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Silent Debate

Mode of Instruction: Partner           Purpose: Present logical arguments

Objective: To use and connect mathematical representations, two students write about concepts and strategies while critiquing the understanding of others. The teacher monitors through circulation.

To improve writing and communications skills, students are prompted to write clear and concise statements about topics. The process is similar to oral debates, except that it is silent. Partners are assigned a topic and one partner writes pro statements while the other responds with con statements. One paper and pencil is shared by the partners. The pro partner begins and writes a statement in favor of the prompt. The con partner reads the statement and writes a statement against it or against the original prompt. The process continues.

  • Students work in pairs.

  • Partner (1) is assigned the pro (for) position, Partner (2) takes the con (against) position.

  • Partners share a pencil and one sheet of paper. A prompt or topic is given by the teacher.

  • Partner (1) makes a pro, or supportive statement in writing.

  • Partner (2) reads the statement, and writes a comment against.

  • Process continues—three or four times.

Six Word Synthesis Protocol

A reading strategy where text is read and marked to gain an understanding of the ideas and applications. Ideas about the reading are synthesized into only six words which could be a sentence, phrase, connection, personal learning, or an Aha. Each member then shares his/her words with the group along with an explanation.  The group could then create a six word synthesis with all of the words.

Standards for Mathematical Practice

Also known as SMPs, are enumerated in the Common Core State Standards and describe varieties of expertise that math teachers should strive to develop in their students. CPM lessons are aligned to the SMPs, which can be found in the Mathematical Practices section of the Teacher Notes.


Status is the perception of students’ academic capability and social desirability.  Status will play a role in all classrooms and in all teams.  To support Collaborative Learning, teachers must continually monitor status and take action to raise a student's status using strategies such as Team Roles and STTS.

Stoplight Problems

Ip5p-8whUW-hfnbVQPYsywoibpnKieXHEowXeW6Ole8u0PD38cQwgrvQceFmL7zmUOAkynL1QJe0T0q-wxuA8FbwD4hHgvEEsHiYgCfyzAwMUF9mQGalNbL_vZrhXXkssoQMMDsy Problems identified with a Stoplight icon. The Stoplight signifies that the problem contains an error, in reasoning or procedure. Stoplight problems often contain multiple subproblems, not all of which contain an error. The question often asks the students to find the error and explain why it is wrong or to solve it correctly.

Strength in Numbers

A book on collaborative learning in secondary mathematics by Ilana Seidel Horn.

Study Team and Teaching Strategies

Sometimes referred to as STTS, these strategies help structure effective collaboration among students. They are set up with particular ways for students to interact. Some are useful for brainstorming, for creating individual think time before team discussion, or for ensuring that all students have an opportunity to be vocal in a discussion. 

Success Criteria

Success Criteria explain how students can demonstrate a Learning Goal.  Success criteria often use words such as explain, describe, model, show, write, justify, or create.  In instances where hinge questions are used, success criteria may designate a particular part of the lesson.

Students will be able to explain the rule and growth after question 4-14b.

Suggested Assessment Plan

The Suggested Assessment Plan is in the Teacher Notes of each Chapter Opening.  It provides suggestions for Team Assessments, Participation Quizzes, and Individual Assessments.  The problems listed in this plan can be shared with students via a Learning Management System in order for teachers to be transparent about the connections between Review & Preview and Summative Assessments.

Support Productive Struggle in Learning Mathematics

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 consistently provides students, individually and collectively, with opportunities and supports to engage in productive struggle as they grapple with mathematical ideas and relationships.

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