A Teaching Experience With a Content-Specific Open-Ended Task
Abstract
We report on a teaching experience that had two objectives: to assess the mathematical potential of an open-ended task and to explore whether working with it promotes the emergence of the triangle inequality property in a geometric context. A standard task from a textbook was modified, and the productions of 116 secondary school students (aged between 13 and 15) were analyzed basing on the following criteria: semiotic representations, numerical sets used, ways of indicating the multiplicity of solutions, the case of the equilateral triangle, strategies used, and the emergence of the triangle inequality property. The results show that the emergence of this property is conditioned by the semiotic representation registers employed. Based on the students’ work, it is concluded that the task has high mathematical potential and promotes flexibility.
Keywords
Open-ended mathematical tasks, Flexibility, Representation registers, Triangle inequalityReferences
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