How to Understand Maths
“But I don’t understand!”
The third part in a 3 part series to help parents and kids be better at maths!
To some, complex Mathematics is perfectly logical, sequential and workable; to others it may appear as a meaningless jumble of symbols. This article attempts to unpack some of the mystery that surrounds understanding Mathematics.
Literacy, as it applies to Mathematics, is possibly the biggest hurdle for students to overcome, not numeracy. Teachers use mathematical terms and symbols – the language of Mathematics – which may, at first, appear confusing, but it cannot be avoided, if understanding is going to happen.
Understanding of mathematical concepts does not come easily; it comes with familiarity, confidence, and time. Make maths familiar territory by visiting it often, rather than keeping it as a suspicious and foreign zone that is rarely entered. Linked to this is confidence. In this case, confidence means that students approach new work with a sense that even though they don’t get it straight away, with some persistence, they will. Very few people understand what is going on with a new Mathematics topic straight away; it takes time. The confident student deals with the initial period of uncertainty knowing that if they persist, and become increasingly familiar with what they are doing, then the understanding will come, eventually!
Strange as it may seem, needing to understand before moving on can actually be a real barrier to understanding. For example, a seed placed in the ground and provided with adequate water and sunlight, will eventually germinate and grow into a plant. We might know the sequence, but not necessarily understand it. However, working with the sequence over time increases our ability to use it, and our understanding of the links between the steps develops. The point is that while the sequence itself requires no understanding, through working and experimenting with it, we can increase our understanding of it. But, if we won’t put a seed in the ground because we don’t understand how a plant results, we will go hungry!
Students also need to examine exactly what it is that they should be trying to understand. Maths is full of patterns and relationships such as the simple number fact 2 + 3 = 5. Everyone can accept this and work with it. However, when students step into new and unfamiliar territory, things may go pear-shaped. Trigonometry is a perfect example. It is full of new and unfamiliar words and symbols such as sin30o = ½, (must appear in text as follows: ) which is a statement of a relationship that exists in a right angled triangle. It is one part of a simple pattern that involves putting side lengths of right triangles together into fractions. If the sequence or the pattern is followed correctly, something mathematically useful emerges. The pattern involved is not something that needs to be understood, just applied. If it can be remembered it can be worked with, so that the understanding part of trigonometry reveals itself.
The real challenge for students of Mathematics is to achieve familiarity with more and more procedures, in more complex contexts. To do this, the advice is relatively simple: learn the language, go there often, and confidently work with things not fully understood, knowing that the understanding will come – eventually!
Head of Faculty – Mathematics
Cannon Hill Anglican College