One week ago I gave a presentation at the maths conference in Sheffield. 400 maths teachers signed up for the event and over 90 of these were in my presentation. There were of course other presentations on at the same time.

The focus for my presentation was Instrumental Understanding and Relational Understanding by Richard Skemp. In order to cover what I wanted I only discussed his article from 1976 and my aim was to provoke thinking amongst my audience. This was a time for reflection on how we teach with reference to an article from 41 years ago.

Instrumental Understanding can be thought of as ‘Rules without reasons’. An example of this is when a quick fix is given so that the pupil is able to get the correct answers. The problem with this is that they don’t always know why it works and they can’t apply the rule to different situations. I gave examples involving multiplying two digits by two digits, the addition of fractions and solving equations.

When I was at school I remember that I was taught a whole bunch of rules but I didn’t know why they worked and I couldn’t apply them if the questions were slightly different. Yes, I was the product of Instumental teaching and I admitted that I have used this in my teaching. I have used it to get results when time is short, especially when an exam is imminent.

I gave a meaning to ‘Relational Understanding’ as ‘Knowing what to do and why’. My examples of multiplication, adding fractions and solving equations were taken right back to basics and I offered ‘concrete ways of teaching these. I used Dienes Blocks, Cuisenaire Rods and Algebra Tiles to illustrate relational understanding. In an ideal world this is great but do the pressures of having to get through the curriculum stop us doing this?

The objective of the presentation was to get the teachers to think about what they are doing and the learning that is taking place in their classrooms. I had quite a few conversations with teachers afterwards and I believe that the objective was achieved.