AJ Tutoring Blog

Connecting you to news, advice and academic resources

Critical Thinking & Problem Solving in Math


“I’m not sure what to do.” It is one of the most frustrating situations for a student because you can feel completely lost and without a sense of 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 an understanding as to why. This deprives students of the practice in 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 level math: periodically glanced at but not deemed to be of utmost importance. Instead, those new concepts and formulas are given priority, and students are tasked with memorizing those formulas and applications. This may be beneficial to students who already possess critical thinking skills, but for those unlucky ones who haven’t yet developed such strong talent, it weakens that critical mathematical foundation.

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.

Let's discuss your student's academic tutoring, test prep, or college counseling needs!

Our test prep, academic tutoring, and college admissions counseling professionals are here to help you navigate the test taking maze, share our experience with your local school, and inspire your student.

Talk to a Director
Peninsula Main Phone Number (650) 331-3251
Free Consultation