Supporting students’ comparisons of different conceptions of variables by telling stories – Insights from a design research study
Résumé
Despite instructional efforts to help students understand variables as generalizers (e.g., in generalization activities), they often confound this meaning of the variable with a second meaning, the variable as an unknown (e.g., in equation-solving activities). In the present design research study, a learning environment was developed and investigated in which both meanings of the variable can be constructed and compared to each other. For such comparisons, students are engaged in constructing mathematical narratives. The design experiments with seventh and eighth graders indicate that such narratives are a suitable means to initiate in-depth comparisons, because the possibilities of a narrative allow students to reflect on the epistemic specificities of the two meanings of variables. In addition to this potential, three challenges to students’ narrative construction are empirically identified.
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