I hope this blog will be of use to anyone who cares about Maths – whether as a teacher (primary, secondary or home-schooler), as a student or as a parent.
I’m now in my 17th year of teaching Maths in a high performing comprehensive in the NE of England. I am regularly frustrated by A-Level students who don’t have the first idea about how to present a properly argued solution. I am convinced that the bad habits seen in Year 12 and 13 students are embedded in primary school and in the early years of secondary school.
My main mathematical inspiration is the Maths teacher I was privileged to be taught by in the late eighties – Mr Trotter of Dumfries High School. He drilled us in proper layout and much of what I plan to demonstrate on this blog goes back to him. So if he’s reading this – thank you so much…I hope it does you justice.
The following basic question & solution from the start of AS-Level Maths is here to illustrate why it is so important to set the proper foundations in arithmetic at a young age. It is not necessary for you to understand the solution itself – the aim of this first example is to convince you that the layout on the page gives the solution greater clarity.
If a student has been setting their working out unhelpfully since they were in primary school then the habits will be very hard to break. For example, the three lines highlighted above are quite simple, and possible for much younger students to understand. The three sections shown below how they might develop over the years:
The development on the right is much easier to follow, and is what I advocate in the first image. Yet most young children are taught to show their work on one line as in the example in the top-left of the image.
Why is this done? To save trees? Buy exercise books from sustainably-kept forestry!
Why does this matter? After all, not everyone goes on to study Maths at A-Level or further. We cannot judge who will or will not go on to develop an interest to this level. If we limit students when they are young, they will still be limited when they are older. Help the student develop habits which are suitable for further study later in life, should they wish to do that at that time. Don’t put them in a position where they cannot break your bad habits!
Future posts will attempt to develop these ideas and give principles by which students can succeed in algebraic techniques.