Using Teachers' and Students' Sense-Making in Coaching: Supporting Development of Real-World Mathematical Connections

• In Event: 21.051 - Mathematics Coaching for Sense-Making: Shifting the Lens to Teachers in the Coaching Relationship

Abstract

Purpose
Researchers and policymakers increasingly press for mathematics teachers to connect curricula to the real world (Gainsburg, 2008); similarly, movements to teach math for social justice call for mathematics teaching that is connected to real-world social injustices (e.g., Gutstein, 2003). However, authentically situating mathematics in real-world contexts can be a complex, demanding endeavor, sometimes requiring significant conceptual change for teachers (Leonard et al., 2010). To date, research has given insufficient attention to how teachers can be supported in developing meaningful real-world mathematical connections.
Theoretical Framework
To study how mathematics teachers can be supported to develop meaningful links between mathematics and real-world applications, we take a sociocultural perspective on teachers’ learning. In this view learners and mediators in the environment –– such as cultural artifacts, power (Esmonde, 2017), discourses, and agency (Norris & Jones, 2005) –– are co-constitutive. Thus, we emphasize teachers’ sensemaking-in-context.
Methods
Our primary research question was: How can teachers be supported in developing meaningful real-world mathematics connections? As part of a 4-year study, we use ethnographic methods to study two experienced, urban mathematics teachers working with instructional coaches around these aims. Data include: fieldnotes, artifacts, video- and audio-recordings from classroom observations and subsequent coaching sessions. Using grounded theory, we took episodes of pedagogical reasoning (Author, 2005) as the unit of analysis. Coaches are members of the research team, so their decision-making was available.
Findings
Coaches used rich representations of classroom practice to support teachers’ sensemaking around developing real-world mathematical connections. In particular, coaches’ talk around audio recordings of student sensemaking provided important supports for teachers’ sensemaking.
The coach used audio from Bridgette’s classroom to support reflection on how she might facilitate more nuanced student discourse about both math and social issues. Specifically, Bridgette illustrated the concept of functions through examples of sentencing in the criminal “justice” system. Bridgette told the coach that she found debriefing about socio-political issues to be more challenging than wrapping up mathematical concepts, and initially seemed satisfied if, as a result of the lesson, students simply felt more comfortable conversing about social injustices. To press Bridgette’s thinking, the coach used audio from class to highlight students’ simplistic understandings (e.g., assault victims always press charges), helping Bridgette reflect on her practice and consider ways she might challenge students’ (un)critical thinking about socio-political issues.
For Julie, the audio recordings of student conversations offered an opportunity to complicate the real-world examples she employed. In AP Statistics, Julie asked students to generate real-world examples of response bias,but was troubled by their seemingly limited responses. Through the recordings, Julie’s coach highlighted student sensemaking that led Julie to speculate that her choice of representations may have constrained examples available to students and limited conceptual understanding. By using student thinking as a core representation, the coaching conversation opened opportunities to support Julie’s deeper inquiry into her own practice.
Significance
This analysis reveals some of the tensions teachers face in creating real-world mathematical connections and suggests that coaches’ use of student sensemaking can support teachers’ opportunities to learn.

Authors

• Samantha Marshall, Vanderbilt University

• Patricia Buenrostro, Vanderbilt University

• Ilana S. Horn, Vanderbilt University