Teaching for Robust Understanding (TRU)

Part of the Math Assessment Project has involved research into how the materials are used in classrooms, their effect on teaching practices, and how Professional Development can be used to support the goals of the Mathematics Assessment Project materials. A major strand of this has been a joint effort with the Algebra Teaching Study at UC Berkeley and Michigan State to develop the Teaching for Robust Understanding of Mathematics (TRU Math) suite of tools for Professional Development and research. During development of TRU Math, it became clear that the concepts could be generalized into a framework that was applicable across subjects.

The TRU Framework

TRU is a framework for characterizing powerful learning environments in crisp and actionable ways. It provides a straightforward and accessible language for discussing what happens (and should happen) in classrooms, in professional preparation and professional Development (PD). TRU is consistent with what we know to be good practice; and it focuses classroom and administrative attention on what counts in learning. What that means in particular is that high quality instruction and PD will be consistent with TRU – and that if we adopt this framework and language, parallels in instruction across disciplines will be clear.

Central to TRU are the 5 dimensions of classroom activity. Classrooms that do well on these 5 dimensions produce students who are powerful thinkers:

The Five Dimensions of Powerful Classrooms
The Content Cognitive Demand Equitable Access to Content Agency, Authority and Identity Formative Assessment
The extent to which classroom activity structures provide opportunities for students to become knowledgeable, flexible, and resourceful disciplinary thinkers. Discussions are focused and coherent, providing opportunities to learn disciplinary ideas, techniques, and perspectives, make connections, and develop productive disciplinary habits of mind. The extent to which students have opportunities to grapple with and make sense of important disciplinary ideas and their use. Students learn best when they are challenged in ways that provide room and support for growth, with task difficulty ranging from moderate to demanding. The level of challenge should be conducive to what has been called “productive struggle.” The extent to which classroom activity structures invite and support the active engagement of all of the students in the classroom with the core disciplinary content being addressed by the class. Classrooms in which a small number of students get most of the “air time” are not equitable, no matter how rich the content: all students need to be involved in meaningful ways. The extent to which students are provided opportunities to “walk the walk and talk the talk” – to contribute to conversations about disciplinary ideas, to build on others’ ideas and have others build on theirs – in ways that contribute to their development of agency (the willingness to engage), their ownership over the content, and the development of positive identities as thinkers and learners. The extent to which classroom activities elicit student thinking and subsequent interactions respond to those ideas, building on productive beginnings and addressing emerging misunderstandings. Powerful instruction “meets students where they are” and gives them opportunities to deepen their understandings.

The TRU Document Suite

The TRU materials available from this website are:

Introduction to the TRU Framework

This introduction provides an overview of the fundamentals of the TRU framework and the tools that support its use.

Download An Introduction to the TRU Framework (December 2016)

The TRU Professional Development Tools

These can be used by teacher and coach, by a professional learning community, or by teachers reflecting on their own practice, to enhance instruction along the lines that the TRU Framework indicates are important. Two key sets of documents, the TRU Conversation and Observation guides, are available in domain-general and mathematics-specific versions.

The TRU Math Conversation Guides offer five collections of reflection questions, with each collection focused on a key dimension described in Table 1. The purpose of these questions is to guide discussions between teachers and supportive others, with the goal of enhancing understanding and capacity along each dimension.

Download TRU Domain-General Conversation Guide (Beta, September 2016)

Download TRU Mathematics Conversation Guide (Beta, November 2016)

Download TRU Mathematics Conversation Guide for Algebra (Alpha, March 2014)

The Teaching for Robust Understanding Observation Guides are intended to support collegial observations of teaching, whether by coaches, mentor teachers, administrators, or professional learning communities. The Observation Guides provide a series of “look fors” for each dimension, and can be used to facilitate planning, observation, and collaborative reflections on instruction.

Download TRU Domain-General Observation Guide (Alpha, November 2016)

Download TRU Mathematics Observation Guide (Alpha, November 2016)

TRU Math Rubric

The TRU Math Rubric, a tool for researchers to measure mathematics classroom performance along six critically important dimensions (five general, one algebra-specific) of classroom activity.

Download TRU Math Rubric (alpha, July 2014)

Introductory Session

A leader guide, slides and handounts for a workshop introducing TRU, suitable for a wide audience including teachers and school leadership is available as part of the Mathematics Improvement Network project: MathNIC.org

Supporting Papers

Elaboration about the ideas behind the TRU framework can be found in the following papers:

Schoenfeld, A. H. (2013) Classroom observations in theory and practice ZDM, DOI 10.1007/s11858-012-0483-1.

Schoenfeld, A. H. (2014, November).
What makes for powerful classrooms, and how can we support teachers in creating them? Educational Researcher, 43(8), 404-412. DOI: 10.3102/0013189X1455

Schoenfeld, A.H. (2015). Thoughts on scale. ZDM, DOI 10.1007/s11858-014-0662-3.

Schoenfeld, A.H. (2017). The Role of Video in Understanding and Improving Mathematical Thinking and Teaching. To appear in the Journal of Mathematics Teacher Education.