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Critical Thinking in Math

Critical thinking is a key factor in separating those students who can 'do' math from those who truly understand what they're doing. When students do math, they can perform computations and explain concepts because they've learned formulas and definitions through practice and rote memorization. They don't necessarily know why the formula works, but they can use it. Likewise, they may not know how some ancient mathematician defined the concept, but they know the definition.

Real World Problem Solving

Math textbooks only go so far when it comes to presenting real world problems that require mathematical solutions. Texts are organized around concepts, making it easy for students to see what strategies they need to use to solve a problem. If the chapter is on the quadratic formula, students automatically know they will use that formula at some point to answer every question, even a complex word problem. Critical thinking kicks in when students have a variety of options for solving a problem. Students apply critical thinking to find the best strategy out of many possible methods to reach a solution.

Here's a problem that requires mathematical critical thinking:

Based on current trends in rising or falling temperatures, predict the average high and low temperatures for five different places on Earth five years from now.

To solve the problem, students will need to analyze data, determine the trends in each place, and select a method for predicting the future temperatures. They may need to use a variety of formulas and statistical tools to form their predictions. Teachers can take this a step further by asking students to explain and defend the methods they used.

Below are a few ways one can I.prove their critical thinking skills:-

Asking Questions

To think critically is to follow a clear line of logical steps and reasoning. To solve critical thinking problems, math teachers should model the way they think when solving a problem. Students can internalize a set of questions to ask that will help them think their way to a solution.


Bellringers are short activities students do at the beginning of class as a warm-up exercise. Normally, bellringer activities require students to practice or apply skills they have already learned. Bellringers can also stimulate critical thinking.


Solving puzzles is an entertaining way to engage students in critical thinking. Sudoku is a popular style of puzzle that requires students to think critically and mathematically. To solve a Sudoku puzzle students fill in columns, rows, and boxes with numbers from one to nine using each number only once in each area.

Many students enjoy brainteasers with a mathematical twist

Project-Based Learning

Project-based learning tasks require students to apply math concepts and strategies while thinking both critically and creatively. While completing the projects, students not only practice thinking and speaking in mathematical terms, they also learn to collaborate with their peers. They have to think critically to respond to each other's ideas, and they have to frame their criticisms constructively.

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