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Lack of Mathematical Confidence

A student who lacks the ability to produce the desired result or perceives they lack the ability to do so, will be less likely to try when failure is certain.

Supporting Questions to Ask:

Does the student have a fixed mindset or in rare cases a significant learning disability? 

Are there a variety of opportunities and methods for students to demonstrate their mathematical understanding?

Lack of Motivation

Students may appear to be unmotivated when they have several root causes of unproductive struggle. Additionally, a student’s priorities may lead to lack of motivation in class.

Supporting Questions to Ask:

What matters to this student? 

Is there a way to relate the problem to something he or she cares about, or allow them to use their talent/interest in a way that benefits the team?

Learning Goals

Learning Goals specify the learning that is intended for a lesson.  Learning goals are usually restricted to a single lesson and may refer to understanding (i.e. a portion of the Lesson Objective), knowledge, skills, or applications.  They may also reference a process for doing math such as the Standards for Math Practice, or behaviors such as modeling quality collaboration.  These goals may use words such as know, develop, become fluent, apply, understand, use, or extend.  They are often accompanied by success criteria.  They can also be identified by their function:  concept goals, process goals, or product goals.

Learning Log

journal icon final  A writing tool used by students to reflect about understanding of mathematical concepts, consolidate ideas, develop new ways to describe mathematical ideas, and recognize gaps in understanding. It can also be used as a resource to refresh your students' memories.  Learning Logs are most powerful when they are revisited and edited with new understanding.

Learning Management System

Also referred to as the LMS, is a software application system that monitors professional development for CPM users; keeps track of progress; allows interaction with others and CPM specialists.

Listening Post

Mode of Instruction: Teamwork          Purpose: Focus attention

Objective: To establish mathematics goals to focus learning, specific roles situated actions to move through a learning progression. Teacher monitors each team role through circulation.

In teams, two team members are mathematicians and two team members are observers. Team Member (1) and Team Member (2) problem solve, sharing explanations aloud. Team Member (3) listens to Team Members (1) and (2) and asks clarifying questions, as needed. Team Member (4) records observations about explanations and attitudes of participants, but Team Member (4) remains silent throughout the activity. After the assigned time—15 minutes—Team Member (4) shares notes and observations. Team Members (1), (2), and (3) may share their perspectives, as well. Variations of this activity include multiple rounds with the roles rotated to other members.

  • Team Member (1) and Team Member (2) work on a math problem, explaining aloud.

  • Team Member (3) listens and may ask clarifying questions.

  • Team Member (4) only records what is discussed and verbalized—observes body language, team norms, or another focus area.

  • After 15 minutes, Team Member (4) shares notes and observations.

Literacy Tab

A section in the Teacher tab of the Navigation Bar in the eBook that gives teachers strategies to support students struggling with the English language, specifically reading and writing; includes Introduction, Literacy Guide, Student Strategies, Team Strategies, and Reading Strategies.

Look for and express regularity in repeated reasoning

Mathematically proficient students notice if calculations are repeated, and look both for general methods and for shortcuts. Upper elementary students might notice when dividing 25 by 11 that they are repeating the same calculations over and over again, and conclude they have a repeating decimal. By paying attention to the calculation of slope as they repeatedly check whether points are on the line through (1, 2) with slope 3, middle school students might abstract the equation (y - 2)/(x - 1) = 3. Noticing the regularity in the way terms cancel when expanding (x - 1)(x + 1), (x - 1)(x2 + x + 1), and (x - 1)(x3 + x2 + x + 1) might lead them to the general formula for the sum of a geometric series. As they work to solve a problem, mathematically proficient students maintain oversight of the process, while attending to the details. They continually evaluate the reasonableness of their intermediate results.

Look for and make use of structure

Mathematically proficient students look closely to discern a pattern or structure. Students will see 7 × 8 equals the well remembered 7 × 5 + 7 × 3, in preparation for learning about the distributive property. In the expression x2 + 9x + 14, older students can see the 14 as 2 × 7 and the 9 as 2 + 7. They recognize the significance of an existing line in a geometric figure and can use the strategy of drawing an auxiliary line for solving problems. They also can step back for an overview and shift perspective. They can see complicated things, such as some algebraic expressions, as single objects or as being composed of several objects. For example, they can see 5 - 3(x - y)2 as 5 minus a positive number times a square and use that to realize that its value cannot be more than 5 for any real numbers x and y.