Opportunities for proving the rule for fraction multiplication – episodes from a task-based interview
Résumé
The data presented here is part of a study in which we conducted six task-based interviews with students in grade 8. We explore opportunities for a grade 8 student to develop a proof of the rule for multiplying two proper fractions in a task-based interview involving paper folding while being provided with ample guidance. Our analysis focused on to what extent the arguments produced by the student can be classified as proofs, and in what way guidance by the interviewer can lead to the development of a proof. Based on our findings we suggest that it is important to focus on verbal explanations and to discuss generic examples in the development of a proof. We also propose that insight gained from this task-based interview can inform future interventions, including whole-class interventions with proof-based teaching.
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