This is part two of my discussion of problem solving in GCSE maths.
Part of the issue with problem solving is confidence. The key part of the process in answering a GCSE question is the decision a student makes to select the correct strategy based on the given information. For weaker students, this can cause a complete cognitive meltdown and inspire one of the most troublesome interchanges in the mathematics classroom:
“Sir, I don’t get it!”
“But you haven’t even read the question yet…”.
Any attempt to teach students to cope with problems has to begin with baby steps. The challenge is to develop a culture of experiment and freedom of thought, rather than the fixed mind-sets that are brought about by answering endless sets of skill-based exercises. It is useful to explore the idea of problem solving cycles and plaster the principles over classroom walls. ‘Attempt-evaluate-refine’ is a mantra students need to internalise and to also appreciate that ‘evaluate’ is not always as simple as checking if a solution is right or wrong. All mathematics students are capable of adopting this approach; they already do it in many other subjects and the challenge is just to incorporate it into maths teaching as well. Teachers should avoid falling into the trap (which I must confess I spent many years in) of considering mathematics teaching as somehow different and special compared to other teaching (as a subject it definitely is different and special, but we could all learn a lot from how other departments deliver their content).
The type of question too is important; most GCSE questions will have an open middle, but a closed end point. Problems that students experience in the classroom should require them to select a strategy to work towards a clear final answer, where the challenge comes from the very first step. Once an approach has been identified, problem solving becomes much more routine as students can then increasingly apply their selected skills to a variety of question types. While in an exam they won’t always be required to evaluate their approach, it is a useful strategy in lessons to encourage students to do so to help them develop standard approaches that assist in making good decisions. For some students this may mean drawing diagrams, for others using algebra, or underlining key words in the question; the most important thing is that students have a reliable toolkit for solving problems.
What do you think? Please share your thoughts on problem solving through the comments section below or tweet us @OCR_Maths.
In my next blog I will discuss how these strategies can be translated into classroom tasks and activities.
Darren Macey - Subject Specialist - Mathematics
I joined OCR in April 2014 as a Subject Specialist within OCR’s Maths and Technical team, currently I am involved in the development of reformed A Levels in Maths and Further Maths, and commission the creation of resources and CPD events. I also look after the OCR (MEI) A Level course (3890, 3892, 7890 and 7892), as well as the OCR Maths Twitter account and podcast.
I taught maths in a variety of secondary schools in the East of England and also taught PE after coaching rugby, cricket and football. I spend most of my spare time in training for triathlons and endurance events.