Why do some people find mathematics so challenging?

While mathematics is considered as a compulsory subject for most of the curriculums around the world, it is also one of the subjects with a clear distinction of whether it is in one’s favour or not. Children are exposed to numbers and the basics of mathematics from a very young age and are continuously exposed to it from kindergarten all the way up to high school, so why is it that we see so many students finding mathematics as a difficult subject?

Mathematics fundamentally is a subject which aims to educate students on (mathematical) critical and logical thinking skills applied to a problem. This heavily differentiates the idea of mathematics as a “theory” to mathematics as an “application”. In simpler terms — let’s say a student fully understands the concepts within a certain topic. However, if the student simply stops at knowing the theory and is unable to apply it in the necessary areas, it is far from what the fundamental goals of mathematics would be. Applying this context, many school curriculums heavily focus their method of education in problem-solving. In other subjects such as language or philosophy, solving multiple questions may not be the best way to demonstrate one’s knowledge, but within maths? They are simply inseparable.

We will compare two questions; try them yourself and think about how hard they are!

GCSE level mathematics — indices and logarithms

Middle school level mathematics — simultaneous equations

If you have tried both of the questions, I am confident that you found question 1, GCSE level, much easier than question 2, middle school level. The chances are that something like question 2 is more likely to pop up in exams — to differentiate the level of candidates. The theory required in question 2 is no more difficult than question 1, but the level of critical thinking and modelling ability required differ to a large extent.

As the difficulty of mathematics go up, the concepts to getting more and more abstract, which is another key reason why students find the subject to be harder and harder. Recent research done by KICE (Korea Institution for Curriculum and Education) suggested that young children firstly get a negative emotion towards maths in grade 2 — when fractions are first introduced. Before fractions, students only learn basic numbers and calculations which most of the students have been reported to find them manageable. While there can be an easy approach to explaining what math is, some teachers insist on teaching the most basic content in an abstract way — which causes the trigger of “I cannot understand this → I must be bad at maths” in students. It is almost shocking that some students only find out that fraction notation is the same as division only when they start middle school.

So what can you do if you identify yourself as a “math-hater” and want to improve? Well, these 3 steps may benefit.

1) Befriend maths

While this may sound cheesy and all that, you will never be able to learn anything if you cannot overcome the inner wall that blocks you and the subject. With a closed mind, no teachers or resources will be able to fully help you. In this case start from solving the simplest questions (calculations, basic equations, etc) that can be solved quickly over and over again. Think about why people learn mathematics, where mathematics is used, and what are the skills I need to develop.

2) Get your bottom row of the “math tower” strong and well-built

This brings out the first problem with the nature of mathematics; every unit is a building block which cannot be built unless the previous concept has been fully implemented. Many weaker students tend to forget or ignore what they have learned in maths in the past because they think what they are learning now is the important one. While that may be true, if one’s basis in mathematics is not built up properly, it is nearly impossible to fully learn new concepts and theories. Such approach to mathematics simply defile the purpose of mathematical education — no matter how well you understand complex theories, if you cannot use the logical thinking skills required even the simplest theories become a difficult question. The reason why so many people become math haters is that they do not know which aspects they are missing and just try to solve the questions that are in front of them. Try to think about past moments where you couldn’t understand what the teacher was saying so you just copied answers down from your friends. That is probably the aspect you’re missing which stops you from improving your understanding — go back and revise until you get it.

3) How to study for exams

Fundamentally you must practice a lot of calculations involving mental maths. With paper and pencil, write down every single step of the calculation and try fully understand what each step is trying to do. There is limited time for any math exam, and surely having to use a calculator in every single one of the problems is a big waste of time. And the chances are you’re probably going to take a non-calc paper sometime in your life, so it’s definitely important. If you cannot do basic calculations, you will fall to the loophole of “Solve question → Understand concept but miscalculates to a wrong answer → let down → I hate math” again. After you’ve practiced enough calculations move onto solving more complex equations — write down every single step on a paper for any question you are doing. Do not give answers directly without working — whether it’s factorisation, bracket expansion, fractions, indices — make sure your chain of thoughts is clearly expressed. This is the way that will develop your critical thinking skills and help you more.

Written by Min Sik EOM