CPM Glossary

Mode of Instruction: Partner Work           Purpose: Share ideas

Objective: To facilitate meaningful mathematical discourse, students give and receive information about a concept to build shared understanding. Teacher monitors through circulation.

Students explain and critique ideas with members of the class. For example, students write three ideas on separate note cards for creating positive team norms. Students circulate to give one idea to a classmate, while they get one idea. Student names are recorded next to the idea. For closure, a volunteer reads an idea from a classmate, and then the named person continues to share another idea. Allow many to share.

• Students record three ideas to share about a given topic.

• Students circulate and share ideas.

• For each idea the student gives, they get one in return to record on paper - including the name of the student who gives the idea.

• After many ideas are gathered, the teacher asks a volunteer to read an idea from a classmate and their name.

• Named classmate then shares the idea of another classmate and the sharing process continues.

Mode of Instruction: Independent/Teamwork           Purpose: Self/Peer assessment

Objective: To establish goals to focus learning, students self-assess strengths and areas for growth. Teacher monitors the shared understanding to guide instructional decisions.

Students use think time to write one topic, team norm, or idea that is a strength and one topic, team norm, or idea where improvement is needed. Students use Glow and Grow to provide feedback team posters, topics, team roles, team norms, assessment, goals.

• Students share one topic, team norm, or idea that is a strength—Glow.

• Students share one topic, team norm, or idea where improvement is needed—Grow.

A reading strategy where persons in the group read the text silently, highlighting or using Post-it notes to identify those parts in the text that raise questions, confirm beliefs, cause “aha” thoughts, conflict with beliefs, cause reconsideration of prior assumptions and/or show constraints of the problem or topic.  One person reports one idea that he or she recorded while other group members listen, but do not question. The next person does the same until all group members have reported. The group discusses ideas that were reported. 

A reading strategy where persons in the group read the text silently, highlighting or using Post-it notes to identify those parts in the text that raise questions, confirm beliefs, cause “aha” thoughts, conflict with beliefs, cause reconsideration of prior assumptions and/or show constraints of the problem or topic.  Each person then chooses two different “Golden Lines” that they want to share with the group.  Taking turns, members direct others to their line, reading it and explaining the significance. Once everyone has shared, the whole group discusses together.

Mode of Instruction: Teamwork/Teacher-led           Purpose: Task Completion

Objective: To implement tasks that promote reasoning and problem solving, students move throughout the problem set to ensure multiple opportunities for learning conceptually. Teacher monitors through circulation and questioning.

To help teams navigate through a problem set, the GPS strategy is a visual road map of the tasks. Students know the final destination to achieve the goals for the lesson. One member of the team reports the progress on a one-quadrant grid displayed in the room, where the team travels along one axis and the problem numbers travel the other axis. Teachers adjust instruction throughout the lesson monitoring where each team is located. Teachers may send Ambassadors from teams that are further along in the lesson to deepen understanding, or they may utilize a Swapmeet with teams that are similarly located on the grid. If all teams land at one-point on the grid—unable to continue—the teacher may conduct a Huddle to progress teams past that point.

• A one-quadrant grid is displayed for the class—on whiteboard, reusable laminated grid, paper or electronic.

• Teams are informed of the goals of the lesson included within each problem.

• One team member checks off progress on the grid as each problem is completed.

• Teacher makes instructional decisions about STTS used to support teams and/or closure.

These beliefs guide CPM throughout course implementation which are rooted in research about collaborative learning, problem based learning, and mastery over time.

1. Students' involvement in effective study teams increases their ability to learn mathematics.
2. Students have significantly better retention of mathematics when concepts are grounded in context.
3. Students deepen their mathematical understanding when they engage with concepts over time.
4. Effective study teams are guided, supported, and summarized by a reflective, knowledgeable teacher.
5. Assessing what students understand requires more than one method and more than one opportunity.
6. When students and stakeholders embrace a growth mindset, they understand that mastery takes time, effort, and support.

This online tool links each homework problem in the eBooks to the same problem at homework.cpm.org.   Homework help works on most computers and mobile devices.  Many of the problems include interactive eTools to help students visualize and understand the problem.

A Gallery Walk is a STTS where teams display posters or presentations. Students explain and critique as individuals/teams rotate about the classroom. Rotations are completed quietly—Museum Walk—or through discussion—Gallery Walk. If the teacher decides to allow feedback, students provide positive feedback Two Stars and a Wish or Glow and Grow. 

• Teams display posters or presentations. 
• Students explain and critique displayed work. 
• Students rotate to each location. 
• Feedback is given with Two Stars and a Wish or Glow and Grow.