The Mathematics Improvement Network

Teaching Mathematics for Robust Understanding

What makes a mathematically powerful classroom?

This tool introduces the TRU framework as a foundation for thinking about, planning, observing, and reflecting on classroom teaching. It is designed for use by and with the district math team, principals and teachers in professional development or initial training.

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This tool is intended to help develop an understanding of the Teaching for Robust Understanding (TRU) framework for Mathematics as a foundation for thinking about, planning, observing, and reflecting on classroom teaching.


This introduction can be used with a wide variety of groups, including: district personnel who are in a position to coach, observe, or otherwise support teacher professional development; principals who need to provide a supportive environment for staff learning; in-service teachers at the beginning of professional development; tutors and student teachers in the early stages of a teacher preparation course. It provides a compact introduction to the suite of materials on


Reflecting the standards in high-performing countries, the Common Core and related state standards embody a broader and deeper view of mathematics than has been traditional in US schools. As well as emphasizing robust understanding of mathematical content, it includes the practices of doing mathematics. This requires a deeper way of thinking about what matters in classrooms.

Teaching for Robust Understanding in Mathematics (TRU) is a research-based framework for doing this. The five dimensions of TRU are: (i) the mathematics, (ii) cognitive demand, (iii) access to mathematical content, (iv) agency, ownership and identity and (v) formative assessment. If things go well in classrooms along these five dimensions, the students who emerge will be powerful thinkers and problem solvers.

The purpose of this workshop session is to introduce participants to the framework and to some of the tools that can be used with it. By the end of the workshop we hope they will see that:

The approach taken in this workshop is aimed at having participants see TRU emerge from their own thoughts about and discussions of specific examples of teaching. It gives participants a chance to react to the three stimulus videos, so that the analysis that follows is seen as pulling together their own thoughts, not imposing something from ”the outside.”

Session Outline


There are three videos embedded in the PowerPoint file. If you are unable to play these, you can watch them online here:

A lesson on finding angles

This is an extract taken from the TIMMS 1995 video study - see:

The Border Tiles Lesson

From Boaler and Humphreys (2005) Connecting Mathematical Ideas: Middle School Video Cases to Support Teaching and Learning

Fractions, decimals, percents