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Reading protocols

Strategies useful for reading and processing longer passages in a team.

Reason abstractly and quantitatively

Mathematically proficient students make sense of quantities and their relationships in problem situations. They bring two complementary abilities to bear on problems involving quantitative relationships: the ability to decontextualize and the ability to contextualize. Quantitative reasoning entails habits of creating a coherent representation of the problem at hand; considering the units involved; attending to the meaning of quantities, not just how to compute them; and knowing and flexibly using different properties of operations and objects.

Reciprocal Teaching

Mode of Instruction: Partner Work           Purpose: Articulate understanding

Objective: To build procedural fluency from conceptual understanding, students share self-generated, flexible strategies to a partner. Teacher monitors the development of strategies over an extended period of time.

This is an activity that can be done at any time during the class period to check for understanding. At the beginning of the period, students could be asked to explain a concept or definition from the previous day or week. It would serve to remind them of what they have recently learned. Or this might be a way to introduce the topic of the day by remembering some of the parts from previous units which lead up to the new concept. If reciprocal teaching is used during the middle of class it can be used to check the comprehension of what is being learned in that day's lesson. The teacher listens to as many pairs as possible to formatively assess what they have learned and to identify questions and points of confusion.

  • Students work in pairs.

  • Partner (1) pretends that Partner (2) was absent and explains a concept.

  • Switch roles and Partner (2) pretends that Partner (1) was absent and explains a second concept.

  • Teacher circulates to listen to as many pairs as possible.


The Recorder/Reporter shares the team’s results with the class (as appropriate) and serves as a liaison with the teacher when he or she has additional information to share with the class and calls for a Huddle. In some activities, a they may make sure that each team member understands what information he or she needs to record personally. They may also take responsibility for organizing their team members’ contributions as they prepare presentations. 

Typically, a teacher could expect to hear a Recorder/Reporter asking:

“Does everyone understand what to write down?”

“How should we show our answer on this poster?”

“Can we show this in a different way?”

“What does each person want to explain in the presentation?”

Red Light - Green Light

Mode of Instruction: Teamwork/Teacher-led           Purpose: Sequencing of lesson

Objective: To establish mathematics goals to focus learning, teams check in regularly to move through the learning progress in a way that promotes successful completion of tasks. Teacher monitors and adjusts instruction throughout the check-ins.

Teacher ensures that teams verify the correct solution to each problem before proceeding to the next problem. Each team indicates their status—red indicates finished and green indicates in progress. The teacher circulates to red light teams to pose purposeful questions to check for understanding. Students continue to the next problem as instructed by the teacher.

  • Each team has a red cup and green cup, or laminated double-sided red/green card to indicate status.

  • While the team works together on a problem or problems, status is set to a green light.

  • When the team finishes a problem or gets stuck, status is set to red light.

  • Teacher goes over to a red light and poses questions to check for understanding.

  • After speaking with the teacher, teams go to the next problem or set of problems.

    Research Connections Outcome 1

    Gain knowledge of CPM’s Three Pillars of Research and how they are incorporated into the design of CPM curriculum

    Research Connections Outcome 2

    Understand and apply strategies and systems to establish CPM’s Three Pillars of Research in their classroom using the Implementation Progress Tool

    Research Connections Outcome 3

    Build an understanding of NCTM’s Mathematics Teaching Practices, connecting them to the design of CPM curriculum and to their own instructional practice

    Research Connections Outcome 4

    Incorporate knowledge of CPM’s Three Pillars of Research to intentionally build formative and summative assessments

    Research Connections Outcome 5

    Assimilate content from the CPM Newsletters, Position Papers, Principles, and the Teacher Research Corp’s (TRC) action research to reflect on and guide instructional practices

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