TRU
TRU Conversations about teaching
The purpose of this Conversation Guide is not to tell anyone how to teach, but to facilitate coherent and ongoing discussions in which teachers, administrators, coaches, and others learn together. We hope that the questions in the Conversation Guide will support educators with different experiences, different expertise, and different strengths to work together to develop a common vision, common priorities, and common language, in order to collaboratively improve instruction and better support students to develop robust understandings.
The Conversation Guide can be used to support many different kinds of conversations, including (but not limited to):
- Conversations to develop common vision and priorities across groups of teachers (within the same school and/or across different schools)
- Conversations between teachers and administrators and instructional coaches around classroom observations (see also the TRU Observation Guide, available at http://map.mathshell.org/trumath.php)
- Conversations between teachers around peer observations
- Conversations around video recordings of mathematics teaching and learning
- Conversations about planning a particular unit or lesson
- Conversations about a particular instructional strategy or set of strategies
- Ongoing individual reflection
We have found that the Conversation Guide can be useful for facilitating a one-time conversation. But its real power lies in its support for creating coherence across conversations. The Guide can help individuals as well as groups of educators to set an agenda and work on it consistently over time. For example, a teacher team (such as a math department) might decide to spend a semester focusing on issues of Equitable Access to Content (Dimension 3). Meeting time might then be spent reflecting on the kinds of access that are currently available to students and planning lessons with the goal of monitoring and expanding access in mind, using the Equitable Access to Content questions and prompts in this Guide. Members of the team might observe each other’s classrooms with a focus on these same questions and prompts. The principal might find ways to support teachers to attend workshops related to the theme of Equitable Access to Content, rather than supporting a series of disconnected trainings.
- In the remainder of this document we provide an overview of each dimension; discussion questions for each dimension, for your use in reflecting on and planning instruction; and a set of suggestions for how to use the discussion questions.
- We hope you will find the Conversation Guide useful. Happy teaching and learning!
Conversation Guides (By Dimension)
When planning observations, it is useful to think of what the classroom experience looks and feels like from the perspective of a student – students, after all, are the ones experiencing the instruction! The questions below provide an orientation that helps in seeing the lesson from the student perspective.
The Mathematics
Core Questions: How do mathematical ideas from this unit/course develop in this lesson/lesson sequence? How can we create more meaningful connections?
Students often experience mathematics as a set of isolated facts, procedures and concepts, to be rehearsed, memorized, and applied. Our goal is to instead give students opportunities to experience mathematics as a coherent and meaningful discipline. This means identifying the important mathematical ideas behind the facts and procedures, highlighting connections between skills and concepts, and relating concepts to each other – not just in a single lesson, but across lessons and units. It also means engaging students with centrally important mathematics in an active way, so that they can make sense of concepts and ideas for themselves and develop robust networks of understanding.
TRU_conversation_guide_math_2016_math.pdfCognitive Demand
Core Questions: What opportunities do students have to make their own sense of mathematical ideas? To work through authentic challenges? How can we create more opportunities?
We want students to engage authentically with important mathematical ideas, not simply receive knowledge. This requires students to engage in productive struggle. They need to be supported in these struggles so that they aren’t lost, but at the same time, support should maintain students’ opportunities to grapple with important ideas and difficult problems. Finding a balance is difficult, but our goal is to help students understand the challenges they confront, while leaving them room to make their own sense of those challenges.
TRU_conversation_guide_math_2016_cognitive.pdfEquitable Access to Content
Core Questions: Who does and does not participate in the mathematical work of the class, and how? How can we create more opportunities for each student to participate meaningfully?
All students should have access to opportunities to develop their own understandings of rich mathematics, and to build productive mathematical identities. For any number of reasons, it can be extremely difficult to provide this access to everyone, but that doesn’t make it any less important! We want to challenge ourselves to recognize who has access and when. There may be mathematically rich discussions or other mathematically productive activities in the classroom - but who gets to participate in them? Who might benefit from different ways of organizing classroom activity?
TRU_conversation_guide_math_2016_access.pdfAgency, Ownership, & Identity
Core Questions: What opportunities do students have to see themselves and each other as powerful mathematical thinkers? How can we create more of these opportunities?
Many students have negative beliefs about themselves and mathematics, for example, that they are “bad at math,” or that math is just a bunch of facts and formulas that they’re supposed to memorize. Our goal is to support all students – especially those who have not been successful in the past – to develop a sense of mathematical agency and authority. We want students to come to see themselves as mathematically capable and competent – not by giving them easy successes, but by engaging them as sense-makers, problem solvers, and creators of mathematical ideas.
TRU_conversation_guide_math_2016_agency.pdfFormative Assessment
Core Questions: What do we know about each student’s current mathematical thinking? How can we build on it?
We want instruction to be responsive to students’ actual thinking, not just our hopes or assumptions about what they do and don’t understand. It isn’t always easy to know what students are thinking, much less to use this information to shape classroom activities – but we can craft tasks and ask purposeful questions that give us insights to guide our instruction, not just fix mistakes but to integrate students’ understandings, partial though they may be, and build on them.
TRU_conversation_guide_math_2016_formativeassessment.pdf