CPM Glossary

Mode of Instruction: Partner Work           Purpose: Check for understanding

Objective: To promote productive struggle with a topic before mastery is expected, two students share mathematical ideas with each other. Teacher monitors through circulation.

Use when practicing a new skill or procedure, or to pre-assess a topic that will soon be taught. Within each team of four, students work in pairs to solve problems and then check solutions with the other pair. Each set of partners has one sheet of paper and one pencil. While one student writes, the other student explains. If the student writing disagrees with the explanation, then a discussion happens before the step is recorded on the paper. When finished the role of writer is rotated to the other student, and the process continues. After problems are complete, the partners check the explanations of the other team members. If both pairs agree, a checkmark is added to the paper. If pairs disagree, teams conduct error analysis.

• Team Member (1) writes while Team Member (2) explains the first problem.

• Team Member (1) asks clarifying questions to Team Member (2).

• The partners check with the other partners from the team—if they agree, put a ✅, if they disagree, find mistakes.

• Team Member (1) rotates the paper to Team Member (2), and roles are reversed for the next problem.

The Parent Guide with Extra Practice provides an explanation for selected topics, with worked examples, and additional practice problems with answer key. The resource is accessible via free PDF file download by topic, by chapter, or for the entire course. For most courses the Parent Guide with Extra Practice is also available for purchase in softbound format.

Mode of Instruction: Independent/Teamwork           Purpose: Collaboration

Objective: To establish mathematics goals to focus learning, students highlight strengths that will make the team stronger. The teacher monitors the equitable status of all team members.

The purpose of this activity is to provide a quick reminder at the beginning of class about the importance of having every team member contribute to the team's work, and of what is involved in good mathematics work. Examples of what the list of strengths may include are: Looking for patterns, Asking questions, Understanding vocabulary, Making a drawing or model, Acting out the problem, Helping others, Explaining my thinking and justifying answers, Noticing details, Organizing, Predicting, Writing equations from patterns, Looking at things in different ways, Reading aloud, Keeping people on task, Following directions, Learning from our mistakes, Remembering a similar problem, Encouraging your team members to persevere.

• Teacher posts a list of strengths.

• Each student selects and writes down three strengths they can contribute to their team.

• Students take turns sharing their strengths with their team.

• Students use strengths as they work on the lesson.

Thinking about and organizing the activities, sequence, manner of presentation, study team teaching strategies and materials needed to implement a lesson.  The article on Purposefully Planning a Lesson can be found here.

Mode of Instruction: Teamwork           Purpose: Articulate understanding through mathematical discourse

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

Team Member (1) acts as a coach to teach the other members about a topic or concept. Team member (1) shares self-generated strategies to build team comprehension. The team members acting in the role of player may ask clarifying questions.

• Team Member (1) assumes the role of coach.

• Team Members (2), (3), and (4) assume the role of player.

• Team Member explains a topic or concept.

• Team Members (2), (3), and (4) ask clarifying questions.

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 uses purposeful questions to assess and advance students’ reasoning and sense making about important mathematical ideas and relationships.

Articles written that present a position about a topic to an audience that the opinion presented is valid and worth listening to.

Guidance for teachers and all stakeholders regarding assessment practices and suggest teachers create their own tests, work through all assessments, only assess material students have had ample time to engage with, formatively assess as a learning experience for both students and themselves, and be flexible in grading to allow differences in reaching mastery.