MIDDLE SCHOOL MATHEMATICS TEACHERS’ ANTICIPATION OF STUDENT RESPONSES TO CONTEXTUALIZED AND DECONTEXTUALIZED PROBLEMS
Katie Rupe, University of Chicago
Current initiatives to improve mathematics teaching and learning emphasize developing students’ conceptual understanding and mathematical reasoning. With respect to mathematical classroom discourse, Stein, Engle, Smith, & Hughes (2008) have highlighted several practices that allow teachers to orchestrate productive mathematical discussions. They suggest that teachers can facilitate meaningful mathematical discussions by employing a process of five steps, each depending on the previous step. Teachers must anticipate student responses to a task that will be taught, monitor student thinking as they are engaged in the task, purposefully select students to present based on their choice of representations, sequence those representations in a purposeful way, and then make connections among the representations so that students are able to understand key concepts. The first step in this process, anticipating student responses (ASR), is an area where little research has been done. The literature suggests that teachers that engaged in professional learning related to the ASR did were able to anticipate possible student strategies at varying levels (Empson et al., 2017), and could develop those skills over time with explicit feedback (Popovic, Morrissey, & Kartal, 2018). However, research on average middle school mathematics teachers, those that were not enrolled in any professional learning focused on ASR, was absent from the literature.
This study aimed to understand middle school mathematics teachers’ anticipation of student responses. A sample of 19 eighth grade math teachers that represented a variety of years of experience and curriculum use (traditional, reform, and teacher-developed) participated in semi-structured interviews and completed four common eighth grade math problems focused on the content of linear relationships and systems. Teachers’ anticipated student strategies were categorized as showing robust, moderate, limited, or lacking evidence of ASR. Based on the results, all of the teachers fit into one of four categories: those that anticipated student responses at (1) consistently high levels, (2) mixed levels, (3) consistently low levels, and (4) inconsistent levels.
The results of this study found teachers who anticipated student responses at consistently high levels were experienced (over 10 years of experience), had numerous student-centered professional development experiences, considered their teacher-role as that of a facilitator, and had talked about having high expectations for students. They differed with respect to the type of curriculum they used, the certification they held, and the level of detail in their planning practices. Several of the teachers inconsistently anticipated student responses, providing robust and limited evidence for at least one problem. This speaks to the specialized knowledge that teachers have, what Hill and Charalambous (2012a) refer to as local mathematical knowledge for teaching. Among all of the variables considered, curriculum use did not appear to have an impact on teachers’ skills and knowledge related to anticipating student responses, although teachers used their curriculum materials in very different ways. Years of experience, secondary licensure, a student-centered philosophy of teaching, and teachers that described their role as that of a facilitator related to level of evidence of anticipating student responses. Understanding the variables that may impact teachers’ abilities to anticipate student responses, the first of five steps outlined by Stein et al. (2008), is important for supporting teachers as they orchestrate productive classroom discussions around important mathematical concepts.