Traditionally, the Mathematics we are familiar with today either in our homes or in school was entirely different many years ago and was more commonly known as Arithmetic, which basically means the study and understanding of numbers- the operations of subtraction, addition, multiplication and division.
We do seem to have lost the whole reasoning behind why we are studying Mathematics and this can make for much confusion for the student. When one understands why they are doing something then they will make sense of it more quickly and a meaning will be given to it.
Mathematics today seems quite broken- there is no obvious explanation to the child as to why they are learning all these theories or problems. We no longer see the student having to prove anything. Most students will not be able to form proofs. Ancient Arithmetic was taught by the student needing to supply a proof to their work, and they would then be able to understand why they were being taught this theory and how to apply it. A proof is 'a demonstration that if some fundamental statements are assumed to be true, then some mathematical statement is necessarily true.' It must show a statement to be always true, omitting anything which is otherwise.
Mathematics GCSE is worlds apart from this old form of Arithmetic. A student who has studied Arithmetic in a classical form (for example that of the 'Classical Liberal Arts Academy' (http://www.classicalliberalarts.com/page.cfm/page/273/QUADRIVIUM-%7C-Classical-Arithmetic-in-the-CLAA)
will be leaps ahead in their understanding of Mathematics as a whole. Is a combination of these two forms of teaching Mathematics possible? (An interesting question and one I hope to find out. Our 13yr old son is currently studying the CLAA Arithmetic, and along with this is also beginning Maths GCSE. I suspect, in time, the realisation of what he has learnt in the classical approach will make more sense, and he will find it easier to apply himself to the task in hand.) Well, this is the aspiration!
The GCSE requires the student to learn many different mathematical theories and be able to answer a range of questions based on algebra, data handling, statistics, geometry, trigonometry, and numeracy.
As Maths GCSE requires no coursework one can sit this exam easily as a home educator, choosing either the higher or foundation levels.
I won't mention the modular Mathematics as this is to be phased out in 2012, but it is a few, shorter style exams which the student takes through out the two years. They are deemed to be helpful if the student struggles with an aspect of the course as they are only concentrating on one section at a time but research has shown too much time is being wasted on swotting for the examinations and then re-sits (if needed) than any in depth, continued teaching. A good article on the discontinuation of modular exams is here;
The IGCSE is more rigourous and demanding as it includes calculus which doesn't appear until A level usually, and prepares the student more thoroughly should they want to go on and do Further Mathematics and then A level. It would definitely be more advisable if a student is very competent and efficient on Mathematics to opt for the IGCSE instead.
However, the higher tier GCSE Maths still includes some laborious questions and an A or even a B in this subject will allow the student to sit it for A level. (Some schools/colleges do prefer an A or A* in this subject as the leap is particularly noticeable between GCSE and AS level).
Most of the boards offer GCSE and IGCSE Maths; Edexcel is probably the most extensively used, in schools and out, AQA is the other one.
If one has a child who just needs a pass (C grade) at Mathematics (nearly every job at an elementary level will require a Maths GCSE pass) they could opt for the foundation level GCSE where the highest mark they can obtain will be a C but the standard will be easier.
I came across this informative article on Maths qualifications;
Many home educators use a variety of helpful sites for Mathematics. Some are listed on the right hand side in the 'resources' link, but one very popular and much used site is 'Conquer Maths'; http://www.conquermaths.com/
They even have a home school discount.
'Mathswatch' is also highly regarded;
http://www.mathswatch.co.uk/ and one can buy a disc or down load the lessons.
It is believed Mathematics today has become simpler. I still view the higher tier GCSE and certainly the IGCSE Maths as important qualifications in the UK to achieve and they will be of great benefit for our students when applying for (any) University, college or a job of any description.
Has Mathematics become easier? I'd love to hear your opinions and thoughts on this subject.