Using goal-free problems to improve students’ capacity to work with goal-specific problems in secondary mathematics classroom

Jacob Wilson from King Alfred’s Academy investigated how goal-free problems can be a key strategy for teaching mathematics through problem solving.

The majority of problems that students face in their maths education, and their maths exams, tend to be goal-specific; problems that require students to find a particular piece of information. In contrast, goal-free problems have no designated end-goal; they encourage students to explore the given information and calculate what they can from what is known. In recent years, goal-free problems have increased in popularity, with many championing their usefulness in supporting mathematical problem-solving.

His research aimed to explore the extent to which goal-free problems can be used to develop year 10 students’ understanding of circle theorems. The study compared the attainment of an intervention group working on goal-free problems (n = 55) with a control group (n = 43) after a sequence of ten lessons. He then evaluated the impacts on students’ confidence, enjoyment and perceived challenge in answering circle theorem problems.

The findings suggested that intervention students performed significantly better on particular types of multi-step problems but not on other problem types. Although their confidence and enjoyment did not seem to be higher than the students in the control group, the students in the intervention group reported that they found circle theorem problems less challenging,

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