examine and disregard various complex problems in learning Mathematics. Indeed, mathematics learning does not occur, if the learning process has not demonstrated the spirit of developing mathematical critical thinking skills.

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Content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence . Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.

Encyclopedia of Mathematics Education pp 121–125 Cite as

Critical Thinking in Mathematics Education

• Eva Jablonka 2  
• Reference work entry
• First Online: 01 January 2014

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Characteristics

Educational psychologists frame critical thinking (CT) as a set of generic thinking and reasoning skills, including a disposition for using them, as well as a commitment to using the outcomes of CT as a basis for decision-making and problem solving. In such descriptions, CT is established as a general standard for making judgments and decisions. Some descriptions of CT activities and skills include a sense for fairness and the assessment of practical consequences of decisions as characteristics of CT (e.g., Paul and Elder 2001 ). This assumes autonomous subjects who share a common frame of reference for representation of facts and ideas, for their communication, as well as for appropriate (morally “good”) action. Important is also the difference as to what extent a critical examination of the criteria for CT is included in the definition: If education for CT is conceptualized as instilling a belief in a more or less fixed and shared system of skills and criteria for...

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O’Daffer PG, Thomquist B (1993) Critical thinking, mathematical reasoning, and proof. In: Wilson PS (ed) Research ideas for the classroom: high school mathematics. MacMillan/National Council of Teachers of Mathematics, New York, pp 31–40

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Pimm D (1990) Mathematical versus political awareness: some political dangers inherent in the teaching of mathematics. In: Noss R, Brown A, Dowling P, Drake P, Harris M, Hoyles C et al (eds) Political dimensions of mathematics education: action and critique. Institute of Education, University of London, London

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Department of Education and Professional Studies, King’s College London, Waterloo Bridge Wing Franklin-Wilkins Building, SE1 9NH, London, UK

Eva Jablonka

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Stephen Lerman

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Jablonka, E. (2014). Critical Thinking in Mathematics Education. In: Lerman, S. (eds) Encyclopedia of Mathematics Education. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-4978-8_35

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Critical thinking definition

Critical thinking, as described by Oxford Languages, is the objective analysis and evaluation of an issue in order to form a judgement.

Active and skillful approach, evaluation, assessment, synthesis, and/or evaluation of information obtained from, or made by, observation, knowledge, reflection, acumen or conversation, as a guide to belief and action, requires the critical thinking process, which is why it's often used in education and academics.

Some even may view it as a backbone of modern thought.

However, it's a skill, and skills must be trained and encouraged to be used at its full potential.

People turn up to various approaches in improving their critical thinking, like:

• Developing technical and problem-solving skills
• Engaging in more active listening
• Actively questioning their assumptions and beliefs
• Seeking out more diversity of thought
• Opening up their curiosity in an intellectual way etc.

Is critical thinking useful in writing?

Critical thinking can help in planning your paper and making it more concise, but it's not obvious at first. We carefully pinpointed some the questions you should ask yourself when boosting critical thinking in writing:

• What information should be included?
• Which information resources should the author look to?
• What degree of technical knowledge should the report assume its audience has?
• What is the most effective way to show information?
• How should the report be organized?
• How should it be designed?
• What tone and level of language difficulty should the document have?

Usage of critical thinking comes down not only to the outline of your paper, it also begs the question: How can we use critical thinking solving problems in our writing's topic?

Let's say, you have a Powerpoint on how critical thinking can reduce poverty in the United States. You'll primarily have to define critical thinking for the viewers, as well as use a lot of critical thinking questions and synonyms to get them to be familiar with your methods and start the thinking process behind it.

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