Writing and maths

The maze walker does two things that the routine matching pupil does not do. The maze walker is prepared to write out the expression she is working on over and over again with minor changes in each iteration, and also the maze walker is prepared to write out English explanations of what is going on as they make a logical progression from one point in their work to the next. So often I find that pupils do not want to explain the work they've done, and their calculation is just a jumble of numbers whose meaning is far from transparent as far as I, an experienced teacher is concerned. When I see such a jumble of numbers I know that the pupil has not grasped a basic tenet of mathematics, that is, that mathematical working should show a logical argument of how to get from one position to another. So many pupils think that maths is all about manipulating numbers. It is true, number manipulation is involved in maths, but that is not what it is about. Maths is about thinking logically, about reasoning and drawing conclusions, and it is about explaining how conclusions were arrived at. It is not just about getting the right answers - it is the process of arriving at those answers that matters.