Impact of Teachers' Planned Questions on Opportunities for Students to Reason Mathematically in Whole-class Discussions Around Mathematical Problem-solving Tasks

Abstract

While professional developers have been encouraging teachers to plan for discourse around problem solving tasks as a way to orchestrate mathematically productive discourse (Stein, Engle, Smith, & Hughes, 2008; Stein, Smith, Henningsen, & Silver, 2009) no research has been conducted explicitly examining the relationship between the plans that teachers make for orchestrating discourse around problem solving tasks and the outcomes of implementation of those plans. This research study is intended to open the door to research on planning for discourse around problem solving tasks. This research study analyzes how 12 middle school mathematics teachers participating in the Mathematics Problem Solving Model professional development research program implemented lesson plans that they wrote in preparation for whole-class discussions around cognitively demanding problem solving tasks. The lesson plans consisted of the selection and sequencing of student solutions to be presented to the class along with identification of the mathematical ideas to be highlighted in the student solutions and questions that would help to make the mathematics salient. The data used for this study were teachers' lesson plans and the audio-recordings of the whole-class discussions implemented by the teachers. My research question for this study was: How do teachers' written plans for orchestrating mathematical discourse around problem solving tasks influence the opportunities teachers create for students to reason mathematically? To address this research question, I analyzed the data in three different ways. First, I measured fidelity to the literal lesson by comparing what was planned in the ISAs to what was actually took place in the implemented debriefs. That is, I analyzed the extent to which the teachers were implementing the basic steps in their lesson (i.e. sharing the student work they identified, addressing the ideas to highlight and the planned questions). Second, I analyzed the teachers' fidelity to the intended lesson by comparing the number of high-press questions in the lesson plans (that is, questions that create opportunities for the students to reason mathematically) to the number of high-press questions in the implemented discussion. I compared these two sets of data using a linear regression analysis and t-tests. Finally, I conducted a qualitative analysis, using grounded theory, of a subset of four teachers from the study. I examined the improvisational moves of the teachers as they addressed the questions they had planned, building a theory of how the different ways that teachers implemented their planned questions affected the opportunities for their students to