TRU

TRU Observation Guide

Prior to an observation, it is useful for the teacher and observer to discuss the lesson plan and decide on the main points of focus for the observation. The observation might be general; it is possible for a practiced observer to take notes on all dimensions. Alternatively, the teacher and observer might agree to focus on one or two areas the teacher wants to address in detail. Either way, reflecting beforehand on goals for the lesson and for the observation is a good way to make the most of the observation. A useful tool for planning and debriefing is the Teaching for Robust Understanding Conversation Guide (Baldinger, Louie, and the Algebra Teaching Study and Mathematics Assessment Project, 2016). The Conversation Guide lays out a series of questions for each dimension that teacher and observer can use in planning the lesson, and in reflecting on it as well.

The Structure of an Observation Sheet

The top and bottom parts of each observation sheet provide concise descriptions of the relevant dimension and goals for it. Beneath the description of the dimension are some examples of “look fors”- actions on the part of students and teacher that are often indicators that things are going well. They are things to aim for in general, and over time – they are NOT a list of things to be checked off in any particular lesson. We imagine teacher and observer discussing these prior to a lesson and deciding which, if any, might be things to focus on in the upcoming observation. The list is not meant to be comprehensive; teacher and observer may decide on another focus and write it in the space provided. The center of the observation sheet provides space for writing down observations.

A Guide for Each TRU Dimension

Dimension: The Mathematics

Each Student...

Engages with grade level mathematics in ways that highlight important concepts, procedures, problem solving strategies, and applications
Has opportunities to develop productive mathematical habits of mind
Has opportunities for mathematical reasoning, orally and in writing, using appropriate mathematical language
Explains their reasoning processes as well as their answers.

Teachers...

Highlight important ideas and provide opportunities for students to engage with them
Use materials or assignments that center on key ideas, connections, and applications
Explicitly connect the lesson’s big ideas to what has come before and will be done in the future
Support the purposeful use of academic language and of representations (e.g., graphs, tables, symbols) central to mathematics
Support students in seeing mathematics as being coherent, connected, and comprehensible

What are the big ideas in this lesson? How do they connect to what has come before, and/or establish a base for future work? How do the ways students engage with the material support the development of conceptual understanding and the development of mathematical habits of mind?

Goal: All students work on core mathematical issues in ways that enable them to develop conceptual understandings, develop reasoning and problem solving skills, and use mathematical concepts, tools, methods and representations in relevant contexts.

TRU Observation Guide-MATH.pdf

Dimension: Cognitive Demand

Each Student...

Engages individually and collaboratively with challenging ideas
Actively seeks to explore the limits of their current understandings
Is comfortable sharing partial or incorrect work as part of a larger conversation
Reasons and tests ideas in ways that connect to and build on what they know
Explains what they have done so far before asking for help
Continues to wrestle with an idea after the teacher leaves

Teachers...

Position students as sense makers who can make sense of key conceptual ideas.
Use or adapt materials and activities to offer challenges that students can use, individually or collectively, to deepen understandings
Build and maintain classroom norms that support every student’s engagement with those materials and activities
Monitor student challenge, adjusting tasks, activities, and discussions so that all students are engaged in productive struggle
Supports students without removing the challenge from the work they are engaged in

What opportunities do students have to make sense of mathematical content and practices? How are they supported in sense making so that they are not lost – yet real challenge has been maintained, so that they have opportunities to grapple with important ideas?

Goal: All students have opportunities to make their own sense of important mathematical ideas, developing deeper understandings, connections, and applications by building on what they know.

TRU Observation Guide-CD.pdf

Dimension: Equitable Access to Mathematics

Each Student...

Contributes to collective sense making in any of a number of different ways (e.g., proposing ideas, asking questions, creating diagrams...)
Actively listens to other students and builds on their ideas
Supports other students’ developing understandings
Explains, interprets, applies and reflects on important mathematical ideas
Participates meaningfully in the mathematical work of the class

Teachers...

Create safe environments
Use tasks and activities that provide multiple entry points and support multiple approaches to the mathematics
Provide opportunities for students to see themselves, and their personal and community interests, reflected in the curriculum
Validate different ways of making contributions
Build and maintain norms that support every student’s participation in group work and whole class activities
Support particular needs, such as those of language learners, for full participation
Expect and support meaningful mathematical engagement from all students, helping them contribute and build on contributions from others

In what ways does each student engage in the work of the class? How can more opportunities for every student to participate in meaningful ways be created?

Goal: All students are supported in access to central mathematical content, and participate actively in the work of the class. Diverse strengths and needs are built on through the use of various strategies, resources, and technologies that enable all students to participate meaningfully.

TRU Observation Guide-Access.pdf

Dimension: Agency, Ownership and Identity

Each Student...

Takes ownership of the learning process in planning, monitoring, and reflecting on individual and/or collective work
Asks questions and makes suggestions that support analyzing, evaluating, applying and synthesizing mathematical ideas
Builds on the contributions of others and help others see or make connections
Holds classmates and themselves accountable for justifying their positions, through the use of evidence and/or elaborating on their reasoning

Teachers...

Provide time for students to develop and express mathematical ideas and reasoning
Work to make sure all students have opportunities to have their voices heard
Encourage student-to-student discussions and promote productive exchanges
Assign tasks and pose questions that call for mathematical justification, and for students to explain their reasoning
Employ a range of techniques that attribute ideas to students, to build student ownership and identity

What opportunities do all students have to see themselves and others as proficient mathematical thinkers, to grapple with challenges and construct new understandings, to build on others’ ideas, and demonstrate their understandings? How can more of these opportunities be created?

Goal: All students build productive mathematical identities through taking advantage of opportunities to engage meaningfully with the discipline and share and refine their developing ideas.

TRU Observation Guide_AOI.pdf

Dimension: Formative Assessment

Each Student...

Explains their thinking, even if somewhat preliminary
Sees errors as opportunities for new learning
Consistently reflects on their work and the work of peers
Sees fellow students as resources for their own learning
Provides specific and accurate feedback to fellow students
Makes use of feedback in revising their work

Teachers...

Create safe climates in which students feel free to express their ideas and understandings
Use materials that elicit multiple strategies, and have students explain their reasoning, in order to gain information about student’ emerging understandings
Flexibly adjust content and process, providing students opportunities for re-engagement and revision
Provide timely and specific feedback to students, as part of classroom routines that prompt students to make active use of feedback to further their learning
Create opportunities for students’ individual and collaborative reflection on their knowledge and learning

What opportunities exist for all students to demonstrate their understandings? What opportunities exist to build on the thinking that is revealed? How do teachers and/or other students take up these opportunities? Where can more be created?

Goal: Every student’s learning is continually enhanced by the ongoing strategic and flexible use of techniques and activities that allow students to reveal their emerging understandings, and that provide opportunities both to rethink misunderstandings to build on productive ideas.

TRU Observation Guide-FA.pdf

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