How to improve in Maths - some tips and advice

　
Making Maths Relevant 　
　
All too often pupils get bored with maths lessons because the subject is presented in a way which disregards how it can be used in real life situations.
Admittedly there have been useful advances in this area of teaching over recent years, but still the kinds of problem set for discussion or coursework can be artificial and invented specifically to chime with the syllabus rather than the modern world.
In my opinion, one of the most important qualities we need to inculcate in our schools is enthusiasm for the subject, and this applies whether its maths or anything else.
The very small percentage of our pupils who are mathematically gifted and may well go on to study the subject at University and possibly become noted in their field one day will not have a problem in this respect. They will quickly see the shape and meaning of abstract concepts. I am more concerned with helping the vast majority who find maths strange, difficult, or even disagreeable. Given the correct encouragement I'm sure that many of these could become competent if not brilliant mathematicians.
So how do we do this?
In a nutshell, by two principal strategies:-
1. By harnessing their interest, showing how maths is relevant to some important activity in today's world (e.g. computing; encryption and security; driving a car; finance)
2. By encouraging them to master a topic or procedure beyond what the syllabus requires, so that they feel they 're 'good at maths'.
Any teaching scheme incorporating these two elements has to be enormously beneficial to the student.




Some suggestions for encouraging mid-ability pupils to excel in maths.


Here are two suggestions:-
1. Try to specialise in and master some topic in maths which interests you but is a bit beyond your present syllabus level. (E.g. solving simultaneous equations, even if you are only solving simpler single ones in class at the moment).
2. Use books or the internet to find out some of the maths behind modern technology. (E.g. how bar codes work when you are shopping; how online payments are made securely; how governments use encryption of messages to keep things secret.)
(You can find out more on these subjects if you look at my other blogs on the internet).


Now for a few words about the qualities needed to be a really good mathematician. It goes without saying that you need to have all the basic processes of school maths at your fingertips. Moreover, if you specialise in Pure Maths you will need to feel at home with abstract concepts chosen from topics such as Group Theory, Number Systems, symmetries, matrices, non-Euclidean geometries, topology, analysis, etc., and become familiar with the work of great mathematicians from the past, such as Newton, Lagrange, Leibnitz,  Euler, Fourier, Descartes, Galois, etc. (Its well worth looking up their achievements on the internet).

Relevance is less important here, as many great advances in mathematics have been made in the past for purely academic reasons, with their usefulness only being discovered generations later. (Boolean algebra, invented by George Boole in the 1850's, had no practical use until it was found to be a basis for logic systems in computers).

In Applied Maths you are more concerned with the usefulness of the subject in explaining or solving situations which arise in the fields of mechanics, probability, statistics, and the related studies of physics, engineering, and science generally, often using differential equations, mathematical modelling, the calculus of variations, etc., and studying the work of e.g. Newton, Dirac, Lorenz, Maxwell, and Hamilton.