How to Think Critically in Math

Learning how to think critically in math is the foundation on which you may build a lifetime of ever more involved mathematical study. As a primary building block and approach to a plethora of math problems—as well as those in associated disciplines such as physics, architecture, chemistry, and astrophysics—the student is certain to excel, no matter the extent of the problem featured or the scope of the subject matter at hand. With the information on how to think critically in math so easily mastered, it is not surprising that parents, teachers, and even students themselves are shifting their approach to this field of study. If you are ready to join them, continue on with the next few simple steps!

Instructions

Difficulty: Easy

1. Copy the math problem verbatim onto a piece of paper. Do not begin to solve it!
2. State the purpose of the assigned problem. For example, is the problem one that requires multiplication or addition, subtraction or division? In the case of 3+3, the principle is a basic addition. Understanding the purpose of a math problem is the first step to considering it with the help of critical thinking.
3. Define the actual question that is being asked. In the case of a straight addition problem, such as 3+3, this is easy. The question that is being asked may be defined as finding the sum of the equation. With a word problem this is not always so easy. It requires the identification of all known and unknown numerical factors.
4. Sort problems in logical order; while 3+3-2 will always equal 4, the introduction of division and multiplication into the mix will change this order. Sorting the possible equations according to those which must stay together is the next step in learning how to think critically in math.
5. Identify mathematical formulas that may come into play. When the purpose of the problem is identified and it has been accurately identified what the actual question is which is being asked, and the logical order of possible equations has also been sorted out, it is time to be on the lookout for formulas that may come in handy. This is especially true in physics!
6. Estimate the correct answer. You are still a long ways off from actually sitting down and solving the problem, but by thinking critically in math you can get close into the ballpark of the correct answer by giving an estimate. In the 3+3-2 example, it is obvious that the answer must be higher than 3 simply because a subtraction of 2 is not sufficient to counteract an addition of 3. At the same time, the answer must be less than 6 since the 2 takes away from the actual result. Thus, the answer may be 4 or 5.
7. Apply your understanding of the problem’s nature, the type of mathematical problem solving involved, and any formulas you may need to manipulate the figures offered to you and arrive at a logical and correct answer. Application of knowledge is the last step in thinking critically in math.
8. Compare your result with your earlier estimate. Did you come close? If the answer is yes, the odds are good that you mastered this level of critical thinking in math and it is time to increase the level of difficulty. If there is a world of difference between your estimate and the final result, repeat the steps and see if you come to differing results. If you are still far off in your estimate and the final result, find out which answer is correct and then backtrack to see where the problem in your thought process could be found.

Tips & Warnings

• Work with mathematical problems of median difficulty and gradually increase the level of complexity.
• Do not take these steps out of order as they are all vital to set you up for success when establishing a mathematical thought process.

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