“I stewed over that number set for like an hour last night”: Purposeful selection of numbers for fraction story problems

Abstract

This study explored the complexity of teachers’ considerations during number selection, which is a core element of problem planning. We examined teachers’ purposeful number selection for Equal Sharing problems, a type of fraction story problem. Participants included 47 elementary-school teachers engaged in a multiyear professional development focused on enhancing responsiveness to children’s fraction thinking. Our research extends Land’s (2017) work on teachers’ number selection, by focusing on a single content domain (fractions) and by using children’s mathematical thinking as a unifying analytical lens. Findings include descriptive patterns in teachers’ specific number selections and the introduction and illustration of a framework for teachers’ purposeful number selection for fraction story problems. The framework details three categories of considerations: (a) accessibility with respect to children’s existing understandings, (b) the range of strategies children are likely to use to solve the problem, and (c) the mathematics that could be leveraged by discussing children’s strategies.