Before we start I'd like to make it clear that all the posts which follow are designed mainly to help school pupils of average ability. They are not really meant for the small percentage who are high-fliers or have a truly gifted mathematical mind. These pupils will do extremely well anyway and may see the posts as very basic or even trivial by their standards.
The other thing which needs to be pointed out at this stage is that the study of maths is a cumulative process i.e. at each stage it assumes a good command of earlier topics. For example, in arithmetic, you need to understand percentages before you can study problems of compound interest, and trigonometry requires an understanding of graphs and the geometry of triangles. Similarly, in algebra, you have to be able to solve simple linear equations and have an understanding of formulae before moving on to tackle quadratics, and at a higher level the study of calculus presumes a command of a whole range of mathematical skills, including indices, algebraic simplifying, trig. ratios, logarithms, graphs, etc.
There are plenty of analogies and examples of this cumulative process in other fields of activity - e.g. a pianist has to learn things such as musical notation, scales, correct fingering, and posture before becoming a competent performer; to learn a foreign language you have to start with the basics and build up slowly; even in rugby, the game usually goes through several phases before the opponent's line is crossed. So a steady, progressive and patient build-up is the key to ultimate success.
The other thing which needs to be pointed out at this stage is that the study of maths is a cumulative process i.e. at each stage it assumes a good command of earlier topics. For example, in arithmetic, you need to understand percentages before you can study problems of compound interest, and trigonometry requires an understanding of graphs and the geometry of triangles. Similarly, in algebra, you have to be able to solve simple linear equations and have an understanding of formulae before moving on to tackle quadratics, and at a higher level the study of calculus presumes a command of a whole range of mathematical skills, including indices, algebraic simplifying, trig. ratios, logarithms, graphs, etc.
There are plenty of analogies and examples of this cumulative process in other fields of activity - e.g. a pianist has to learn things such as musical notation, scales, correct fingering, and posture before becoming a competent performer; to learn a foreign language you have to start with the basics and build up slowly; even in rugby, the game usually goes through several phases before the opponent's line is crossed. So a steady, progressive and patient build-up is the key to ultimate success.
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