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Facilitate Meaningful Mathematical Discourse
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 facilitates discourse
among students to build shared understanding of mathematical ideas by analyzing and comparing student
approaches and arguments.
Final Say Protocol
A reading strategy where team members read a selection, highlight important information, and select 3 points/quotes that stood out as most important. In small teams, the first person leads by reading their quote aloud. Others take turns responding individually to the quote shared. First person finally explains why they chose the quote, what it meant to them, and any new connections or new thinking that stemmed from the responses of the other team members. Sharing moves to the other group members in the same manner.
Mode of Instruction: Teacher-led Purpose: Modeling
Objective: To establish mathematics goals to focus learning, teams are tasked with modeling an activity for other teams. Teacher monitors the goals of the lesson to ensure that there is an appropriate learning progression.
Teacher facilitates one team modeling an activity for the whole class. Students watch the team collaborate on a task while the teacher highlights positive behaviors and team norms. Questions may be asked about the goals for the lesson.
All of those activities undertaken by teachers and/or by their students, which provide information to be used as feedback to modify the teaching and learning activities in which they are engaged (Black and Wiliam 1998). Formative assessment can be viewed as having two parts: checking for understanding and an action taken based on that check. Both parts can be accomplished by both teachers and students. However, the teacher usually orchestrates effective formative assessment.
Mode of Instruction: Teamwork Purpose: Elicit responses to a prompt before discussion
Objective: To facilitate meaningful mathematical discourse, students share understanding of a topic to analyze and compare other student approaches to the same topic. Teacher monitors through effective circulation.
Teams receive five or six sentence starters (fortunes) related to topics/concepts/norms in an envelope. Team Member (1) draws a sentence starter from the envelope, reads it aloud, and shares a brief—30 second—explanation. Team Member (2) receives the same sentence starter, makes one comment about Team Member (1)'s explanation, and rotates to continue the process for each member.
Team member (2) draws a sentence starter from the envelope, reads it aloud, and shares. Team member (3) receives the same sentence starter, makes one comment about Team Member (2)'s explanation. Continue this rotation for each of the sentence starters in the envelope.
Teacher circulates to make instructional decisions about team discussions. For closure, each sentence starter (fortune) is included on a separate poster—not previously mentioned to the students. Teams rotate through each poster location to add one comment/explanation about the sentence starter.
Four “A’s” Protocol
A reading strategy where the group reads the text silently, highlighting and writing notes in the margin on post-it notes in answer to these four questions: What assumptions does the author of the text hold? What do you agree with in the text? What do you want to argue with in the text? What parts of the text do you want to aspire to? Discussion then occurs within the group to talk about the text in light of each of the “A’s”, taking them one at a time. What do people want to argue with, agree with, and aspire to in the text?
Four Corners Jigsaw
Purpose: Build understanding of a large quantity of information
A study team and teaching strategy where teams work collaboratively to understand a large quantity of information. There are various ways to organize the jigsaw activity, but the central concept is that teams of people are assigned or select topics that they teach to others. The teams decide collectively how they are going to share what they know. One way to acquire knowledge from a large amount of material is to break it into smaller pieces. Each student becomes an expert for part of the material and then shares their knowledge with their team.
Fourth CPM Principle of Assessment
Formative assessment is a learning experience for both the student and the teacher.
Some lessons include additional support for students immediately following the task statement. This section of the lesson has step-by-step instructions for students to follow. Several large investigations in this course will have this structure. This design allows the teacher either to have teams attack the problem using their own strategies and available tools or to have students follow a more directed approach using Further Guidance. The beginning and end of each Further Guidance section is clearly marked.