Elementary school teachers' noticing of essential mathematical reasoning forms: justification and generalization

摘要

Justifying and generalizing are essential forms of mathematical reasoning, yet, teachers struggle both to produce and identify justifications and generalizations. In comparing elementary school teachers' self-reported levels of noticing justifying and generalizing in their own classrooms and the levels researchers observed in two consecutive lessons in those classrooms, we found significant discrepancies. In applying a framework we developed to characterize the teachers' noticing in terms of mathematical content and reasoning form, we found that teachers rarely attended to justifying and generalizing in a manner consistent with the mathematics education community's view and that their lenses for noticing these activities may account for discrepancies between the teachers' reports and the researchers' observations. We conclude by reflecting on the complexity of asking teachers to attend to justifying and generalizing and how these results may affect teacher professional development.