School mathematics curricula across the world give ‘problem-solving’ a high profile, but what exactly does ‘problem-solving’ mean? Can it be taught; and, if it can, how can this be done in an equitable way? These are the questions that I consider in my recent article in the Curriculum Journal (Foster, 2023).
‘Problem-solving’ is sometimes used to mean students answering routine questions, like those seen in any standard school mathematics textbook. Students have been trained on these specific types of question, and they merely imitate the method that their teacher has shown them. But this is not how the term is used in the mathematics education literature. Instead, a ‘problem’ normally refers to ‘a task for which the solution method is not known in advance’ (NCTM, 2000, p. 52).
When problem-solving, students have to be creative and find an approach that they haven’t been shown how to do. Learning standard techniques for important classes of problems is a valuable part of learning mathematics, but this is not the same as learning to be able to solve novel problems for yourself.
To learn to problem-solve, teachers must avoid showing the students how to solve the problem, because that kills the problem-solving and reduces the task to an exercise. However, this is sometimes taken to mean that students should simply be provided with problems and left to struggle, as any hints or suggestions given by the teacher would be deemed to undermine any problem-solving. Some students may succeed with this approach, but it is likely to be those who are already advantaged. This does not seem to be an equitable approach that reliably and efficiently supports all students in becoming powerful problem-solvers.
