Teacher Noticing of Student Algebraic Thinking

• In Event: Differing Notions of Responsive Teaching Across Mathematics and Science: Does the Discipline Matter?

Abstract

Purpose

The work on teacher noticing in mathematics primarily looks at teacher noticing of students’ mathematical thinking in general without focusing on particular mathematical domains. However, exploring teacher noticing in specific domains may be important: paying attention to specific content areas can matter in professional development (e.g., Garet, Porter, & Desimone, 2001; Kennedy, 1998), and PD programs that are specific to the content teachers teach have more positive outcomes in terms of student achievement and student conceptual understanding (e.g., Kennedy, 1998). Therefore, exploring teachers’ attention and responses to students’ thinking in a specific content domain is likely to inform PD efforts to support the teaching and learning of that domain.

Perspectives: Noticing in the Domain of Algebra

Following Schoenfeld (1988, 1998), we take the perspective that teachers’ beliefs about what counts as knowing the discipline and about what students need to know to succeed influences what they attend to respond to in the moment. In the algebra classroom, attending to productive student thinking can be difficult for reasons that may be particular to algebra. Historically, algebra instruction focuses on symbol manipulation and procedures, often at the expense of a more conceptual understanding (e.g. Chazan, 1996, 2000; Kieran, 1992). As a result, many students end up manipulating symbols by rote (Kieran, 1992). We believe teacher attention may play an important role: many teachers tend to focus on symbol manipulation above more conceptual forms of algebraic thinking (Stephens, 2008; Walkoe, 2010). If teachers believe algebraic thinking is synonymous with manipulating symbols and carrying out procedures, they may fail to attend to aspects of students’ reasoning that could serve as a foundation for helping students understand the content on a more conceptual level. In this poster, I describe study that addresses this issue head-on.

Methods of inquiry

Thirteen pre-service mathematics teachers in a large Midwestern city participated in the study. All thirteen teachers were asked to complete a pre and post task as well as six weekly tagging assignments using an online tagging tool that prompted teachers to watch a video and tag and discuss compelling moments of students’ algebraic thinking. However, seven of the thirteen were asked to participate in a video club that focused on algebra classes.

Data sources and evidence

We analyzed what moments the teachers tagged and what they wrote about those moments. Bottom-up categorization of the teachers’ tagged commentaries, followed by quantitative analysis of changes in depth of various types of categories, enabled me to explore differences in noticing of algebraic thinking among members of the video club group and non-video club group.

Results

Compared to the non-video club group, the video club group showed more change over time in what they noticed and how they discussed students’ algebraic thinking.

Scholarly significance

This study illustrates that researchers and teacher educators can gain insights into improving PD by attending to sub-disciplinary aspects of students’ thinking, such as algebra-specific types of symbol manipulations and use of representations.

Authors

• Janet Dawn Kim Walkoe, University of Maryland

• Miriam G. Sherin, Northwestern University