Sharpe-Maths Teaching Guide

A Mathematics Teaching & Learning Resource

This is a revision/self-teaching site for Mathematics. I envision that it will deal with the entire UK GCSE and 'A' Level syllabi eventually but I am starting off with the basics of Fraction arithmetic, Percentages, Ratio & Proportionality, basic Algebraic techniques and Pythagoras' Theorem, which is used as an example below.

Navigation

The hamburger icon at the top right of the title bar (by default) brings the menu in and the image is changed to a close icon.
If you prefer the menu over on the right, then go to the Settings at the bottom of the menu and check the checkbox there.
The system will keep track of whether you like the menu to be open or closed, or to the right or left, when the site loads.
The bold italic rows in the menu open a folder containing other items.
Standard typeface entries are links which open pages or topics.

Every topic on the site contains one or more of the following:

Intro — An introduction, giving some basic information or history pertaining to the topic.

Eg list — A set of worked examples which are used to talk about the underlying principles. Clicking on the list will open the example so it can be followed.

Eg open — A set of worked examples which are used to talk about the underlying principles. Clicking on the list will open the example so it can be followed.

question — A set of exercises for self-assessment with an eye to click on to check your answer.

with answer — A set of exercises for self-assessment with an eye to click on to check your answer.

activity — Interactive activities related to the topic. This Pythagoras jigsaw let's the student play around with the squares and triangles to demonstrate to themselves that areas of the two smaller squares are equal to the big one.

problem — Some puzzles, which relate to the topic. (These are currently in short supply due to time constraints, but they are going to happen, so long as I don't drop dead any time soon.)

Hint — Some puzzles, which relate to the topic. (These are currently in short supply due to time constraints, but they are going to happen, so long as I don't drop dead any time soon.)

My expectation is that students will be guided (if possible) through the introduction and worked examples. You should play with the activities as you will. However, it should be fun, not torture! You should then try the exercises, in which the questions are largely ordered according to difficulty. You must then check your answers after each and every question you attempt. This is something which many students of all ages are pretty bad at, as it takes additional time. This is true, but I would argue that the advantages outweigh the disadvantages. The method which most students (and even some teachers) adopt is to do an exercise and then mark it, which in my opinion is worse than pointless, as all it achieves is to make the student practises their errors until they become second nature. Just as when playing music, practising your mistakes makes you good at your mistakes. This is not a desired outcome. Now the authoritarians out there will be tearing their hair and bellowing about cheating and such. The only cheating that I know about is the pretense that you understand something which you do not. Do not practise your mistakes. Please! Check your answers every time. That way, you don't need to waste time doing questions which you have already mastered and can move on to the fun stuff later on. It is important to note at this point that mathematics gets more fun as you progress.

Enjoy!

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