CPM Glossary

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I Have...Who Has...

Mode of Instruction: Teacher-led            Purpose: Elicit final reflective comment

Objective: To facilitate mathematical discourse, students share understanding of a concept/topic and critique the sharing of others. Teacher makes instructional decisions about the concept/topic based on sharing.

To review, build vocabulary, connect mathematical representations, or connect mathematical threads, Teacher leads I Have...Who Has... Student receives a card with one problem and one answer. Student (1)—starter card—states, "Who has...[problem]." Student (2)—with the solution—says, "I have...[answer]." This continues throughout the set of cards.

This strategy may be modified for independent practice, partners, or teams. Consider time restrictions and multiple rounds.

  • Student receives a card with one problem and one answer to a different problem.

  • Student (1) asks, "Who has..." and states the problem.

  • Student (2)—with the solution—says, "I have..." and states the answer.

  • Process continues until all problems have answers.

I Spy

Mode of Instruction: Independent/Teamwork           Purpose: Share ideas

Objective: To support productive struggle in learning mathematics, students visit other teams to generate ideas about a concept/topic. Teacher makes instructional decisions after posing purposeful questions.

A team becomes stuck while problem solving. The Resource Manager becomes a spy for the team and silently circulates to listen for ideas from other teams. The Resource Manager refrains from any team interactions while spying on other teams. The Resource manager reports back to the team to share information about the problem.

  • Team becomes stuck at one point while problem solving.

  • The Resource Manager circulates around the classroom, silently listening to, or spying on the teams' work.

  • The Resource Manager reports back to the team to share information about the problem.

I Used to Think..., Now I Think... Protocol

reading strategy where group members read text and then reflect using “I used to think...” and “Now I think…”  Responses are shared with partners, groups and/or the whole class.

Implement Tasks that Promote Reasoning and Problem Solving

One of the eight Mathematics Teaching Practices from Principles to Actions that needs to be a consistent component of every mathematics lesson.  Effective teaching of mathematics engages students in solving and discussing tasks that promote mathematical reasoning and problem solving and allow multiple entry points and varied solution strategies.

Implementation Support Visits

Also known as ISVs, these classroom visits are conducted by a trained and experienced CPM specialist using CPM's Implementation Progress Tool in order to provide individual support, non-evaluative feedback, and an opportunity for teacher reflection. Each new teacher is eligible to receive up to two visits per year during the first two years of implementation.

Instructional Strategies Outcome 1

Apply knowledge of NCTM’s Mathematics Teaching Practices and connect them to instructional strategies

Instructional Strategies Outcome 2

Implement instructional strategies that support the Standards for Mathematical Practice

Instructional Strategies Outcome 3

Understand how multiple modes of instruction ensure access for all students

Instructional Strategies Outcome 4

Establish and reinforce routines and roles that clearly define expectations for multiple modes of instruction

Instructional Strategies Outcome 5

Understand how intentional circulation and purposeful questioning provide feedback to students and teachers

Instructional Strategies Outcome 6

Experience and reflect on instructional strategies through model lessons and a typical day

Instructional Strategies Outcome 7

Know that lesson closure provides opportunities for students to make connections among key mathematical ideas and provides opportunities to reflect on the math goal

Instructional Strategies Outcome 8

Understand the importance of using a variety of instructional strategies and activities to engage students in chapter closure

Intentional Planning Outcome 1

Create, implement and reflect on purposefully planned CPM lessons

Intentional Planning Outcome 10

Integrate Desmos and other eTools into purposefully planned lessons that engage students with content

Intentional Planning Outcome 2

Create, implement, reflect on and revise an Implementation Action Plan that will guide classroom procedures and expectations

Intentional Planning Outcome 3

Incorporate suggested Universal Access strategies to support all students

Intentional Planning Outcome 4

Plan for intentional use of instructional strategies that support formative assessment

Intentional Planning Outcome 5

Use the course preparation resources to inform individual school decisions

Intentional Planning Outcome 6

Plan each chapter using the opening teacher notes

Intentional Planning Outcome 7

Plan for intentional use of instructional strategies that support status and equity

Intentional Planning Outcome 8

Incorporate multiple modes of instruction to support all learners

Intentional Planning Outcome 9

Utilize the Implementation Progress Tool to reflect on student learning and instructional strategies


The most common type of teacher to student discourse is IRE.  The teacher Initiates a question, the student Responds, and the teacher Evaluates the response. This type of discourse is the most widely used discourse technique but valuable only in a limited number of situations such as T: "Can someone tell me when the test is" S: "Tuesday" T: "Correct".  However, in most cases IRE is not very effective at getting students to think or for that matter motivating them to try. There is too much risk and it gives failure a bad rap. In addition, it positions the teacher as the only one in the room that can be correct.  Talk Moves are a better choice.

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