Before our residential tomorrow we were asked to read the following article by Richard Skemp
Relational and instrumental understanding in mathematics
Briefly he discusses how the word ‘understanding’ can have two meanings. Relational understanding is where we understand things in context, the how and why of a thing. Instrumental understanding is where we know a rule for doing something although we may not know why this rule works. This is obviously particularly apparent in maths teaching and there have been several discussions on this particular point recently.
Instrumental maths is often easier in the short term and can lead to success
The rewards are more immediately apparent (pages of ticks) and so can create a feeling of success and confidence.
Relational maths is more adaptable to new tasks and situations.
Once grasped, it is easier to remember as it makes sense as a whole. It can also be effective as a goal in itself and may lead to further exploration and growth for its own sake.
The author was heavily in favour of relational maths teaching but looked at why teachers so often use instrumental teaching. These reasons basically boiled down to curriculum and test demands on teachers and schools.
I am as guilty as anyone of teaching children how to do something because they need to be able to perform a particular type of calculation or operation and either there isn’t time to fully develop their understanding or they haven’t grasped the teaching. I hope that as time goes on, then they will develop the understanding behind the rule. That was certainly true in my own case. I remember being taught decompostion at primary because that was how subtraction was done. A few years later, the penny dropped as to why the method worked.
Curriculum demands are a very valid point. The maths curriculum that ‘must’ be covered seems to allow no time for reflection and development of understanding by pupils. The new framework has tried to address the problems of the NNS by making links between areas and using the ‘little and often’ method. However this just seems to mean having to move on before anything is properly understood as there is so much to cover in each unit.
These are exactly the same problems that came up with the first reading Teaching children to think mathematically. As teachers we have a duty to our schools to get children to the required standard as well as teaching to the best of our ability. Sometimes it seems that it is not possible to do both things at once. Teaching children to think mathematically and using methods to ensure that they have relational understanding have no time allocation in the curriculum. It is much quicker just to teach the rule and leave the understanding for another time.
It is a sort of tightrope that has to be walked. Balancing the demands of the curriculum with the requirements of the subject and the needs of the children and trying not to fall off.