A TRU Story: Integration of Mathematical and Social Practices in One Teacher's Learning Trajectory

• In Event: 42.057 - Teacher Noticing for Equity: A TRU Perspective

Abstract

This paper uses the TRU framework to understand one teacher’s learning trajectory toward exemplary math instruction under constrained circumstances. The learning trajectory also demonstrates that all dimensions of TRU, not only Dimension 3, are necessary to support teaching for equity.

Ms. A is a 6th grade math and science teacher at Adams middle school, an urban, neighborhood, public school serving low-income Latinx and Black students. In 2013-14, teachers at Adams partnered with researchers to support students’ mathematical sensemaking. Researchers facilitated collaborative planning of Formative Assessment Lessons (FALs) (http://map.mathshell.org/lessons.php).

Ms. A was intimately aware of structural inequities and a national discourse that positions her students as low-achieving and in need of remedial work with a procedural focus (see, e.g. Ladson-Billings 2010). This context lent urgency to her efforts to foster student engagement in rigorous, conceptually-oriented mathematics. Over three years, two strengths of Ms. A’s class became increasingly integrated with powerful mathematics: a strong classroom culture of revision and creating a safe space for students to talk about their work.

Data sources include observations of Ms. A’s classroom and collaborative planning sessions from 2013-14 and 2015-16 (no data collection occurred in 2014-15). Our analysis focuses on student presentations because they are ubiquitous in Ms. A’s teaching and they offer insight into the discourse norms of the class Using a coding scheme derived from TRU, we analyzed 85 student presentations from 21 observed lessons.

Correctness was not a prerequisite for presenting. Instead, presenting students were held accountable to respond to peer feedback, revising their work if necessary. This supported broad participation in student presentations (Dimension 3) throughout the study: 84% of students presented during 2014-15 observations. Ms. A selected and taught FALs in ways that increasingly supported a focus on the central mathematical concepts, so that student revision became increasingly tied to conceptual understanding (Dimension 1). The unusual length and difficulty of the FALs increased cognitive demand (Dimension 2) while maintaining broad participation.

Student thinking was elicited by Ms. A throughout the study, but ways student ideas were built on became increasingly rich as the study progressed (Dimensions 4 and 5). FALs supported increased take-up of student ideas by the teacher (44% of FAL vs. 29% of non-FAL presentations), another student (51% FAL vs. 32% non-FAL), or through a related follow up presentation (36% FAL vs 12% non-FAL). Students were more likely to revise small group work based on presentations (26% of FAL vs 6% non-FAL).

All five dimensions of TRU contribute to understanding changes in Ms. A’s practice that support her equity goals. Ms. A began the study with strong relational equity in her classroom (Dimension 3), meaning that opportunities to participate centrally in the classroom were broadly available. But the nature of the mathematics the students were participating in, and therefore their opportunities develop enduring understandings of grade-level content, improved during the research collaboration. These improvements occurred at the intersection of the mathematical and social aspects of classroom practice, and corresponded to Dimensions 1, 2, 4 and 5 of TRU.

Authors

• Alyssa Manogue Dray Sayavedra, Merritt College

• Kimberly Seashore, San Francisco State University