3 Hidden Math Skills That Can Take You from Good to Excellent

When most people think about learning and studying Math, they think about understanding concepts, learning formulas, and doing practice questions to improve their skills.

But what if you already do all of that and still feel like you are hitting a wall?

Why can some students seem to breeze through challenging Math questions while you are still struggling to figure out where to begin?

This is especially true for students who are already doing reasonably well. You may understand the concepts, complete your homework, and perform well on straightforward questions – but find that you can’t solve the most difficult questions to get that A1 grade. The truth is that there are many unspoken skills that students need to develop in order to excel in Mathematics.

Here are three of the skills we help students in our secondary math tuition classes develop as they work towards the next level.

Identifying the topic and concepts quickly

Here’s one important difference between doing a tutorial worksheet and sitting for an examination:

For a tutorial worksheet, you usually know which topic you are practising. If you are given a worksheet on differentiation, you already know that the questions will require you to apply differentiation.

An examination is different.

Before you can even solve the problem, you first need to figure out what concepts the question is testing.

Being able to pick out clues from a question and identify the relevant topic is an important problem-solving skill. Some topics are relatively obvious because they contain distinctive symbols or terminology – for example, Permutations and Combinations or Matrices.

Others are much less straightforward. A challenging question might combine concepts from algebra, functions, differentiation, and trigonometry, making it difficult to immediately identify the best approach.

This skill improves with practice, but simply doing more questions isn’t always enough. Students also need to learn what to look out for.

Our tutors help students recognise common clues, identify the mathematical concepts being tested, and develop a systematic approach to breaking down unfamiliar questions. Over time, students become faster at moving from “What is this question asking?” to “I know how to approach this.”

Applying methods in different ways

Everyone knows the Alphabet.

But how many can recite the alphabet backwards?

What if I asked you to only list out every other letter, like A, C, E, G, and so on?

Knowing the alphabet is not the same as being able to use it flexibly.

Math works in a similar way.

Many students think they have mastered a concept once they know the relevant formula and can use it to solve a straightforward question. But when the same concept is presented in an unfamiliar way, they suddenly find themselves stuck.

This is often where the difference between knowing a method and truly understanding it becomes apparent.

Advanced Math questions are not a test of memory – instead, they are a test of mastery. To solve tricky questions, students may need to work backwards, deal with missing information, combine multiple concepts, or recognise that a familiar formula can be applied in an unfamiliar context.

Knowing how to apply a formula when all the necessary values are provided is one level of understanding. Knowing how to manipulate that formula to find an unknown value – or recognise when it can be combined with another concept – is a much deeper level of expertise.

This is why our tutors do more than demonstrate a standard method and ask students to repeat it. We expose students to different variations of a concept and encourage them to think about why a particular method works, not just what steps to memorise.

The goal is to help students become flexible problem-solvers rather than students who can only solve questions that look familiar.

Knowing how to check your answers

School teachers often tell students to “check your answers” after completing a paper.

But what does that actually mean?

Does it simply mean flipping through the paper to make sure you haven’t left any questions blank?

In reality, checking your answers is a skill in itself.

If you have plenty of time remaining, you may be able to work through your calculations again and verify each step. But during an examination, time is limited. Students need to know how to use the time they have effectively.

Depending on the situation, checking could involve:

• Verifying that your final answer actually answers the question being asked.
• Checking that you have transferred values and signs correctly.
• Looking out for calculation errors.
• Reviewing key steps in your working.
• Checking whether your answer makes sense in the context of the question.

Not every question requires the same level of checking. Learning how to prioritise your checks can help you catch avoidable mistakes and ensure your results reflect your actual abilities.

In our IP Math tuition classes, we don’t assume that students automatically know how to check their work effectively. We first guide them through the process, explaining what to look out for and why it matters. As students become more confident, we encourage them to develop their own checking habits and apply them independently.

The difference between knowing and mastering mathematics

For students in many of Singapore’s top secondary schools, simply knowing the syllabus is often not enough.

School examinations increasingly require students to apply concepts in unfamiliar situations, connect different areas of Mathematics, and reason through problems independently.

This is why at Future Academy, our approach for our high-ability students goes beyond repeating concepts that students have already learnt. Our tutors coach students through challenging problems, expose them to different question types, and help them develop the habits needed to approach unfamiliar questions with confidence.

Our Advanced Math assessment book series is also a valuable resource, focusing on helping students get exposed to high-ability questions that promote deep conceptual understanding. Through guided practice and individualised feedback, we help students bridge the gap between textbook knowledge and true mastery.

Because sometimes, the difference between a good Math student and an excellent one isn’t how much more they know. It’s knowing how to use what they already know.

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