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What student responses do middle school mathematics teachers anticipate for contextualized and decontextualized problems about linear relationships?
Title
What student responses do middle school mathematics teachers anticipate for contextualized and decontextualized problems about linear relationships?
Creator
Rupe, Kathryn Mary
Date
2019
Description
The recent transition to the Common Core State Standards for Mathematics is in line with current initiatives to improve mathematics teaching...
Show moreThe recent transition to the Common Core State Standards for Mathematics is in line with current initiatives to improve mathematics teaching and learning through the emphasis of conceptual understanding and mathematical reasoning. Much research has been done on how to develop conceptual understanding for students in kindergarten through twelfth grade. Stein, Engle, Smith, & Hughes (2008) highlighted the importance of orchestrating productive classroom discussions. They suggest that this goal can be attained through the 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 practice did so 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 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 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 concepts.
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