Taking the Problem out of Problem Solving?
Jacques, Laurie, Mathematics Teaching
One of the most refreshing and useful resources to have been published by the national numeracy strategy tor primary teachers has been Mathematical challenges for able pupils in key stage 1 and 2 . The national curriculum for mathematics  requires teachers to integrate 'Using and applying mathematics' within the other programmes of study (Number, Shape, space and measures and Data handling). However, the Framework for teaching mathematics from YR to Y6 , which was published simultaneously with this revised national curriculum (and is a suggested means of implementing it), lacks guidance on how to embed problem solving into its recommended teaching strategies. Working originally as a Leading Mathematics Teacher and presently as an Advanced Skills Teacher, I find that many primary colleagues still view 'school mathematics' as a sequence of procedures and skills to be taught and the Framework document goes some way to perpetuating this by bolting on 'reasoning about mathematics' as a separate teaching unit each term. This creates a tension when attempting to develop practice so that non-specialist primary teachers can begin to view mathematics as a way of thinking rather than a way of doing. When Mathematical challenges for able pupils was published a few years after the Framework, there was at last a starting point for supporting teachers in this change. My only criticism of the book was the title 'for more able pupils' suggesting that thinking mathematically should be reserved for 'clever' pupils.
The recent drive  to return 'creativity' to the primary curriculum has meant that the mathematics team from the Primary National Strategy (PNS) have now begun to consider how this can be done in mathematics. In their wisdom they have chosen to use Mathematical challenges in a structured two-part INSET pack  which has been available to schools since last year. The pack includes details for a short staff meeting and a set of teaching resources for each year group. Teachers are invited to try out the resources and discuss outcomes and implications at a further staff meeting.
The school in which I work has a rapidly rising roll and last year three new teachers joined the team so there was scope for reviewing how pupils learn and how mathematics is taught across the school from YR to Y6. From a specialist's point of view I was very worried about the messages being conveyed about problem solving in the INSET pack. Firstly they attempt to classify problems in order to decide which strategies should be used to solve a problem:
* Finding all possibilities;
* Logic problems;
* Finding rules and describing patterns;
* Diagram problems and visual puzzles;
* Word problems.
Secondly, the guidance suggests that 'specific strategies to solve particular types of problem' (pp5-6) need to be taught. They say 'simply giving children problems is not enough' (p12). I intepreted this as meaning that pupils have to be taught strategies to solve a problem rather than develop them from engaging with problems themselves and from this I wonder how the pupil is problem solving? It seems problem solving has also been made into a sequence of skills to be learned rather than a process of mathematical thinking and taking the problem out of problem solving!
The INSET pack tocused specifically on 'finding all possibilities' problems (eg, see image, right)
These were intended to teach pupils systematic strategies for problem solving. The plans stuck to the traditional three-part lesson structure and most problems included two parts with the second extending the number of possibilities. I he plans also modelled the types of questions that teachers should ask and encouraged collaborative working. I wanted to use the INSET materials in my school to try and gauge how non-specialists might change their practice in the light of the guidance. …