Why memorising maths formulas isn't enough: the power of understanding

Have you ever memorised every formula possible for your math exam, only to be completely stuck when facing an unfamiliar exam question?

A big misconception students typically have about mathematics is that doing well simply means remembering formulas and substituting numbers into them. Whilst memorisation is important, knowing how to apply the formulas is of greater importance.

Knowing a formula doesn't mean you understand it
Consider the quadratic formula. Whilst you may be able to recall this formula perfectly and substitute the correct values, do you understand what the discriminant represents? Do you know when to use the quadratic formula opposed to completing the square or factorisation?

This is where conceptual understanding becomes important. A student should understand what the formula does, why it works and when it should be applied.

Why understanding matters in exams
Math exams usually test more than the student's ability to recall information. Questions may be created to present familiar concepts in unfamiliar ways, requiring students to identify the appropriate method and apply their knowledge.

For example, knowing the formula for the area of a circle may be useful, but what happens if the question provides the circumference instead of the radius? How can you manipulate the formulas to gain your answer?

Students who understand the relationship between mathematical concepts can work through these problems logically rather than relying on memorised procedures.

So how can you study smarter?
1. Ask WHY: Understand what each variable represents, why the formula works and when to use it.
2. Practice different question types: By exposing yourself to more unfamiliar questions, you are able to learn different methods in approaching challenging questions
3. Understand how formulas can interconnect amongst each math topic: recognise which formulas and concepts frequently are tested together and understand these relationships.

So don't just learn the formula. Learn the mathematics behind it!!