Check Out the New Website Shop!

## Novels & Picture Books

## Anchor Charts

- Critical Thinking

## How To Encourage Critical Thinking in Math

By Mary Montero

## Share This Post:

- Facebook Share
- Twitter Share
- Pinterest Share
- Email Share

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.

## You might also like…

## Leave a Reply Cancel reply

Your email address will not be published.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

## 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

©2023 Teaching With a Mountain View . All Rights Reserved | Designed by Ashley Hughes

Username or Email Address

Remember Me

Lost your password?

## Review Cart

No products in the cart.

- Our Mission

## 5 Ways to Stop Thinking for Your Students

Too often math students lean on teachers to think for them, but there are some simple ways to guide them to think for themselves.

Who is doing the thinking in your classroom? If you asked me that question a few years ago, I would have replied, “My kids are doing the thinking, of course!” But I was wrong. As I reflect back to my teaching style before I read Building Thinking Classrooms by Peter Liljedahl (an era in my career I like to call “pre-thinking classroom”), I now see that I was encouraging my students to mimic rather than think .

My lessons followed a formula that I knew from my own school experience as a student and what I had learned in college as a pre-service teacher. It looked like this: Students faced me stationed at the board; I demonstrated a few problems while students copied what I wrote in their notes. I would throw out a few questions to the class to assess understanding. If a few kids answered correctly, I felt confident that the lesson had gone well. Some educators might call this “ I do, we do, you do .”

What’s wrong with this formula? When it was time for them to work independently, which usually meant a homework assignment because I used most of class time for direct instruction, the students would come back to class and say, “The homework was so hard. I don’t get it. Can you go over questions 1–20?” Exhausted and frustrated, I would wonder, “But I taught it—why didn’t they get it?”

Now in the “peri-thinking classroom” era of my career, my students are often working at the whiteboards in random groups as outlined in Liljedahl’s book. The pendulum has shifted from the teacher doing the thinking to the students doing the thinking. Do they still say, “I don’t get it!”? Yes, of course! But I use the following strategies to put the thinking back onto them.

## 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 test’; and (3) keep thinking questions—questions that students ask so they can get back to work.” He suggests that teachers acknowledge “proximity” and “stop thinking questions” but not answer them.

Try these responses to questions that students ask to keep working:

- “What have you done so far?”
- “Where did you get that number?”
- “What information is given in the problem?”
- “Does that number seem reasonable in this situation?”

2. Don’t carry a pencil or marker. This is a hard rule to follow; however, if you hold the writing utensil, you’ll be tempted to write for them . Use verbal nudges and hints, but avoid writing out an explanation. If you need to refer to a visual, find a group that has worked out the problem, and point out their steps. Hearing and viewing other students’ work is more powerful .

3. We instead of I . When I assign a handful of problems for groups to work on at the whiteboards, they are tempted to divvy up the task. “You do #30, and I’ll do #31.” This becomes an issue when they get stuck. I inevitably hear, “Can you help me with #30? I forgot how to start.”

I now require questions to use “we” instead of “I.” This works wonders. As soon as they start to ask a question with “I,” they pause and ask their group mates. Then they can legitimately say, “ We tried #30, and we are stumped.” But, in reality, once they loop in their group mates, the struggling student becomes unstuck, and everyone in the group has to engage with the problem.

4. Stall your answer. If I hear a basic computation question such as, “What is 3 divided by 5?” I act like I am busy helping another student: “Hold on, I need to help Marisela. I’ll be right back.” By the time I return to them, they are way past their question. They will ask a classmate, work it out, or look it up. If the teacher is not available to think for them, they learn to find alternative resources.

5. Set boundaries. As mentioned before, students ask “proximity” questions because I am close to them. I might reply with “Are you asking me a thinking question? I’m glad to give you a hint or nudge, but I cannot take away your opportunity to think.” This type of response acknowledges that you are there to help them but not to do their thinking for them.

When you set boundaries of what questions will be answered, the students begin to more carefully craft their questions. At this point of the year, I am starting to hear questions such as, “We have tried solving this system by substitution, but we are getting an unreasonable solution. Can you look at our steps?” Yes!

Shifting the focus to students doing the thinking not only enhances their learning but can also have the effect of less frustration and fatigue for the teacher. As the class becomes student-centered, the teacher role shifts to guide or facilitator and away from “sage on the stage.”

As another added benefit, when you serve as guide or facilitator, the students are getting differentiated instruction and assessment. Maybe only a few students need assistance with adding fractions, while a few students need assistance on an entirely different concept. At first, you might feel like your head is spinning trying to address so many different requests; however, as you carefully sift through the types of questions you hear, you will soon be comfortable only answering the “keep thinking” questions.

## 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?

## Share this:

- Pingback: Critical Thinking, Mathematics, and McDonald’s | Engaging Maths
- Pingback: Beach Towels and Pencil Cases: Interesting, Inquiry-based Mathematical Investigations | Engaging Maths

## Leave a comment Cancel reply

- Already have a WordPress.com account? Log in now.
- Subscribe Subscribed
- Copy shortlink
- Report this content
- View post in Reader
- Manage subscriptions
- Collapse this bar

## How to Improve Problem-Solving Skills: Mathematics and Critical Thinking

In today’s rapidly changing world, problem-solving has become a quintessential skill. When we discuss the topic, it’s natural to ask, “What is problem-solving?” and “How can we enhance this skill, particularly in children?” The discipline of mathematics offers a rich platform to explore these questions. Through math, not only do we delve into numbers and equations, but we also explore how to improve problem-solving skills and how to develop critical thinking skills in math. Let’s embark on this enlightening journey together.

## What is Problem-Solving?

At its core, problem-solving involves identifying a challenge and finding a solution. But it’s not always as straightforward as it sounds. So, what is problem-solving? True problem-solving requires a combination of creative thinking and logical reasoning. Mathematics, in many ways, embodies this blend. When a student approaches a math problem, they must discern the issue at hand, consider various methods to tackle it, and then systematically execute their chosen strategy.

But what is problem-solving in a broader context? It’s a life skill. Whether we’re deciding the best route to a destination, determining how to save for a big purchase, or even figuring out how to fix a broken appliance, we’re using problem-solving.

## How to Develop Critical Thinking Skills in Math

Critical thinking goes hand in hand with problem-solving. But exactly how to develop critical thinking skills in math might not be immediately obvious. Here are a few strategies:

- Contextual Learning: Teaching math within a story or real-life scenario makes it relevant. When students see math as a tool to navigate the world around them, they naturally begin to think critically about solutions.
- Open-ended Questions: Instead of merely seeking the “right” answer, encourage students to explain their thought processes. This nudges them to think deeply about their approach.
- Group Discussions: Collaborative learning can foster different perspectives, prompting students to consider multiple ways to solve a problem.
- Challenging Problems: Occasionally introducing problems that are a bit beyond a student’s current skill level can stimulate critical thinking. They will have to stretch their understanding and think outside the box.

## What are the Six Basic Steps of the Problem-Solving Process?

Understanding how to improve problem-solving skills often comes down to familiarizing oneself with the systematic approach to challenges. So, what are the six basic steps of the problem-solving process?

- Identification: Recognize and define the problem.
- Analysis: Understand the problem’s intricacies and nuances.
- Generation of Alternatives: Think of different ways to approach the challenge.
- Decision Making: Choose the most suitable method to address the problem.
- Implementation: Put the chosen solution into action.
- Evaluation: Reflect on the solution’s effectiveness and learn from the outcome.

By embedding these steps into mathematical education, we provide students with a structured framework. When they wonder about how to improve problem-solving skills or how to develop critical thinking skills in math, they can revert to this process, refining their approach with each new challenge.

## Making Math Fun and Relevant

At Wonder Math, we believe that the key to developing robust problem-solving skills lies in making math enjoyable and pertinent. When students see math not just as numbers on a page but as a captivating story or a real-world problem to be solved, their engagement skyrockets. And with heightened engagement comes enhanced understanding.

As educators and parents, it’s crucial to continuously ask ourselves: how can we demonstrate to our children what problem-solving is? How can we best teach them how to develop critical thinking skills in math? And how can we instill in them an understanding of the six basic steps of the problem-solving process?

The answer, we believe, lies in active learning, contextual teaching, and a genuine passion for the beauty of mathematics.

## The Underlying Beauty of Mathematics

Often, people perceive mathematics as a rigid discipline confined to numbers and formulas. However, this is a limited view. Math, in essence, is a language that describes patterns, relationships, and structures. It’s a medium through which we can communicate complex ideas, describe our universe, and solve intricate problems. Understanding this deeper beauty of math can further emphasize how to develop critical thinking skills in math.

## Why Mathematics is the Ideal Playground for Problem-Solving

Math provides endless opportunities for problem-solving. From basic arithmetic puzzles to advanced calculus challenges, every math problem offers a chance to hone our problem-solving skills. But why is mathematics so effective in this regard?

- Structured Challenges: Mathematics presents problems in a structured manner, allowing learners to systematically break them down. This format mimics real-world scenarios where understanding the structure of a challenge can be half the battle.
- Multiple Approaches: Most math problems can be approached in various ways . This teaches learners flexibility in thinking and the ability to view a single issue from multiple angles.
- Immediate Feedback: Unlike many real-world problems where solutions might take time to show results, in math, students often get immediate feedback. They can quickly gauge if their approach works or if they need to rethink their strategy.

## Enhancing the Learning Environment

To genuinely harness the power of mathematics in developing problem-solving skills, the learning environment plays a crucial role. A student who is afraid of making mistakes will hesitate to try out different approaches, stunting their critical thinking growth.

However, in a nurturing, supportive environment where mistakes are seen as learning opportunities, students thrive. They become more willing to take risks, try unconventional solutions, and learn from missteps. This mindset, where failure is not feared but embraced as a part of the learning journey, is pivotal for developing robust problem-solving skills.

## Incorporating Technology

In our digital age, technology offers innovative ways to explore math. Interactive apps and online platforms can provide dynamic problem-solving scenarios, making the process even more engaging. These tools can simulate real-world challenges, allowing students to apply their math skills in diverse contexts, further answering the question of how to improve problem-solving skills.

## More than Numbers

In summary, mathematics is more than just numbers and formulas—it’s a world filled with challenges, patterns, and beauty. By understanding its depth and leveraging its structured nature, we can provide learners with the perfect platform to develop critical thinking and problem-solving skills. The key lies in blending traditional techniques with modern tools, creating a holistic learning environment that fosters growth, curiosity, and a lifelong love for learning.

Join us on this transformative journey at Wonder Math. Let’s make math an adventure, teaching our children not just numbers and equations, but also how to improve problem-solving skills and navigate the world with confidence. Enroll your child today and witness the magic of mathematics unfold before your eyes!

## FAQ: Mathematics and Critical Thinking

1. what is problem-solving in the context of mathematics.

Problem-solving in mathematics refers to the process of identifying a mathematical challenge and systematically working through methods and strategies to find a solution.

## 2. Why is math considered a good avenue for developing problem-solving skills?

Mathematics provides structured challenges and allows for multiple approaches to find solutions. This promotes flexibility in thinking and encourages learners to view problems from various angles.

## 3. How does contextual learning enhance problem-solving abilities?

By teaching math within a story or real-life scenario, it becomes more relevant for the learner. This helps them see math as a tool to navigate real-world challenges , thereby promoting critical thinking.

## 4. What are the six basic steps of the problem-solving process in math?

The six steps are: Identification, Analysis, Generation of Alternatives, Decision Making, Implementation, and Evaluation.

## 5. How can parents support their children in developing mathematical problem-solving skills?

Parents can provide real-life contexts for math problems , encourage open discussions about different methods, and ensure a supportive environment where mistakes are seen as learning opportunities.

## 6. Are there any tools or apps that can help in enhancing problem-solving skills in math?

Yes, there are various interactive apps and online platforms designed specifically for math learning. These tools provide dynamic problem-solving scenarios and simulate real-world challenges, making the learning process engaging.

## 7. How does group discussion foster critical thinking in math?

Group discussions allow students to hear different perspectives and approaches to a problem. This can challenge their own understanding and push them to think about alternative methods.

## 8. Is it necessary to always follow the six steps of the problem-solving process sequentially?

While the six steps provide a structured approach, real-life problem-solving can sometimes be more fluid. It’s beneficial to know the steps, but adaptability and responsiveness to the situation are also crucial.

## 9. How does Wonder Math incorporate active learning in teaching mathematics?

Wonder Math integrates mathematics within engaging stories and real-world scenarios, making it fun and relevant. This active learning approach ensures that students are not just passive recipients but active participants in the learning process.

## 10. What if my child finds a math problem too challenging and becomes demotivated?

It’s essential to create a supportive environment where challenges are seen as growth opportunities. Remind them that every problem is a chance to learn, and it’s okay to seek help or approach it differently.

## Related posts

## Summer Math Programs: How They Can Prevent Learning Loss in Young Students

As summer approaches, parents and educators alike turn their attention to how they can support young learners during the break. Summer is a time for relaxation, fun, and travel, yet it’s also a critical period when learning loss can occur. This phenomenon, often referred to as the “summer slide,” impacts students’ progress, especially in foundational subjects like mathematics. It’s reported…

## Math Programs 101: What Every Parent Should Know When Looking For A Math Program

As a parent, you know that a solid foundation in mathematics is crucial for your child’s success, both in school and in life. But with so many math programs and math help services out there, how do you choose the right one? Whether you’re considering Outschool classes, searching for “math tutoring near me,” or exploring tutoring services online, understanding…

- Math Resources Links
- Math in the Real World
- Differentiated Math Unlocked
- Math in the Real World Workshop

## 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 ↓

## Share this:

7 thoughts on “20 math critical thinking questions to ask in class tomorrow”.

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!

Pingback: How to Teach Problem Solving for Mathematics -

Pingback: 5 Ways Teaching Collaboration Can Transform Your Math Classroom

Pingback: 3 Ways Math Rubrics Will Revitalize Your Summative Assessments

Pingback: How to Use Math Stations to Teach Problem Solving Skills

Pingback: How to Seamlessly Add Critical Thinking Questions to Any Math Assessment

## Leave a Reply Cancel reply

## 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.

## Are there any services that can help me use more critical thinking?

We understand that it's difficult to learn how to use critical thinking more effectively in just one article, but our service is here to help.

We are a team specializing in writing essays and other assignments for college students and all other types of customers who need a helping hand in its making. We cover a great range of topics, offer perfect quality work, always deliver on time and aim to leave our customers completely satisfied with what they ordered.

The ordering process is fully online, and it goes as follows:

- Select the topic and the deadline of your essay.
- Provide us with any details, requirements, statements that should be emphasized or particular parts of the essay writing process you struggle with.
- Leave the email address, where your completed order will be sent to.
- Select your prefered payment type, sit back and relax!

With lots of experience on the market, professionally degreed essay writers , online 24/7 customer support and incredibly low prices, you won't find a service offering a better deal than ours.

## Critical Thinking in Mathematics Education

- Reference work entry
- First Online: 01 January 2014
- Cite this reference work entry

- Eva Jablonka 2

829 Accesses

2 Citations

16 Altmetric

## 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...

This is a preview of subscription content, log in via an institution to check access.

## Access this chapter

- Available as PDF
- Read on any device
- Instant download
- Own it forever
- Available as EPUB and PDF
- Durable hardcover edition
- Dispatched in 3 to 5 business days
- Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Appelbaum P, Davila E (2009) Math education and social justice: gatekeepers, politics and teacher agency. In: Ernest P, Greer B, Sriraman B (eds) Critical issues in mathematics education. Information Age, Charlotte, pp 375–394

Google Scholar

Applebaum M, Leikin R (2007) Looking back at the beginning: critical thinking in solving unrealistic problems. Mont Math Enthus 4(2):258–265

Bacon F (1605) Of the proficience and advancement of learning, divine and human. Second Book (transcribed from the 1893 Cassell & Company edition by David Price. Available at: http://www.gutenberg.org/dirs/etext04/adlr10h.htm

Common Core State Standards Initiative (2010) Mathematics standards. http://www.corestandards.org/Math . Accessed 20 July 2013

Ernest P (2010) The scope and limits of critical mathematics education. In: Alrø H, Ravn O, Valero P (eds) Critical mathematics education: past, present and future. Sense Publishers, Rotterdam, pp 65–87

Fawcett HP (1938) The nature of proof. Bureau of Publications, Columbia, New York City. University (Re-printed by the National Council of Teachers of Mathematics in 1995)

Fenner P (1994) Spiritual inquiry in Buddhism. ReVision 17(2):13–24

Fish M, Persaud A (2012) (Re)presenting critical mathematical thinking through sociopolitical narratives as mathematics texts. In: Hickman H, Porfilio BJ (eds) The new politics of the textbook. Sense Publishers, Rotterdam, pp 89–110

Chapter Google Scholar

Garfield JL (1990) Epoche and śūnyatā: skepticism east and west. Philos East West 40(3):285–307

Article Google Scholar

Jablonka E (1997) What makes a model effective and useful (or not)? In: Blum W, Huntley I, Houston SK, Neill N (eds) Teaching and learning mathematical modelling: innovation, investigation and applications. Albion Publishing, Chichester, pp 39–50

Keitel C, Kotzmann E, Skovsmose O (1993) Beyond the tunnel vision: analyzing the relationship between mathematics, society and technology. In: Keitel C, Ruthven K (eds) Learning from computers: mathematics education and technology. Springer, New York, pp 243–279

Legrand M (2001) Scientific debate in mathematics courses. In: Holton D (ed) The teaching and learning of mathematics at university level: an ICMI study. Kluwer, Dordrect, pp 127–137

National Council of Teachers of Mathematics (NCTM) (1989) Curriculum and evaluation standards for school mathematics. National Council of Teachers of Mathematics (NCTM), Reston

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

Paul R, Elder L (2001) The miniature guide to critical thinking concepts and tools. Foundation for Critical Thinking Press, Dillon Beach

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

Skovsmose O (1989) Models and reflective knowledge. Zentralblatt für Didaktik der Mathematik 89(1):3–8

Stallman J (2003) John Dewey’s new humanism and liberal education for the 21st century. Educ Cult 20(2):18–22

Steiner H-G (1988) Theory of mathematics education and implications for scholarship. In: Steiner H-G, Vermandel A (eds) Foundations and methodology of the discipline mathematics education, didactics of mathematics. In: Proceedings of the second tme conference, Bielefeld-Antwerpen, pp 5–20

Walkerdine V (1988) The mastery of reason: cognitive development and the production of rationality. Routledge, London

Walshaw M (2003) Democratic education under scrutiny: connections between mathematics education and feminist political discourses. Philos Math Educ J 17. http://people.exeter.ac.uk/PErnest/pome17/contents.htm

Download references

## Author information

Authors and affiliations.

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

Eva Jablonka

You can also search for this author in PubMed Google Scholar

## Corresponding author

Correspondence to Eva Jablonka .

## Editor information

Editors and affiliations.

Department of Education, Centre for Mathematics Education, London South Bank University, London, UK

Stephen Lerman

## Rights and permissions

Reprints and permissions

## Copyright information

© 2014 Springer Science+Business Media Dordrecht

## About this entry

Cite this entry.

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

## Download citation

DOI : https://doi.org/10.1007/978-94-007-4978-8_35

Published : 31 July 2014

Publisher Name : Springer, Dordrecht

Print ISBN : 978-94-007-4977-1

Online ISBN : 978-94-007-4978-8

eBook Packages : Humanities, Social Sciences and Law

## Share this entry

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

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

Provided by the Springer Nature SharedIt content-sharing initiative

- Publish with us

Policies and ethics

- Find a journal
- Track your research

JavaScript seems to be disabled in your browser. For the best experience on our site, be sure to turn on Javascript in your browser.

- Order Tracking
- Create an Account

## 200+ Award-Winning Educational Textbooks, Activity Books, & Printable eBooks!

- Compare Products

Reading, Writing, Math, Science, Social Studies

- Search by Book Series
- Algebra I & II Gr. 7-12+
- Algebra Magic Tricks Gr. 2-12+
- Algebra Word Problems Gr. 7-12+
- Balance Benders Gr. 2-12+
- Balance Math & More! Gr. 2-12+
- Basics of Critical Thinking Gr. 4-7
- Brain Stretchers Gr. 5-12+
- Building Thinking Skills Gr. Toddler-12+
- Building Writing Skills Gr. 3-7
- Bundles - Critical Thinking Gr. PreK-9
- Bundles - Language Arts Gr. K-8
- Bundles - Mathematics Gr. PreK-9
- Bundles - Multi-Subject Curriculum Gr. PreK-12+
- Bundles - Test Prep Gr. Toddler-12+
- Can You Find Me? Gr. PreK-1
- Complete the Picture Math Gr. 1-3
- Cornell Critical Thinking Tests Gr. 5-12+
- Cranium Crackers Gr. 3-12+
- Creative Problem Solving Gr. PreK-2
- Critical Thinking Activities to Improve Writing Gr. 4-12+
- Critical Thinking Coloring Gr. PreK-2
- Critical Thinking Detective Gr. 3-12+
- Critical Thinking Tests Gr. PreK-6
- Critical Thinking for Reading Comprehension Gr. 1-5
- Critical Thinking in United States History Gr. 6-12+
- CrossNumber Math Puzzles Gr. 4-10
- Crypt-O-Words Gr. 2-7
- Crypto Mind Benders Gr. 3-12+
- Daily Mind Builders Gr. 5-12+
- Dare to Compare Math Gr. 2-7
- Developing Critical Thinking through Science Gr. 1-8
- Dr. DooRiddles Gr. PreK-12+
- Dr. Funster's Gr. 2-12+
- Editor in Chief Gr. 2-12+
- Fun-Time Phonics! Gr. PreK-2
- Half 'n Half Animals Gr. K-4
- Hands-On Thinking Skills Gr. K-1
- Inference Jones Gr. 1-6
- James Madison Gr. 10-12+
- Jumbles Gr. 3-5
- Language Mechanic Gr. 4-7
- Language Smarts Gr. 1-4
- Mastering Logic & Math Problem Solving Gr. 6-9
- Math Analogies Gr. K-9
- Math Detective Gr. 3-8
- Math Games Gr. 3-8
- Math Mind Benders Gr. 5-12+
- Math Ties Gr. 4-8
- Math Word Problems Gr. 4-10
- Mathematical Reasoning Gr. Toddler-11
- Middle School Science Gr. 6-8
- Mind Benders Gr. PreK-12+
- Mind Building Math Gr. K-1
- Mind Building Reading Gr. K-1
- Novel Thinking Gr. 3-6
- OLSAT® Test Prep Gr. PreK-K
- Organizing Thinking Gr. 2-8
- Pattern Explorer Gr. 3-9
- Practical Critical Thinking Gr. 8-12+
- Punctuation Puzzler Gr. 3-8
- Reading Detective Gr. 3-12+
- Red Herring Mysteries Gr. 4-12+
- Red Herrings Science Mysteries Gr. 4-9
- Science Detective Gr. 3-6
- Science Mind Benders Gr. PreK-3
- Science Vocabulary Crossword Puzzles Gr. 4-6
- Sciencewise Gr. 4-12+
- Scratch Your Brain Gr. 2-12+
- Sentence Diagramming Gr. 3-12+
- Smarty Pants Puzzles Gr. 3-12+
- Snailopolis Gr. K-4
- Something's Fishy at Lake Iwannafisha Gr. 5-9
- Teaching Technology Gr. 3-12+
- Tell Me a Story Gr. PreK-1
- Think Analogies Gr. 3-12+
- Think and Write Gr. 3-8
- Think-A-Grams Gr. 4-12+
- Thinking About Time Gr. 3-6
- Thinking Connections Gr. 4-12+
- Thinking Directionally Gr. 2-6
- Thinking Skills & Key Concepts Gr. PreK-2
- Thinking Skills for Tests Gr. PreK-5
- U.S. History Detective Gr. 8-12+
- Understanding Fractions Gr. 2-6
- Visual Perceptual Skill Building Gr. PreK-3
- Vocabulary Riddles Gr. 4-8
- Vocabulary Smarts Gr. 2-5
- Vocabulary Virtuoso Gr. 2-12+
- What Would You Do? Gr. 2-12+
- Who Is This Kid? Colleges Want to Know! Gr. 9-12+
- Word Explorer Gr. 6-8
- Word Roots Gr. 3-12+
- World History Detective Gr. 6-12+
- Writing Detective Gr. 3-6
- You Decide! Gr. 6-12+

- Special of the Month
- Sign Up for our Best Offers
- Bundles = Greatest Savings!
- Sign Up for Free Puzzles
- Sign Up for Free Activities
- Toddler (Ages 0-3)
- PreK (Ages 3-5)
- Kindergarten (Ages 5-6)
- 1st Grade (Ages 6-7)
- 2nd Grade (Ages 7-8)
- 3rd Grade (Ages 8-9)
- 4th Grade (Ages 9-10)
- 5th Grade (Ages 10-11)
- 6th Grade (Ages 11-12)
- 7th Grade (Ages 12-13)
- 8th Grade (Ages 13-14)
- 9th Grade (Ages 14-15)
- 10th Grade (Ages 15-16)
- 11th Grade (Ages 16-17)
- 12th Grade (Ages 17-18)
- 12th+ Grade (Ages 18+)
- Test Prep Directory
- Test Prep Bundles
- Test Prep Guides
- Preschool Academics
- Store Locator
- Submit Feedback/Request
- Sales Alerts Sign-Up
- Technical Support
- Mission & History
- Articles & Advice
- Testimonials
- Our Guarantee
- New Products
- Free Activities
- Libros en Español

## Customers love our products...

Tell us your story ».

"My children love Balance Benders™; in fact, I would not be exaggerating if I said they were addicted to them. I sincerely thank you for a product that makes what can be extremely difficult skills to master an absolute blast for my children."

"The wealth of game-like activities and colorful illustrations in Fun-Time Phonics!™ make it feel like play rather than work, allowing kids to enjoy themselves while acquiring the skills and confidence that lead to fluency."

"Reading Detective® is the best reading comprehension teaching material I have found! I love that your material teaches the student HOW to comprehend, and how to look for the answers in the text. I love your evidence-seeking approach!"

"I love the Language Smarts™ curriculum. My son enjoys it very much and can follow the simple instructions with ease. Thanks to The Critical Thinking Co.™, my son scores high on his standardized and placement tests."

"U.S. History Detective® is fabulous. You have to do more than just figure out the correct answer -- you have to give the sentence number(s) that best supports your answer. I love that. You have to read the text and support your conclusions."

"The fun thing about Mathematical Reasoning™ is that every page is a little different. No rote facts or boredom here! Mix that in with a few game-like activities and lots of colors and pictures, and they had my kiddo hooked."

"We did an experiment to see if Building Thinking Skills® would help students perform better on standardized and state tests. The improvement was remarkable. Test scores went up even after the first few months!"

"Word Roots is everything I was searching for and more. It goes beyond spelling tests and teaches students to decipher words based upon prefixes, suffixes, and roots. The focus is on meaning, which in turn increases comprehension."

"You wouldn't think something so fun could have such a profound effect on your thought process! Mind Benders® sharpen organizational and informational processing skills as well as strengthen reading skills."

## US history, civics scores drop for nation's 8th graders. What experts say is to blame.

Another set of test results shows the effects of the COVID-19 pandemic on American students: National history scores dropped yet again, and eighth graders lost significant ground in civics for the first time.

Nearly all of the nation's eighth graders fell behind in U.S. history and civics in 2022 compared with 2018 on the National Assessment for Education Progress , also called the Nation's Report Card, according to scores released Wednesday. Declines were expected because of the shift to remote teaching and the loss of instruction time when the pandemic hit. But for these subjects, experts also worry friction over what students are taught in American history classes, especially about race and slavery, are a factor.

The test results follow a national plunge in reading and math performance among fourth- and eighth-grade students from the same year. Reading and math are getting much of the attention this year as teachers across the country focused on helping students catch up in those subjects. Subjects like history and science may become an afterthought, experts said. Fewer students took courses solely focused on U.S. history last school year than in the past, said Peggy Carr, commissioner of the National Center for Education Statistics, or NCES, which may have contributed to the drops.

"Whether students know U.S. history and civics is a national concern," Carr said on a call with reporters Tuesday. "A well-rounded education includes a grounding in these democratic principles."

Despite political pressure: US teachers lead complex history lessons on race and slavery

## What do the test results show?

Fewer eighth graders scored at a level considered proficient in both subjects, and more students performed at below basic levels than before.

In U.S. history, the results show a continued drop in student achievement: Scores first dropped in 2018 after steadily climbing since the test was first given in 1994. Overall, 13% of students performed at or above what the NCES considers proficient in 2022, compared with 15% who reached proficiency in 2018. Students who perform at the proficient level, as defined by NCES, "demonstrate solid academic achievement performance and competency over challenging subject matter." The measure does not directly correlate to grade-level proficiency.

In addition, 46% performed at the basic level and 40% performed below the basic level, compared with 34% of students who performed at below the basic level in 2018. Students who perform at the basic level, as defined by NCES, demonstrate "partial mastery of prerequisite knowledge and skills fundamental for proficient work at each grade."

Can we recover? Half of nation's students fell behind a year after COVID school closures.

In civics, scores dropped notably for the first time since the test was administered in 1998. That follows a small drop between 2014 and 2018. Of all test takers in 2022, 22% of students performed at or above the national assessment's level of proficiency compared with 24% who reached proficiency or above in 2018. Forty-eight percent of students performed at the basic level and 31% of students performed below the basic level, compared with 27% who performed below the basic level in 2018. The civics test measures students' knowledge of American government and their ability to participate in civic activities.

Carr said she was shocked to see that so few students reached the proficient level in both subjects, calling the results "concerning." The most notable drop occurred among already low-performing students, Carr said, and there was no significant change for any specific racial or ethnic student group compared with 2018.

How did your state fare? Reading and math test scores fell across US during the pandemic

## Critical thinking skills key to test success

Despite the national reading score inching down, Carr attributed the U.S. history and civics declines in part to a lack of critical-thinking skills among America's students.

On the history test, a nationally representative group of 8,000 students were queried on their knowledge of topics including democracy, culture and technology. One question prompted students to think about Dr. Martin Luther King Jr.'s "I Have a Dream" speech, for example, and how it incorporates two ideas from the U.S. Constitution or Declaration of Independence.

"Students have to be able to read and know literacy skills, but they need critical thinking to know how to extrapolate an answer to that question," Carr said.

Carr said educators must get history content in front of students, especially with students opting out of classes solely dedicated to U.S. history. NCES said 68% of eighth graders took classes focused on U.S. history in 2022, 4% less than in 2018.

"It's not just about reading, it's about context, facts, dates, information about our constitutional system. Students don't know this information. That is why they're scoring so low."

More: How critical race theory went from conservative battle cry to mainstream powder keg

## What should be done to address the deficits?

Schools should improve the quantity and quality of history and social studies content moving forward, experts and policymakers say.

- Education Secretary Miguel Cardona criticized recent attacks on U.S. history books and curricula , especially aspects involving race and racism. "Banning history books and censoring educators from teaching these important subjects does our students a disservice and will move America in the wrong direction."
- Kerry Sautner of the nonprofit National Constitution Center, which works to teach Americans about the Constitution, said that from conversations with teachers, she has gleaned that students are losing interest in history taught at school. "Students are beginning to disengage from − and become more fearful of expressing their opinions on − history, government and other topics important to civic learning," she said.
- Current and former members of the National Assessment Governing Board urge schools to act soon. "The young people who took these tests represent the future of our country. We must maintain high expectations while closing learning gaps that pre-date but were exacerbated by the pandemic," said Haley Barbour, a former assessment governing board chair and former Mississippi governor.

US history is complex: Scholars say this is the right way to teach about slavery, racism.

Contact Kayla Jimenez at [email protected]. Follow her on Twitter at @kaylajjimenez.

## IMAGES

## VIDEO

## COMMENTS

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 ...

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.

critical thinking skills by indicating optional methods and perhaps simplifying the process. Below is an example of how critical thinking can be used with simple mathematics. Students can develop and enhance their critical thinking skills as a result of instructors providing optional methods for simplifying the mathematical process.

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 ...

developing skills that can be applied to other subjects inside and outside the discipline of mathematics. Critical Thinking and Mathematics While core critical thinking skills, such as logic and argumentation, have a home in every discipline, certain fields provide opportunities to focus on specific critical thinking topics.

Discover effective strategies for promoting critical thinking, problem-solving, and mathematical reasoning in the classroom. ... The beauty is that the point of these tasks isn't just the mathematical thinking but the process skills they practice. Similarly, when teaching a unit on place value, you could have students work on problems where ...

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 ...

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 ...

Definition. Mainstream educational psychologists view critical thinking (CT) as the strategic use of a set of reasoning skills for developing a form of reflective thinking that ultimately optimizes itself, including a commitment to using its outcomes as a basis for decision-making and problem solving.

How to Develop Critical Thinking Skills in Math. Critical thinking goes hand in hand with problem-solving. But exactly how to develop critical thinking skills in math might not be immediately obvious. Here are a few strategies: Contextual Learning: Teaching math within a story or real-life scenario makes it relevant. When students see math as a ...

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 ...

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 ...

1.1 Critical thinking as a twenty-first century competence for STEM education. The debate about what kind of values and skills do individuals need to fully participate in a complex rapidly changing world has inspired different initiatives promoted by international organisations (EU, OECD, UNESCO) indicating a strong interest in defining and promoting those key competences.

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.

Therefore, learners' critical thinking about their own mathematics learning process was analyzed by using the self-examination and self-correction sub-skills of the sixth core cognitive critical thinking, self-regulation (Figure 1). The APA consensus' definitions of sub-skills self-examination and self-correction were adapted to analyze ...

According to the University of the People in California, having critical thinking skills is important because they are [ 1 ]: Universal. Crucial for the economy. Essential for improving language and presentation skills. Very helpful in promoting creativity. Important for self-reflection.

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 ...

Abstract. Teachers' low mathematical critical thinking skills (MCTS) resulted in students' low MCTS in the learning process. A teacher needs to have a good foundation of MCTS so that they can pass on their MCTS to their students. This study aims to improve the teaching and learning activities of teachers through prospective teachers and to find ...

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.

Keywords: Critical thinking skill, Develop logical, Mathematical problems, Learning in the 21st century, Rational thinking. 1. Introduction. Critical thinking is the careful application of reason in the determination of whether a claim is true. Notice that it is not so much coming up with claims, true or otherwise, that constitutes critical ...

Beyond the borders of South Africa, mathematics plays a significant role in improving students' critical thinking skills (Afriansyah, Herman, & Dahlan, 2021). For this reason, generally, it ...

To develop mathematical critical thinking skills, students are expected to have a fighting attitude in solving mathematical problems. This can support learning that is oriented towards students ...

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 ...

The Critical Thinking Co. publishes PreK-12+ books and software to develop critical thinking in core subject areas. ... Math, Science, Social Studies. Search by Grade & Subject ... "We did an experiment to see if Building Thinking Skills® would help students perform better on standardized and state tests. The improvement was remarkable.

Most eighth graders did worse on national U.S. history and civics tests in 2022 than four years ago. Experts blame a lack of critical-thinking skills.

Cultivating students' thinking skills, including critical thinking, is essential and aligns with the competency-based and character-building educational goals of the 2018 Vietnamese General Education Program. Argumentation in mathematics teaching is a valuable tool for fostering critical thinking skills as it encourages students to consider multiple perspectives, reason, debate, and make ...