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Mathematics Teaching Practices

Metacognition Icon

Although a metacognitive approach is embedded throughout CPM's curriculum, many lessons in the Pre Calculus text contain specific prompts that encourage students to stop and reflect on becoming a better learner.

Micro Lab Protocol

A reading strategy where group members read a text and then share individually for two minutes while other members listen attentively without comment or interruption. Pause for 30 seconds of silence to take in what was said. This is repeated and then a group discussion occurs referencing the comments that have been made and making connections between the responses.

Mixed, Spaced Practice

Research says students learn ideas more permanently when they are required to engage and re-engage with those ideas for months or even years. 

Mixed, Spaced Practice is evident in a classroom when

  • both individual lessons and chapters are followed, using suggested pacing. 
  • Review & Preview problems are assigned and valued as an essential part of learning.

Model with mathematics

Mathematically proficient students can apply the mathematics they know to solve problems arising in everyday life, society, and the workplace. Mathematically proficient students who can apply what they know are comfortable making assumptions and approximations to simplify a complicated situation, realizing that these may need revision later. They are able to identify important quantities in a practical situation and map their relationships using such tools as diagrams, two-way tables, graphs, flowcharts and formulas. They can analyze those relationships mathematically to draw conclusions. They routinely interpret their mathematical results in the context of the situation and reflect on whether the results make sense, possibly improving the model if it has not served its purpose.


  • Listen, observe, identify key strategies
  • Keep track of approaches
  • Ask questions of students to get them back on track or to think more deeply

Monitoring is Step 2 of the 5 Practices for Orchestrating Productive Math Discussions 

More Knowledgeable Other

Describes the role of the teacher as proactively supporting students' learning through co-participation. Stresses the importance of designing learning environments that support problematizing mathematical ideas, giving students mathematical authority, holding students accountable to others and to shared disciplinary norms, and providing students with relevant resources (Engle & Conant, 2002).

Multiple Modes of Instruction

Teachers use a variety of instructional strategies to engage students in teamwork, partner work, individual work, teacher-led discussions, presentations, and more.  Multiple modes of instruction provides differentiated learning opportunities for student engagement in a collaborative classroom.


This UDL principle connects to the Second Math Teaching Practice

Practice 2: Implement tasks that promote reasoning and problem solving. 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.


Notice & Wonder

Mode of Instruction: Independent/Teamwork           Purpose: Introduce concepts

Objective: To establish mathematics goals to focus learning, students respond to two prompts as a topic is introduced. Teacher monitors notices and wonders to make instructional decisions.

Students view a picture, math problem, peer work, favorite mistake. Students critique a team poster, observe a team for their teamwork, etc. Students are prompted with the questions—What do you notice? and What do you wonder?

  • Student (1) receives a topic, picture, piece of work, math problem, sample student work, reading, etc.

  • Complete the prompt: I notice...

  • Complete the prompt: I wonder…

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