# Myth: Maths is a subject you understand and not a subject you can study for

I often hear learners say that you cannot study for a maths test or, on the flip side, that they enjoy maths because if you understand it, you do not have to study for Maths. This mentality is why many learners’ marks drop significantly when they enter the FET phase (Grade 10-12).

During the primary school years, the focus of maths education is the introduction of various mathematical basic concepts and ‘rules’, including basic operations, defining and converting between fractions, decimals and percentages, the properties of 2-dimensional and 3-dimensional shapes, the basic definitions and concepts of probability and data handling (later to become statistics) and the interpretation of simple graphs.

These concepts and ‘rules’ are applied in a routine and simple manner. During these years, the learners who develop an early understanding of the concepts often do not have to invest much time studying for a maths test or exam.

However, as the learners progress into high school, the focus shifts from routine applications of definitions to more complex problem solving, over and above the introduction of more complex mathematical concepts. Basic operations and fractions are now subjected to algebraic laws of distribution and association.

The beloved concept of BODMAS gets turned on its head when learners are expected to solve complex equations to solve a problem. They have to learn the laws of exponents and, later, of logarithms. They are introduced to trigonometric definitions and identities and eight different functions, and they are required to know not less than 12 geometric theorems.

Students get taught a poster full of formulae (I prefer to call them our tools), which need to be applied correctly to the correct topic. These posters range from patterns to financial maths, trigonometry, analytical geometry, calculus, probability, and statistics. To raise standards, equations should be applied differently depending on the topic or difficulty.

I have been a maths tutor for the past seven years, and I spend much time revisiting maths theory with my learners. When struggling new learners start tutoring with me, I take the time to test their theoretical knowledge of mathematical concepts and often find it lacking.

Suppose the learners do not entirely understand the theory underpinning mathematical concepts. In that case, they cannot possibly be expected to apply it correctly. Alternatively, my learners who take the time to study the theory can apply it correctly in various contextual situations. My students are always encouraged to write a one-page “cheat sheet” explaining the most critical theory underlying each topic before practising problems.

Furthermore, suppose we are working through papers, and they get stuck on a question. In that case, my guidance always asks them about the theory and how that toolbox can be used to take just one further step in solving the problem at hand. That usually gets the ball rolling.

In summary, learners do need to take the time to study the theory for their maths tests, the way they would study for a content subject like Geography or Business Studies. It is not conducive to only examples as the examples, and the questions will continually change. The theory never changes, and a strong knowledge of it will help learners to apply it flexibly to a wide array of questions.