Computers were so called because they computed, but some 60 years after their introduction and nearly 30 years after Holmes book using computers for mathematics are notable by their absence in the classroom as mathematical tools. True some CAS and Dynamic Geometry software has found good use such as The Geometer's Sketchpad, Cabri, TinkerPlots, Fathom, TI-Nspire CAS, Autograph etc. all look good and playing with Autograph I found most enlightening.

Mathematics by programming, be it exploration or solving, seems not to have made it into the classroom in schools but has to wait until university and then with the likes of MathCad, MatLab, Maple and Mathematica. Nearly 30 years ago it was touted as the panacea for children in the Logo movement following the ideas of Seymour Papert, as found in his book Mindstorms: Children, Computers, and Powerful Ideas (1980). Sadly the Logo experiment failed remaining but still with a small following to this day.

A large stumbling block is that the maths curriculum is designed around pencil and paper methods so what is the incentive to use computers in this way as it will not gain any brownie points in in the mythical ways schools are judged. But to use computer maths at school does pose and have its problems. Some math seems impossible to do by programming while easy to do by brain (with or with out a pencil). The value of programming comes in when lengthy computation is involved or writing a programme once to solve many similar problems.

I have put some computable problems on a pdf which are not found in the code challenges. Are these easier by pencil/paper or by computer? Can they all be done by pencil/paper or by computer? In some cases to have a computer solution you have to emulate the pencil/paper method, so why use a computer. Others could possibly be done by pencil/paper but only after laborious computations. But then how do you know your programme is giving the right answer? Most of these challenges should be solvable with Scratch without too many lines of code (define large! 10, 100, 1000, 10000 etc.) so possibly done in one or two lessons. Some lend themselves to graphical or picturesque solutions, but could easily be done without. For instance No.21 done in the mind but what about a programme where the gears rotate correctly. Some give themselves to heuristic simulation, perhaps No.18. There’s another question hidden inside No.11 what is it? No.2 the extension for aN^m + bN^(m-1) + cN^(m-2)…...cN^r is only for the adventurous but if you do attempt it how does this lead on to calculus?

An obvious argument is that post school most math problems in the real world will be done with the aid of computers be it in engineering, science or social studies. A powerful argument is made by Conrad Wolfram. My own gripe is the teaching of statistics in schools has been so dumbed down to make the subject worthless and even lead to misconceptions in statistical understanding. Either schools should use computers in teaching statistics or drop the subject.

The great danger in using computers is the possibility of relying on the computer, with no understanding of the underling ideas, and readily accepting “the computer says”. My own experience is by writing code for mathematical problems increases the understanding both for myself and the few students I have used it with up to A level. For some I have used text based languages but here I have kept to Scratch. I hope I give lie to the idea that Scratch can only be used for trivial programmes and freeing the student with wrestling with syntax and the complexities of the IDE. It’s powerful sprite engine allows students to readily engage with visual appealing programs. True for some of the challenges I first modelled in a text based language as there’re easier in that medium

The task I have set myself is can a computer programming course be viable for KS3-KS4 and how would this mesh with mental and none code computable problems. Some of the ideas are here on this web site starting with easy challenges to more demanding both in coding and mathematical understanding. I have had some trouble in increasing the complexity finding the ramp up is probably too steep. Hopefully with more experience with students much refinement can be made or even find it is a fools errand.