About Me

I started teaching in 1986 having trained initially as an engineer. My background in engineering, where I had worked in a design office and actually produced calculations which were used to build structures gave me a good appreciation of how mathematics is actually used. It influenced my thinking on how Mathematics should be written down so other people can check it and have confidence in the abilities of the person doing it.

At an early stage, on marking a set of exams, a senior teacher observed “David’s classes certainly know how to write things down.”

I like to use visual aids in my teaching. I was sent on a very expensive course about ‘The Singapore Method’, where pupils are encouraged to use physical apparatus, moving to representational diagrams and then to an abstract understanding. I realised that that is what I had been doing for years. So, for instance, on problems involving percentages, rather than rote methods I prefer to use ‘bar modelling’ where the whole of something is represented by a long rectangle and parts of it marked off with the percentages, fractions and amounts. With the correct development of ideas the calculations needed to obtain the answer can easily be seen.

Of course, I also developed, over a long period, the physical models which you see in my main photo. I find these really help students to understand the more abstract concepts.

I insist on using clear diagrams – in a triangle question it is important to be able to see which angle is meant to be the right angle, for example.

An examiners’ report actually said:
“Use of a formula

Where a method involves using a formula that has been learnt, the advice given in recent examiners’ reports is that the formula should be quoted first.”

and this is what I have always insisted upon. One of my students, Hannah, once said:

“At first I found it irritating that you were insisting that I write everything down properly, but later I realised that it gave me a framework which I could fit any question into.”
I noticed that students who did best in exams also tended to write things down neatly. It occurred to me that the two things were not unconnected: pupils who wanted their work to look neat were thinking about what they were going to put down at each stage to avoid having to make crossings out. This thinking caused them to learn the mathematics more thoroughly. Conversely, where I have had pupils who do not want to write things carefully and completely, they tend not to do so well.