Critical thinking is a concept that can apply to all manner of different subjects. It is, after all, a tool used for problem-solving. One of the most obvious applications is its use in mathematics. In fact, most schools push the idea of critical thinking in math rather heavily.
On this page, we want to give you an overview of what critical thinking in mathematics is, and how it is used.
What Is Critical Thinking in Mathematics?
Critical thinking in mathematics is exactly like critical thinking in any other subject area. When you critically think in math, you aren’t just solving the problem, you are coming up with a reasoned answer as to why the method you have chosen is the correct one.
Critical thinking leans on the knowledge a person has gained previously to reach their reasoned answers. This often comes from being able to spot patterns or determine what worked out well for you in the past. For example, if you saw this problem, how would you solve it?
- 10 + 8 + 4
It is a simple problem, and you can probably work out the answer even if you are quite terrible at math. However, people’s brains may work in a different way to solve it. For example:
- One person could add the numbers 10 to 8 and then add the 4 on top.
- Others could add the 8 and 4 and then add the 10.
- Write down all the numbers as lines on a page and then add them up.
It doesn’t really matter how you got to the answer. What matters is that you can think about your reasons why you chose the method that you used and then, ultimately, critically determine whether it is the correct method. For example, the last method is clearly going to give you the same answer, but it is incredibly cumbersome and a critical thinker probably wouldn’t opt to use that. They may test it to see if it works, but they probably wouldn’t settle on that answer.
Don’t worry if this is a bit confusing. You will see what we mean as we move on.
How Is Critical Thinking Used in Mathematics?
There are two main concepts of critical thinking in math:
- Solving a problem
- Justifying your answer
For example, you may see this question:
- 82 + 89 = 867. Is this correct? Justify.
Obviously, we know that 82 + 89 does not equal 867. The problem is easy to solve. We can say “it is incorrect”. The difficult part is explaining why it is incorrect. This is what critical thinking in math is all about. It is about tapping into your brain and using the knowledge that you have gained to determine why an answer is what it is. It is an incredibly complicated thing to do.
Of course, with this, you only have to show what the real answer of 82 + 89 is. Show your rationale for that answer, and you have justified it. Pretty simple. The real complicated part of critical thinking in math comes when you do math as a profession.
We know that many of the people on this page may not necessarily be apt at math, and that is completely fine. So, we are not going to give you a ton of details about complicated math problems here, but we do want to highlight one theorem to show you how critical thinking relates to math.
- Goldbach’s Conjecture
This theorem is pretty simple, or it looks pretty simple:
“Every even number (greater than two) is the sum of two primes.”
Seems simple, right? Well, yes. Most mathematicians believe this to be the case. They have checked countless numbers, and there is literally nothing that indicates that this isn’t the case. The problem is that a “true” or “false” answer to this cannot yet be justified, and thus the problem remains ‘unsolved’. This is what critical thinking is all about, justifying your answer. If you can’t do that when doing math, then you aren’t critically thinking.
Hopefully, by now, you will see what we mean. When you critically think in math, you are giving a reasoned argument for your answer. If you can’t do that, have you really solved the problem?
Critical Thinking in Mathematics Classrooms
Many schools now teach critical thinking in mathematics from an incredibly early age. Many teachers are not giving their students a ready-made method for working out the answer to a problem. The student is meant to lean on the experience they have solving other equations to come up with their own problem-solving method.
Many teachers find this a far better method for teaching math because it is really tapping into a person’s knowledge and engaging their logical thinking patterns. Just giving people the exact method for solving an issue doesn’t.
What really helps is students discussing their justifications after. As we said before, people will always have different solutions to the problem. The job of the students is to claim their solution is the best one, and it can often trigger a few discussions in the classroom. A lot of people get educated about new methods they can possibly use here, something that you wouldn’t get with standard math practice.
You can even see this on exam questions. Almost every question in a math test will ask you to show how you managed to work out the answer. Examiners want to see critical thinking at work.
Why Is Critical Thinking in Mathematics Important?
Not a lot of teachers will tell you this, but math isn’t actually about teaching you math. Chances are that you aren’t going to leave school and use algebra in your day-to-day life. You probably won’t need to know the value of Pi again. However, math is important. It is one of the most important subjects in school, in fact.
Math is all about boosting a person’s problem-solving and logic skills. When a person is good at math, they tend to be much, much better at being able to think critically. They can justify their reasons for things, and work out the best solution for any problem they are facing, even if it does not deal with numbers. You want to be able to analyze any situation that you face. It is a good life skill.
Even in the world of math, critical thinking is important. When critical thinking is taught, people find it easier to tackle new problems, even if they have not been given the correct method for solving them. This can often result in the person being able to spot patterns, work out which methods work in which situations, and even develop new techniques for solving problems.
Conclusion
We know that this is a lot of information about critical thinking in mathematics, and we understand that some of it can be quite confusing. Pretty much everybody gets confused about the concept. However, don’t overthink it. All you really need to know is that critical thinking in mathematics is about two things:
- Coming up with answers
- Justifying your reasons for that answer.
That’s it. If you can nail that, then you are thinking critically.
References
https://tc2.ca/uploads/PDFs/TIpsForTeachers/CT_elementary_math.pdf
http://activemath.com/wp-content/uploads/2017/05/ten_minute_math.pdf
