My daughter is 15 years old and enjoys her maths classes (perhaps only because her maths homework takes her the least amount of time). Until now I have managed to introduce her to subject matter before she comes across it at school. Recently she was asking me to tell her about some new things..
Some obvious things spring to mind such as complex numbers, series, matrices, calculus etc. But I know just enough about maths to not be entirely comfortable with the UK GCSE syllabus. For example, if I were to ask her what she thought an axiom was, she would be clueless.
I want to start teaching her some 'ground-level' stuff. Things like:
The meaning of axioms, statements, theorems & proofs; (classical origins & alternatives ?!)
The formal definition of a function; limits
Sets of numbers (eg: just what is Natural number ?).
Operations: associativity; commutativity etc.
(Or even some historical background; eg: she knows of Newton & Fermat but has not even heardof the likes of Gauss or Fourier; knows how to use a blur-tool though)
But I am not a maths teacher; just a parent with a vague frustrated feeling that the above mentioned concepts are important & better off understood sooner rather than later by someone interested in learning about mathematics. Am I kidding myself?
If anyone has any additions to the above and better still suggestions of where and how to start, then I would be delighted! I realise (hope even) that this may be highly subjective.
I was thinking of sitting down with her for just an hour or two of a weekend. I don't mind spending a bit longer than that sorting out a plan before-hand.