Maths is not a memory game!

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A-level Maths By: Please log in to see tutor details
Subject: Maths » A-level Maths
Last updated: 22/08/2012
Tags: patterns, proof, relationships between numbers, symbols are numbers, the reons why

Something that surprises me over and over again when tutoring students is that they have the idea that maths is some kind of collection of processes involving strange symbols that they just have to learn by heart. Then they have to pick the right formula (trick) to solve a given question.

I have taught an A level student whose aim was to turn his expected B to an A. Overall, he was definitely very able, but he could not explain to himself why the internal angles in any quadrilateral total 360⁰. It was no surprise then that he had not been shown why dy/dx of x2 is 2x. Another student thought she had to learn by heart two block totaling 18 formulae relating to trigonometric identities. She had not been shown how they were all interrelated.

 It took not very much time to show each the reasoning behind the rule relating the internal angles of all polygons and to fill in the particular gaps in understanding/ knowledge mentioned. Both felt as if their eyes had been opened and moved ahead in leaps and bounds.

All students should be aware that this beautiful subject builds up from the bottom. Right from its basic numerical beginnings, it is about patterns and relationships between numbers. Indeed, it is often argued that there is nothing to maths but adding and multiplying!

We may use odd names and symbols to refer to particular numbers or sets of numbers but even cosines and arctans are simply numbers with certain properties and origins. It is therefore important to ensure that maths students have some idea of why things are as they are and how they fit together. It is even better if they are helped to prove at least some of the results that are currently handed down like tablets of gibberish.

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