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Critical Thinking & Problem Solving in Math


Enhancing Math Critical Thinking Skills: Introduction

In today’s rapidly evolving world, the ability to solve complex problems and think critically is more valuable than ever. With its logical structure and problem-solving core, mathematics serves as a perfect medium to cultivate these essential skills. Critical thinking in math involves more than just crunching numbers; it’s about understanding concepts, analyzing problems from different angles, and applying logical reasoning to find solutions. This blog explores practical strategies to enhance your math critical thinking abilities, a vital skill set for academic success and beyond.

  • Develop a Growth Mindset: The first step towards improving your math critical thinking skills is to develop a growth mindset. Believe in your ability to learn and improve in mathematics. This positive attitude encourages resilience, allowing you to tackle challenging problems with determination rather than fear.
  • Engage with Real-world Problems: Applying math to real-world scenarios significantly boosts critical thinking. When you see how mathematical concepts apply to everyday life, you’re more likely to understand and retain these concepts. Try to solve problems that require you to apply various mathematical principles, encouraging you to think critically about which methods are most appropriate for each situation.
  • Practice Strategic Questioning: Asking questions is at the heart of critical thinking. In mathematics, this might mean questioning how different formulas are derived, why a specific solution method is used, or what the real-world implications of a mathematical concept are. By engaging in strategic questioning, you deepen your understanding of mathematics and enhance your ability to think critically.
  • Embrace Challenges and Learn from Mistakes: Challenging problems encourage deeper cognitive processing, which is essential for developing critical thinking skills. When faced with difficult math problems, embrace them as opportunities to improve. Moreover, learning from mistakes is crucial. Analyze where you went wrong and why, as this reflection process is invaluable for building critical thinking and problem-solving skills.
  • Collaborate and Share Ideas: Collaboration in mathematics encourages the exchange of different problem-solving approaches, providing insights into various ways of thinking and solving problems. Discussing mathematical problems with peers or mentors allows you to see multiple perspectives and enhances your critical thinking skills.

Here are some more specifics from one of our best math tutors

“I’m not sure what to do.” It is one of the most frustrating situations for a student because you can feel completely lost without direction. Time and time again, students get stumped on an assignment or dreaded word problem. They have just recently learned the concepts, formulas, or theorems, but they find themselves tangled in the hurdle of application. Thankfully, sometimes we as tutors are able to be there to help them.

It’s not as simple as just providing or explaining the answer. Algebra and Geometry classes cover the foundational concepts of mathematics necessary in all future high-level courses. However, some classes focus too heavily on memorization of notes and formulas. They sometimes provide a sample solution that students mimic without understanding why. This deprives students of the practice and development of necessary critical thinking and problem-solving skills.

These skills might seem to be basics expected of middle school and high school students, mastered back in the earlier grade levels when they were the primary focus. Critical thinking and problem solving skills sometimes are put on the back burner in high school math: periodically glanced at but not deemed important. Instead, those new concepts and formulas are given priority, and students are tasked with memorizing those formulas and applications. This may benefit students who already possess critical thinking skills, but it weakens that critical mathematical foundation for those unlucky ones who haven’t yet developed such strong talent.

Instead of just focusing solely on content, we should ideally discuss the critical thinking process. When facing a difficult problem, it is important to first break down the problem by reading carefully, separate out important and unimportant information, and identify what is being asked for. We can only solve a problem confidently by completely understanding the problem.

No coach or player goes into a game blind. Now we can develop a game plan. It is important to think ahead, as there are so many things we can do with math. We don’t want to be tricked into going down the wrong path. By looking at the problem as a whole, we can make sure every line of work that we do is a step in the right direction towards what we were asked for. As we work through the problem, it is almost like connecting the dots. We want to flow from one line of math to another, connecting each with those logical concepts, formulas, and theorems. Sometimes the next step is a little unclear, but there are plenty of critical thinking and problem solving strategies that we can use to help us recognize the next step. What information are we given? What are we looking to find? What information do we need in order to apply this formula? Can I work backwards?

These are a few of the basic but essential strategies to not just knowing a formula, but fully understanding how to apply a concept. The next time your student is struggling with an assignment, it might be best to help guide them through the critical thinking steps, and they’ll slowly but surely pick up those essential problem solving skills! Give us a call to learn more about our approach to math education and connect with a tutor.


Improving your math critical thinking skills is a journey that requires patience, practice, and persistence. By developing a growth mindset, engaging with real-world problems, practicing strategic questioning, embracing challenges, and collaborating with others, you can significantly enhance your mathematical critical thinking abilities. Remember, the goal is not just to find the right answers but to understand the process of getting there, fostering a deep and lasting comprehension of mathematical concepts.



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