Mastering Mathematics


Author: Daniel Tung

SME, Maths


Students tend to excuse their poor grades in mathematics by saying, `I’m not good at maths’. It is a lame excuse. There is no such thing as the inability to learn Maths or any subject. Most people are able to master mathematics. How? The answer may sound like a mundane one – practice.
I was quite mediocre at maths, or even worse. Then something happened. I enjoyed the maths lessons for the first time. It was coordinate geometry. I found it interesting, and when I was able to solve problems, it took me by surprise. The lessons started in a simple way, and I didn’t miss a single step. I found the next step always easy.
Each time you learn something new, the neurons in your brain are being rewired to represent the new information. When you recall the new piece of knowledge through practice, the neural connection will be activated again and again, resulting in stronger connections. This means you will become more effective in processing the information next time you see it. Practice makes perfect.
There is a saying that you need 10 thousand hours to master something. Don’t take it literally, and don’t give up at the start. The good news is, you don’t really need to spend a lot of time to be good at learning or mastering maths skills. You missed algebra? Never mind, you can still be good at geometry. All you need is a maximum of 20 hours of practice! On average, this is the amount of time you need to practise one topic. Never give up. Look at this cool video of a guy who learned to play a new musical instrument in just 20 hours.
As shown in the video, one key method to learn any skill in just 20 hours is by breaking down the skill into smaller pieces. You will be able to master the skill quickly by learning the smaller pieces and combine them later. Just concentrate on one maths problem, one rule, one step, one trick. Master it and move on to the next one. Try this today to learn a new skill, for example, coordinate geometry!


Another reason practice makes perfect is that practice helps build up your confidence. Confidence is an important element in mastering any skills. If you are not confident in what you are doing, you will try to avoid doing it, which will make yourself even less capable in it. Making small mistakes during practice is less devastating. By getting accustomed to it and learning from the mistakes, students’ confidence gradually increases.

Deliberate/Purposeful practice

However, not any kind of practices will do. We will not progress very far if the practice is too easy, or by practicing the same thing over and over again. Educators say, if you practice a test and your result is over 80%, you wasted your time, as you didn’t learn anything.
On the other hand, if the practice is too difficult, we will get frustrated easily and give up very soon.
Mastery requires what the researchers call deliberate or purposeful practice. It is to learn something purposefully, with a clear goal, and by choosing those practices that lie just on the edge of our ability. The aim is to push ourselves away from our comfort zone, to attain real improvements.
Therefore, the practices should be suitably challenging – not too easy that they could be done mindlessly, yet not too challenging that it lies far beyond our current ability. Deliberate practice requires a good teacher (or good interactive learning tools) that can tailor practice activities based on our performances, and provide feedback to guide us in the process. When you are stuck with a problem, you have a couple of options, like asking for help (teacher), go back to an easier problem, or just look up the answer. The most effective way to learn is the second one because obviously, the problem was too challenging for you. In this case, looking at the solution or teacher’s explanation won’t help in the learning process.


Even so, deliberate practice is not a fun process. Everyone likes simple exercises that always confirms skills – it makes them feel good. Constantly put your ability to test could be very frustrating. Therefore, we need something to hold us up and move us forward. This is our passion for what we do. Students passionate about a subject will persevere when they face challenging questions. They will find ways to solve it by looking for new information, or by looking for new ways to think about the question.
So, we think that a major characteristic of a good teacher, a good book, and a good education system in general, is that they are able to ignite the passion for a student. Skills will follow later.