Representations of Ambitious and Equitable Instruction: Issues of Grain Size and Purpose (Poster 2)

• In Event: Expanding Coaching and Representations to Support Teacher Sense-Making Toward Disrupting Inequitable Mathematics Teaching Practices

Abstract

Purpose
This paper presents, compares, and contrasts three representations of aspects of the Teaching for Robust Understanding (TRU) Framework (https://truframework.org/), whose primary purpose is to support equitable and ambitious instruction.

Theoretical Perspectives, Data, and Methods
The work is embedded in the learning sciences, drawing upon multiple and mixed methods as described below. The study indicates the importance of employing representational tools from differing perspectives and at different levels of grain size, to triangulate on findings and to increase the likelihood of practical impact.

Results and Significance
The first representation was designed to be memorable. TRU identifies five key dimensions of learning environments. The better a classroom does along those five dimensions, the more likely it is that students will emerge as knowledgeable, resourceful, and agentive disciplinary thinkers. TRU came out of a distillation of the literature, in which aspects of classroom environments found to enhance student outcomes (including equity and identity) were clustered. It was then tested against a large body of classroom data and found to be robust. See Figure 1. The history of the Framework’s development is given in Author (2013, 2014). This representation is telegraphic, and people who use it internalize the five dimensions rapidly. This is essential for use in practice. However, any such representation necessarily provides a superficial summary of exceedingly complex issues.

In contrast, our second representation consists of three very detailed case studies, which provide opportunities to delve deeply into the five key TRU dimensions of the framework. The case studies, based on PD work done by the TRU team, simulate moderated in-person discussions, and work best when teachers discuss the case studies collectively. They are based on the professional development work done by the TRU team. This volume (Author & colleagues, 2022a), which contains text materials to provide case study discussions, provides the depth lacking in the first representation.

The third representation (Author & colleagues, 2022b) is different, in that it is aimed directly at supporting teacher change. The specific tool described here, which is part of a suite of tools for teacher reflection and action, is a novel representation of classroom artifacts and activities. The goal of this tool, called Mathematics Teaching on Target, is to support teachers in examining the properties of assignments and activity structures. How do they do along the five dimensions, and how might they be modified so that they can be more supportive of ambitious and equitable instruction? The representation uses a series of targets, or “bullseyes” – the question for any activity being, where does it sit on the target now; and, can it be modified to move closer to the bullseye? Figure 2 provides one such target, which focuses on leveraging student strengths in the service of equitable access for all.

The presentation will discuss interrelations and complementarities between the representations, and describe their affordances, limitations, and synergies.

Author

• Alan H. Schoenfeld, University of California - Berkeley
  Presenting Author