Orchestrating productive whole class discussions: the role of designed student responses - Evans, Sheila; Dawson, Clare (Mathematics Education Research Group of Australasia, Inc., 2017)
The value of students publicly sharing and discussing their solutions to unstructured problems is widely recognized. This can, however, be pedagogically challenging. The solutions may be partial, unclear and unpredictable. For many teachers, particularly those new to working with such problems with their students, the improvisation needed to orchestrate productive discussions can be unmanageably high. In this paper we present a pedagogical tool to help teachers. Specifically, teachers orchestrate discussions of designed, worked-out solutions to unstructured problems. The worked-out solutions have been carefully pre-designed for teachers to use in lessons. Knowing the range of distinct solutions students are to work with supports teachers’ planning. The reduced need for improvisation means they are better placed to learn and practice new ways of probing students’ reasoning. These acquired practices may then be applied to discussions of students’ own responses to a problem. In the study we explore the question: for a teacher new to working with unstructured problems, how do discussions of worked-out solutions (called in this paper designed student responses) differ from discussions of students’ own solutions? Our findings indicate that discussions of authentic student solutions tend to focus on procedural descriptions, whereas the discussions of designed solutions stimulated student explanation and evaluation. The work reported here represents the initial part of an on-going study.