This is a shameless commercial post because I am really excited that schools who have bought our Illuminate Gifted and Talented Course for key stage 3 have posted on-line reviews on the National STEM centre web site. Obviously I would only be saying this if they like it, but they really like it a lot and that is really exciting.
Our aim was to produce a course in mathematics, so that school students had the opportunity to see what Maths is really all about. It is full of puzzles and games and tricky things to think about. But it takes them to the next level by unpicking fundamental ideas notably proof and isomorphism and giving students an incite. Maths gives a way of definitively saying how we know what we know. We use Pythagoras Theorem to unpick the idea of proof. From the essential structuring idea that sets up the proof to the language needed to be clear and the sequencing of the statements to construct the complete argument. It is thrilling that schools are reporting that students are able and interested to work on this. It is hard, but interesting things are, but students are game to carry on. Then we compare cyclic and Klein groups with isometries and modulo arithmetic. I cannot think there is anything more wonderful for the beginning mathematician to see that we can show that two complete areas of operation, so apparently dissimilar as arithmetic of clocks and transformational geometry have exactly the same underlying structure and hence, if we know something about one, we necessarily know the same thing about the other. That, to me is what maths is really all about. The mechanical processes that students learn for their GCSE and A Levels give no insight into this amazing world.
So, well done to those schools for being brave enough to work this way and really well done to the students who are becoming serious young mathematicians. Clearly we would be delighted for you to try it too. Just ask for some trial materials of the Illuminate course.
Also, come to ATM sessions and meet Danny Brown. Danny is the head of maths at the Greenwich Free School and he is getting his kids working on deep mathematical ideas all the time. Danny has presented regularly to ATM London Branch and has a web site of the amazing stuff he does. I persuaded Danny to get this out in book form and the first volume, on Number, is nearly ready, so look out for that.