For our university session this week, we were asked to read an article by Paul Ernest ‘ The impact of beliefs on the teaching of mathematics’. This explores how a teacher’s beliefs about the way maths should be taught impacts on their teaching and therefore on children’s learning.
Ernest makes the distinction of 3 different beliefs or philosophies about maths;
1 – The instrumental view that maths is an accumulation of knowledge, a set of unrelated rules and facts
2 – Maths is a static but unified body of knowledge that just needs to be learned
3- Maths is a process of discovery and learning. It is not static but continually being created and revised.
He sees these as a hierarchy with instrumental teaching leading to passive learning as the lowest and the problem solving approach as the highest.
I would argue against teachers necessarily following any one of these philosophies. I think that in my own practice I use all three approaches at different times. When learning any new skill or concept I may well start with the instrumental approach hopefully drawing on what the children already know. I would then move onto putting this into context with other skills, making the links with existing knowledge explicit. Finally I would set problems that would give the children a chance to explore, apply and extend those skills. The different teaching approaches could be appropriate at different times and in different contexts.
Ernest identifies 3 patterns in the use of materials depending on which philosophy you follow;
1 – the strict following of a book or scheme
2- modifying the scheme with addtional problems and activities
3- the teacher or school constructing the maths curriculum.
Certainly in my own we don’t have any scheme that we follow. We use the framework simply as a framework which is adapted as necessary and is constantly evolving as lessons are evaluated and changed.
I don’t know of any primary school that does follow a scheme strictlybut neither do I know of anywhere that has created their own maths curriculum from scratch. Any school that did that would still be bound by the requirements of the National Curriculum. I think that most schools do take a middle road approach to the use of materials. We use pages of text books where the practice of a certain skill is appropriate and create problems or real life contexts where we can.
I do agree with his point about social context and it is one that I have made before in this blog. The system of assessment and the requirements of the curriculum do have an effect on teaching and this is probably especially true in years 5 and 6. It doesn’t really matter what your belief system is when you are expected to get all of your children to jump through level 4 hoops on a certain day in May.
The article was written in 1988 and I feel is perhaps less relevant now than it was then. In my experience (admittedly not wide) primary school teachers make a huge effort to make maths real for children and do not follow an instrumental approach rigidly. Problem solving is an increasingly important element of the maths curriculum at all ages.
It will be interesting to see what other people in my group feel about this tomorrow.