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How To Encourage Critical Thinking in Math

By Mary Montero

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Critical thinking in math helps students learn to analyze and evaluate math concepts, identify patterns and relationships, and explore different strategies.

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.

Critical thinking in math helps students learn to analyze and evaluate math concepts, identify patterns and relationships, and explore different strategies.

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. 

free marvelous mathematician posters

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??

Nrich domino challenge math puzzler for critical thinking in math

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.

fifteen cards Nrich math puzzler for critical thinking in math

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. 

fourths math puzzler

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!

 math logic puzzles for critical thinking in math

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! 

fraction math puzzlers for critical thinking

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.

math projects upper elementary

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

Place Value Detectives Lay 804151 2642763 1

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.

Division Strategies Error AnalysisIMG 0763 3512378 6647195 jpg

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. 

analyzing errors anchor chart for error analysis

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 .

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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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One Comment

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.

Screen Shot 2017-06-25 at 5.40.37 pm

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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critical thinking maths questions

Increasing Critical Thinking Skills in Math

  • Math , Planning

It’s important that we are building critical thinking skills in math. Too often these are overlooked or assumed that students do it because they have to problem solve sometimes. While that does help build the all-important critical thinking skills, we need to make sure we are also finding ways to purposely bring it into instruction.

One such way that I like to implement critical thinking skills in my math class is through a game called Puzzlers. Recently I discussed why you should use games in the classroom and this one is no exception. Games go beyond just having fun and “entertaining” students. They aren’t just fillers.

It's so important that students are increasing their critical thinking skills in math each day. Learn how I use the game puzzlers to do just that! Save this pin and then check it out!

Building Critical Thinking Skills with the Puzzler Game

The puzzler game is a game that not only increases critical thinking skills, but it also practices both fact fluency and the order of operations!

In the puzzler game, students are given a target number. This happens by rolling a die or dice, but it can also be any chosen number between 1 and 36. For instance, I have randomly chosen the date before.

Next, students are provided with a 3×3 grid of the numbers 1 through 9 mixed up. (See the image below.)

It's so important that students are increasing their critical thinking skills in math each day. Learn how I use the game puzzlers to do just that! Save this pin and then check it out!

Once students have their target number and a mixed up grid of the numbers 1-9, they are ready to begin. This is where the critical thinking skills will come in.

Now, students will need to come up with a way to use ONLY three numbers (in a row, diagonally, or in a column) to get that target number. They will do this by creating equations that total the target number. They can add, subtract, multiply, divide, or even come up with a combination of them. If needed, they can use parentheses. This is where knowing the order of operations is necessary!

For instance, let’s take the example above with the 9 numbers on the sticky notes. Let’s say that the target number was 18. The student could create these two equations to come up with the solution of the target number 18:

  • (9 x 6) ÷ 3
  • (9 + 8) – 1

Here’s an example of a puzzler card with multiple solutions:

It's so important that students are increasing their critical thinking skills in math each day. Learn how I use the game puzzlers to do just that! Save this pin and then check it out!

What I love about this puzzler game is the variety of ways it can be used to help build critical thinking skills! For instance, students could list all of the equations, or solutions, to get the target number:

It's so important that students are increasing their critical thinking skills in math each day. Learn how I use the game puzzlers to do just that! Save this pin and then check it out!

or go through multiple cards trying to list as many solutions as they can:

It's so important that students are increasing their critical thinking skills in math each day. Learn how I use the game puzzlers to do just that! Save this pin and then check it out!

Or they could skip rolling the dice altogether and see how many solutions they can find for the target numbers one through ten. Why not even through in zero?!

It's so important that students are increasing their critical thinking skills in math each day. Learn how I use the game puzzlers to do just that! Save this pin and then check it out!

Students love this game and it’s perfect for independent work, early finishers, small groups, and even enrichment. It’s differentiated and there are cards that are strictly for adding and subtracting for students who can’t multiply yet.

You don’t have to purchase my puzzler resource to play this critical thinking skills builder! You can easily create it in your classroom as a bulletin board and change out the numbers each day!

If you want to save some time, grab the extra differentiated materials, and the specifics, head to my store now to purchase it! It’s definitely worth it!

It's so important that students are increasing their critical thinking skills in math each day. Learn how I use the game puzzlers to do just that! Save this pin and then check it out!

Click here to purchase this Puzzler Game.

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Forget boring math lessons and dreaded drill sheets.  These fun, colorful books use engaging lessons with easy-to-follow explanations, examples, and charts to make mathematical concepts easy to understand.  They can be used as textbooks or comprehensive workbooks with your textbooks to teach the math skills and concepts that students are expected to know in each grade—and several concepts normally taught in the next grade. Every lesson is followed with a variety of fun, colorful activities to ensure concept mastery.  The lessons and activities spiral slowly, allowing students to become comfortable with concepts, but also challenging them to continue building their problem-solving skills.  These books teach more than mathematical concepts; they teach mathematical reasoning, so students learn to devise different strategies to solve a wide variety of math problems.  All books are written to the standards of the National Council of Teachers of Mathematics.

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Understanding Pre-Algebra This book teaches and develops the math concepts and critical thinking skills necessary for success in Algebra I and future mathematics courses at the high school level.  It was written with the premise that students cannot problem solve or take leaps of reasoning without understanding the concepts and elements that lead to discovery.  The author—with 35 years of experience teaching mathematics—is a firm believer that understanding leads to confidence and confidence gives students the resolve to succeed in higher level mathematics rather than fear it.   It is standards-based, but what makes it different from other pre-algebra books is that it organizes concepts in a logical fashion, stressing practice and critical thinking. It avoids the mistakes—found in many other math books—of trying to teach new concepts before students receive the prerequisite skills and practice necessary for success. The concepts are presented clearly and in connection to other concepts. Math vocabulary is very important to success in higher mathematics, so this book includes easy-to-follow explanations and a user-friendly glossary.

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Understanding Pre-Algebra Contents

Understanding Geometry The successful completion of this colorful 272-page book will prepare middle schoolers for high school geometry. It covers more than 50% of the concepts taught in high school geometry using a step-by-step approach and teaches the reasoning behind the properties taught in geometry–instead of merely asking them to memorize them. Students are also taught the basics of geometric proofs and coordinate geometry in a way middle school students can understand. Students who struggle with high school geometry usually have lower standardized test scores because it is a fundamental subject in high school standardized testing. A glossary of terms that every student should master is included. This book can be used as a classroom textbook in Grades 7, 8, or 9 (usually over a two-year period) or as a reference for high school students. This book covers more than the National Math Standards for middle school mathematics.

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NOTE:  It is our recommendation that students complete Understanding Pre-Algebra (see description above) before attempting Understanding Geometry .

Understanding Algebra I This is a one-year Algebra I course for Grades 7-9. Students who have a solid algebra background will have no trouble with the algebra problems from SAT and even the GRE.  This 384-page book highlights vocabulary and notation, and has examples from the history of math. What makes this book unique and different from other algebra textbooks is that it is built from the experiences of an award-winning algebra teacher with more than 30 years of teaching experience. Many textbooks are written by a committee of authors, and many of those authors have little experience teaching beginning algebra students in middle school or high school. Understanding Algebra I presents the most essential concepts and skills needed to fully understand and gain confidence in algebra in a step-by-step fashion, teaching students that algebra is generalized arithmetic. It helps students see the connection between mathematics that they already know and algebra, so that learning algebra becomes easier and less abstract. This book provides students with real strategies to succeed in solving word problems by using charts and translating strategies that guarantee success.

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Essential Algebra for Advanced High School and SAT

Discover Essential Algebra for Advanced High School and SAT , a 241-page math book in the esteemed Mathematical Reasoning series written by award-winning author and teacher with 30 years of expertise in secondary mathematics. This powerful resource teaches the ‘essential’ connection of arithmetic and geometric concepts with algebraic concepts. Without this understanding, students tend to memorize Algebra I problem-solving steps—which is sufficient to pass Algebra I—but leaves them unprepared for math courses beyond Algebra I and the SATs. Algebra, the essential language of all advanced mathematics, lies at the core of this book's teachings. By delving into the generalized arithmetic that underpins algebra, students develop a solid foundation in the rules governing number and fraction operations, including factors and multiples. This vital knowledge empowers students to move beyond mere memorization of Algebra I problem-solving steps and confidently tackle the complexities of math courses beyond Algebra I. Without the knowledge and skills taught in this book, students often struggle or even fail in advanced mathematics courses and on the SATs. Imagine a good high school student who sees a problem like 3•x•y•4 and hesitates to write 12xy due to uncertainty about the rules governing multiplication. Or not understanding how to add 2x to 1/4y to combine it into a single fraction. Or why –6 2 is different than (–6) 2 . It is easy to see that not having a strong understanding of the foundational rules of algebra can stop even the smartest students from succeeding in advanced high school math courses. Essential Algebra for Advanced High School and SAT serves as a companion to an Algebra I course or aids in post-Algebra I readiness. To ensure students’ long-term success in advanced math beyond Algebra I, this book teaches the following 'essential' mathematics skills and concepts:

  • Understanding Terms and Order of Operations
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  • Solving Equations and Inequalities
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  • How Algebra is Used in Geometry
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Engage student's critical thinking skills with the use of these worksheets in the classroom.

critical thinking maths questions

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critical thinking maths questions

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Building a Thinking Classroom in Math

Over more than a decade, the author has developed a 14-point plan for encouraging students to engage deeply with math content.

Two students work together on a math problem on a whiteboard.

One day in 2003, I was invited to help June implement problem solving in her grade 8 classroom. She had never done problem solving with her students before, but with its prominence in the recently revised British Columbia curriculum, she felt it was time.

June, as it turned out, was interested in neither co-planning nor co-teaching. What she wanted from me was simply a collection of problems she could try with her students. The first one I gave her was a Lewis Carroll problem that I’d had much success with, with students of different grade levels: If 6 cats can kill 6 rats in 6 minutes, how many will be needed to kill 100 rats in 50 minutes?

June used it the next day. It did not go well. A forest of arms immediately shot up, and June moved frantically around the room answering questions. Many students gave up quickly, so June also spent much effort trying to motivate them to keep going. In general, there was some work attempted when June was close by and encouraging the students, but as soon as she left the trying stopped. This continued for the whole period.

The following day I was back with a new problem. The results were as abysmal as they had been on the first day. The same was true the third day. Over the course of three 40-minute classes, we had seen little improvement in the students’ efforts to solve the problems, and no improvements in their abilities to do so. So June decided it was time to give up.

I wanted to understand why the results had been so poor, so I stayed to observe June and her students in their normal routines. After three full days of observation, I began to discern a pattern. That the students were lacking in effort was immediately obvious, but what took time for me to realize was that the students were not thinking. More alarming was the realization that June’s teaching was predicated on an assumption that the students either could not or would not think.

Once I realized this, I proceeded to visit 40 other mathematics classes in a number of schools. In each class, I saw the same thing—an assumption, implicit in the teaching, that the students either could not or would not think. Under such conditions it was unreasonable to expect that students were going to be able to spontaneously engage in problem solving.

This motivated me to find a way to build, within these same classrooms, a culture of thinking. I wanted to build what I now call a thinking classroom—one that’s not only conducive to thinking but also occasions thinking, a space inhabited by thinking individuals as well as individuals thinking collectively, learning together, and constructing knowledge and understanding through activity and discussion.

Over 14 years, and with the help of over 400 K–12 teachers, I’ve been engaged in a massive design-based research project to identify the variables that determine the degree to which a classroom is a thinking or non-thinking one, and to identify the pedagogies that maximize the effect of each of these variables in building thinking classrooms. From this research emerged a collection of 14 variables and corresponding optimal pedagogies that offer a prescriptive framework for teachers to build a thinking classroom.

1. The type of tasks used: Lessons should begin with good problem solving tasks. In the beginning of the school year, these tasks need to be highly engaging, non-curricular tasks. Later these are gradually replaced with curricular problem solving tasks that then permeate the entirety of the lesson.

2. How tasks are given to students: As much as possible, tasks should be given verbally. If there are data, diagrams, or long expressions in the task, these can be written or projected on a wall, but instructions should still be given verbally.

3. How groups are formed: At the beginning of every class, a visibly random method should be used to create groups of three students who will work together for the duration of the class.

4. Student work space: Groups should stand and work on vertical non-permanent surfaces such as whiteboards, blackboards, or windows. This makes the work visible to the teacher and other groups.

5. Room organization: The classroom should be de-fronted, with desks placed in a random configuration around the room—away from the walls—and the teacher addressing the class from a variety of locations within the room.

6. How questions are answered: Students ask only three types of questions: proximity questions, asked when the teacher is close; “stop thinking” questions—like “Is this right?” or “Will this be on the test?”; and “keep thinking” questions—ones that students ask in order to be able to get back to work. The teacher should answer only the third type of question.

7. How hints and extensions are used: The teacher should maintain student engagement through a judicious and timely use of hints and extensions to maintain a balance between the challenge of the task and the abilities of the students working on it.

8. Student autonomy: Students should interact with other groups frequently, for the purposes of both extending their work and getting help. As much as possible, the teacher should encourage this interaction by directing students toward other groups when they’re stuck or need an extension.

9. When and how a teacher levels their classroom: When every group has passed a minimum threshold, the teacher should pull the students together to debrief what they have been doing. This should begin at a level that every student in the room can participate in.

10. Student notes: Students should write thoughtful notes to their future selves. They should have autonomy as to what goes in the notes and how they’re formatted. The notes should be based on the work already on the boards done by their own group, another group, or a combination.

11. Practice questions: Students should be assigned four to six questions to check their understanding. They should have freedom to work on these questions in self-selected groups or on their own, and on the vertical non-permanent surfaces or at their desks. The questions should not be marked or checked for completeness—they’re for the students’ self-evaluation.

12. Formative assessment: Formative assessment should be focused primarily on informing students about where they are and where they’re going in their learning. This will require a number of different activities, from observation to check-your-understanding questions to unmarked quizzes where the teacher helps students decode their demonstrated understandings.

​ Chart of the author’s 14-point plan

13. Summative assessment: Summative assessment should focus more on the processes of learning than on the products, and should include the evaluation of both group and individual work. Summative assessment should not in any way have a focus on ranking students.

14. Reporting out: Reporting out of students’ performance should be based not on the counting of points but on the analysis of the data collected for each student within a reporting cycle. The data need to be analyzed on a differentiated basis and focused on discerning the learning a student has demonstrated.

My research also shows that the variables and accompanying pedagogical tools are not all equally impactful in building thinking classrooms. And there is an optimal sequence for both teachers and students when first introducing these pedagogies. This sequence is presented as a set of four distinct toolkits that are meant to be enacted in sequence from top to bottom, as shown in the chart. When these toolkits are enacted in their entirety, an optimal transformation of the learning environment has been achieved in the vast majority of classrooms.

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100+ Critical Thinking Questions for Students To Ask About Anything

Critical thinkers question everything.

critical thinking maths questions

In an age of “fake news” claims and constant argument about pretty much any issue, critical thinking skills are key. Teach your students that it’s vital to ask questions about everything, but that it’s also important to ask the right sorts of questions. Students can use these critical thinking questions with fiction or nonfiction texts. They’re also useful when discussing important issues or trying to understand others’ motivations in general.

“Who” Critical Thinking Questions

Questions like these help students ponder who’s involved in a story and how the actions affect them. They’ll also consider who’s telling the tale and how reliable that narrator might be.

  • Is the protagonist?
  • Is the antagonist?
  • Caused harm?
  • Is harmed as a result?
  • Was the most important character?

critical thinking maths questions

  • Is responsible?
  • Is most directly affected?
  • Should have won?
  • Will benefit?
  • Would be affected by this?

critical thinking maths questions

  • Makes the decisions?

“What” Critical Thinking Questions

Ask questions that explore issues more deeply, including those that might not be directly answered in the text.

  • Background information do I know or need to know?
  • Is the main message?
  • Are the defining characteristics?

critical thinking maths questions

  • Questions or concerns do I have?
  • Don’t I understand?
  • Evidence supports the author’s conclusion?
  • Would it be like if … ?
  • Could happen if … ?
  • Other outcomes might have happened?
  • Questions would you have asked?
  • Would you ask the author about … ?
  • Was the point of … ?
  • Should have happened instead?
  • Is that character’s motive?
  • Else could have changed the whole story?

critical thinking maths questions

  • Can you conclude?
  • Would your position have been in that situation?
  • Would happen if … ?
  • Makes your position stronger?
  • Was the turning point?
  • Is the point of the question?
  • Did it mean when … ?
  • Is the other side of this argument?
  • Was the purpose of … ?
  • Does ______ mean?
  • Is the problem you are trying to solve?
  • Does the evidence say?
  • Assumptions are you making?
  • Is a better alternative?
  • Are the strengths of the argument?

critical thinking maths questions

  • Are the weaknesses of the argument?
  • Is the difference between _______ and _______?

“Where” Critical Thinking Questions

Think about where the story is set and how it affects the actions. Plus, consider where and how you can learn more.

  • Would this issue be a major problem?
  • Are areas for improvement?
  • Did the story change?
  • Would you most often find this problem?

critical thinking maths questions

  • Are there similar situations?
  • Would you go to get answers to this problem?
  • Can this be improved?
  • Can you get more information?
  • Will this idea take us?

“When” Critical Thinking Questions

Think about timing and the effect it has on the characters or people involved.

  • Is this acceptable?
  • Is this unacceptable?

critical thinking maths questions

  • Does this become a problem?
  • Is the best time to take action?
  • Will we be able to tell if it worked?
  • Is it time to reassess?
  • Should we ask for help?
  • Is the best time to start?
  • Is it time to stop?
  • Would this benefit society?

critical thinking maths questions

  • Has this happened before?

“Why” Critical Thinking Questions

Asking “why” might be one of the most important parts of critical thinking. Exploring and understanding motivation helps develop empathy and make sense of difficult situations.

  • Is _________ happening?
  • Have we allowed this to happen?
  • Should people care about this issue?

critical thinking maths questions

  • Is this a problem?
  • Did the character say … ?
  • Did the character do … ?
  • Is this relevant?
  • Did the author write this?
  • Did the author decide to … ?
  • Is this important?

critical thinking maths questions

  • Did that happen?
  • Is it necessary?
  • Do you think I (he, she, they) asked that question?
  • Is that answer the best one?
  • Do we need this today?

“How” Critical Thinking Questions

Use these questions to consider how things happen and whether change is possible.

  • Do we know this is true?
  • Does the language used affect the story?
  • Would you solve … ?
  • Is this different from other situations?

critical thinking maths questions

  • Is this similar to … ?
  • Would you use … ?
  • Does the location affect the story?
  • Could the story have ended differently?
  • Does this work?
  • Could this be harmful?
  • Does this connect with what I already know?
  • Else could this have been handled?
  • Should they have responded?

critical thinking maths questions

  • Would you feel about … ?
  • Does this change the outcome?
  • Did you make that decision?
  • Does this benefit you/others?
  • Does this hurt you/others?
  • Could this problem be avoided?

More Critical Thinking Questions

Here are more questions to help probe further and deepen understanding.

  • Can you give me an example?

critical thinking maths questions

  • Do you agree with … ?
  • Can you compare this with … ?
  • Can you defend the actions of … ?
  • Could this be interpreted differently?
  • Is the narrator reliable?
  • Does it seem too good to be true?

critical thinking maths questions

  • Is ______ a fact or an opinion?

What are your favorite critical thinking questions? Come exchange ideas on the WeAreTeachers HELPLINE group on Facebook .

Plus, check out 10 tips for teaching kids to be awesome critical thinkers ., you might also like.

Examples of critical thinking skills like correlation tick-tac-Toe, which teaches analysis skills and debates which teach evaluation skills.

5 Critical Thinking Skills Every Kid Needs To Learn (And How To Teach Them)

Teach them to thoughtfully question the world around them. Continue Reading

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Math Critical Thinking Questions For Grade 1

Math Critical Thinking Questions For Grade 1 - Displaying top 8 worksheets found for this concept.

Some of the worksheets for this concept are 81 fresh fun critical thinking activities, The critical thinking, The test of critical thinking, Unit1criticalthinking unitlength2weeks, 7 critical thinking skills of common core, When and how, 2013 math framework grade 1, Math mammoth grade 4 a.

Found worksheet you are looking for? To download/print, click on pop-out icon or print icon to worksheet to print or download. Worksheet will open in a new window. You can & download or print using the browser document reader options.

1. 81 Fresh & Fun Critical-Thinking Activities

2. the critical thinking, 3. the test of critical thinking, 4. unit%1:%critical%thinking% % % % unit%length:%2%weeks ..., 5. 7 critical thinking skills of common core -, 6. when and how, 7. 2013 math framework, grade 1, 8. math mammoth grade 4-a.

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  6. 5 Important Reasoning Questions

COMMENTS

  1. 20 Math Critical Thinking Questions to Ask in Class Tomorrow

    Start small. Add critical thinking questions to word problems. 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. When you want your students to justify their opinions. When you want your students to think outside of the box.

  2. PDF 81 Fresh & Fun Critical-Thinking Activities

    This arrangement will help you and your students more clearly understand and identify the specific critical-thinking skills they are using. For each thinking skill in this book, there are two kinds of activities: (1) those that you, as the teacher, will lead, and (2) student reproducibles for indepen-dent work.

  3. PDF 100 questions that promote Mathematical Discourse

    diferent something get a fair is chance. 22 Can you draw a picture or make a. 18 to talk, use the to show that? model. answer? mathematically correct. How would. manipulatives, 23 or How did you you reach explain that ___ conclusion? to someone. 15 Where would his or her answer? you go for.

  4. Critical Thinking Math Problems: Examples and Activities

    Critical thinking is an important factor in understanding math. Discover how critical thinking can help with real-world problem solving, using examples and activities like asking questions ...

  5. Rich Tasks

    Rich Tasks. Every student deserves to have the opportunity to problem-solve and engage in genuine mathematical thinking. Rich tasks are designed to make these rich learning experiences possible. We've written these tasks to launch quickly, engage students, and promote the habits of mind mathematicians need: perseverance & pattern-seeking ...

  6. 10 Brilliant Math Brain Teasers

    10 Brilliant Math Brain Teasers. Tap into rigorous problem-solving and critical thinking with these playful math brain teasers for middle and high school students. To break the ice during the first few awkward moments of class in the new school year, high school math teacher Lorenzo Robinson uses an unusual strategy: He reads his students' minds.

  7. Critical Thinking in Elementary Math

    In order to choose questions that guide conversation, here are some guidelines: 1. Make it real. Kids can tell if the question is a setup or something you really want to know. 2. Keep it simple. Frame the question in the simplest way possible. Simple questions leave the most room for creativity and thinking. 3.

  8. How To Encourage Critical Thinking in Math

    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 ...

  9. Promoting Creative and Critical thinking in Mathematics and Numeracy

    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 ...

  10. Promoting Independent Critical Thinking in Math

    5 Ways to Get Your Students to Think. 1. Answer questions with a refocus on the students' point of view. Liljedahl found in his research that students ask three types of questions: " (1) proximity questions—asked when the teacher is close; (2) stop thinking questions—most often of the form 'is this right' or 'will this be on the ...

  11. Increasing Critical Thinking Skills in Math

    The puzzler game is a game that not only increases critical thinking skills, but it also practices both fact fluency and the order of operations! In the puzzler game, students are given a target number. This happens by rolling a die or dice, but it can also be any chosen number between 1 and 36. For instance, I have randomly chosen the date before.

  12. 101 Great Higher-Order Thinking Questions for Math

    The answer is by utilizing higher-order thinking questions for math. Higher-order thinking questions are critical thinking questions that require students to infer, apply, predict, connect, evaluate, and judge knowledge in new ways. The answers to these questions require prior knowledge and an expansive schema so that readers can see beyond the ...

  13. Using Questioning to Stimulate Mathematical Thinking

    Within the context of open-ended mathematical tasks, it is useful to group questions into four main categories (Badham, 1994). These questions can be used be the teacher to guide the children through investigations while stimulating their mathematical thinking and gathering information about their knowledge and strategies. 1. Starter questions.

  14. Math Detective® Series

    The questions in Math Detective® are modeled after questions found on high-stakes math assessments, but require more critical thinking. These problems are excellent preparation for assessments that require students to explain and support their answers.

  15. Critical Thinking Math Problems & Activities

    Print Worksheet. 1. A student who applies critical thinking to a problem involving a right triangle can _____. explain how to use the Pythagorean theorem to solve the problem. input numbers into ...

  16. Creative and Critical Thinking in Primary Mathematics

    In mathematics, creative thinking occurs when students generalise. Generalising involves identifying common properties or patterns across more than one case and communicating a rule (conjecture) to describe the common property, pattern or relationship. In order to generalise students need to first analyse the problem to notice things that are ...

  17. Critical Thinking Questions for 6th Grade Math

    Open Questions. Asking open questions is a way to provide an opportunity for your students to think critically. For example, asking the sixth grade students how many polygons they can make with an area of 24 units is an open question. A closed question with the same objective is to have a polygon drawn and ask them the area of that polygon.

  18. Mathematical Reasoning™ Series

    Essential Algebra for Advanced High School and SAT. Discover Essential Algebra for Advanced High School and SAT, a 241-page math book in the esteemed Mathematical Reasoning series written by award-winning author and teacher with 30 years of expertise in secondary mathematics. This powerful resource teaches the 'essential' connection of ...

  19. PDF Critical Thinking Worksheet Grades 6-8: Mathematical Concepts

    Click here: critical_thinking_034-download.pdf to download the document. EW Lesson Plans More than 1,000 FREE Lessons Reading, Writing, Math, Science, History & Every-Day Edits!

  20. Building a Thinking Classroom in Math

    Critical Thinking. Building a Thinking Classroom in Math. Over more than a decade, the author has developed a 14-point plan for encouraging students to engage deeply with math content. ... and "keep thinking" questions—ones that students ask in order to be able to get back to work. The teacher should answer only the third type of question.

  21. Critical Thinking Questions: The Big List for Your Classroom

    In an age of "fake news" claims and constant argument about pretty much any issue, critical thinking skills are key. Teach your students that it's vital to ask questions about everything, but that it's also important to ask the right sorts of questions. Students can use these critical thinking questions with fiction or nonfiction texts.

  22. Thinking Deeply with Fractions

    2/3 and 6/9. 3/4 and 2/5. Open Question. Find 3 fractions smaller than 1/3. Find 3 fractions equal to 2/3. Find 3 fractions greater than 2/5. Effective tasks are ones that encourage thinking and analysis, enable students to build upon previous knowledge, and reveal misunderstandings.

  23. Math Critical Thinking Questions For Grade 1

    Math Critical Thinking Questions For Grade 1 - Displaying top 8 worksheets found for this concept. Some of the worksheets for this concept are 81 fresh fun critical thinking activities, The critical thinking, The test of critical thinking, Unit1criticalthinking unitlength2weeks, 7 critical thinking skills of common core, When and how, 2013 math ...

  24. Download Pdf Evan-Moor Skill Sharpeners Critical Thinking ...

    Listen to this episode from Nishida Haruka on Spotify. Read or Download Evan-Moor Skill Sharpeners Critical Thinking, Kindergarten Workbook, Problem Solving Skills, Activities, Higher-Order, Open-Ended Questions and Challenges, Science, Math, Social Studies, Language Arts by Evan-Moor Educational Publishers Visit Link Bellow to Download Or Read Free Books Visit Here : https://globalbooks.site ...