Welcome!! Please sit in teams of 4 Five Powerful, But Manageable, Practices for Productive Classroom Discussion Welcome!! Please sit in teams of 4 Susan Hoffmier susanhoffmier@cpm.org Laura Lethe lauralethe@cpm.org

Agenda The case of David Crane Engaging in the 5 Practices Purpose and Agenda Essential Question: How do we deliver instruction so that our students develop a deeper mathematical understanding? Agenda The case of David Crane Engaging in the 5 Practices Welcome and introduce presenters. Focus on the EQ and the two large chunks of this session. Let participants know that if they’ve already read the book and feel like they have mastered the 5 practices then they are free to attend another session.

Leaves and Caterpillars Please solve the following problem: A fourth-grade class needs 5 leaves each day to feed its 2 caterpillars. How many leaves would the students need each day for 12 caterpillars?

The Case of David Crane Read pages 3 and 4 and think about strengths and areas for growth in this lesson. Assign a rating from 1 to 4 for this lesson (4 being an exemplary lesson). Share and justify your thinking with your team.

Set the why - Glasser quote proposes that the most learning occurs with discussion, experiencing, and teaching others. Think of this as the ‘red zone’ of teaching.

The Five Practices Model Essential Question: How do we deliver instruction so that our students develop a deeper mathematical understanding? We want to teach in the red zone and the 5 Practices book is the how. Great companion guide to CPM, although it is a way of teaching and does not dictate content, only process.

The Five Practices are: Anticipating student responses to challenging mathematical tasks; Monitoring students’ work and engagement with the tasks; Selecting particular students to present their mathematical work; Sequencing the student responses that will be displayed in a specific order and Connecting different students’ responses and connecting the responses to key mathematical ideas This accompanies the one-pager each participant will get that summarizes the practices.

Lesson 4.1.1 Mathematical Goal Students will develop connections between multiple representations of the pattern. First you will briefly engage in a math task.

Lesson 4.1.1 Extend the pattern: Draw Figures 0, 4, and 5. Then describe Figure 100. Give as much information as you can. What will it look like? How will the tiles be arranged? How many tiles will it have? (15 min) Allow teams to work on this problem. We want teachers to find Figure 0, talk about how they see the pattern growing, and a formula so they engage enough to follow student video conversations

Likely Student Responses 1. Anticipating Likely Student Responses Involves considering: The array of strategies that students might use to approach or solve a challenging mathematical task How to respond to what students produce Which strategies will be most useful in addressing the mathematics to be learned Supported by: Doing the problem in as many ways as possible Doing so with other teachers Drawing on relevant research when possible Documenting student responses year to year (15 min) Think-Ink-Share - After 3-4 minutes of private think/write time, teams discuss and fill in their anticipation guide. Give handout (template for anticipating)

Study Teams as they Explore 2. Monitoring Study Teams as they Explore Involves: Monitoring and adjusting, by watching and listening, while students work on the problem Recording interpretations, strategies, and points of confusion Asking probing questions to get students back “on track” or to advance their understanding (no telling!) Supported by: Anticipating student responses beforehand Using recording tools (5 min) Review this slide and connect to our own monitoring while they were working on the tile pattern today. Call out what we were looking for and the type of interactions we were having with table groups (questioning, probing, clarifying, etc..).

Monitoring - Types of Questions Chapter 6 pg 63 5 Powerful Questions: What do you think? Why do you think that? How do you know this? Can you tell me more? What questions do you still have? Principles to Actions - Types of questions as you are monitoring.

Links to Videos https://vimeo.com/186372154 https://vimeo.com/187284786 https://vimeo.com/186372153 https://vimeo.com/187284931 https://vimeo.com/187284779 First single link takes you to vimeo and all the videos are linked together but not in the order we want them. Second set of links might be in the order we want them. Check against the order listed in slide 20

Student Responses to Highlight 3. Selecting Student Responses to Highlight Involves: Choosing particular teams to present based on their reasoning Ensuring all students, over time, have the opportunity to demonstrate competence Gaining some control over the content of the discussion (no more “who wants to present next”) Supported by: Anticipating and monitoring Planning in advance which types of responses to select Perhaps considering an incorrect solution as it illustrates a typical misconception. Being ready to consider unanticipated solutions. Possible - use selected participant work if there’s time while doing slide 16 Handout student work (susan) Select

Student Work D B Participants will have 5 pieces of student work to sort and sequence. In pairs, how would you sequence the work? Would you use all of these pieces? How would you connect these? E

Selecting Lesson Objective: Develop connections between multiple representations of the pattern. With your partner, select student work that best shows the reasoning around the lesson objective. You may decide on 2 pieces, 3 pieces, ??? Which ones would be good to help with closure on the lesson objective. 8 minutes

Student Responses during the Discussion 4. Sequencing Student Responses during the Discussion Involves: Purposefully ordering presentations so as to make the mathematics accessible to all students Building a mathematically coherent story line from prior knowledge to current grade level standards. Supported by: Anticipating, monitoring, and selecting During anticipation work, considering how possible student responses are mathematically related Possibly use participant work from patterning problem Use same student work to go into sequencing Monitor and select some groups to present

Mathematical Ideas During Closure 5. Connecting Mathematical Ideas During Closure Involves: Encouraging students to make mathematical connections between different student responses through questioning Making the key mathematical ideas that are the focus of the lesson salient Considering extensions as they come from the students or the teacher. Supported by: Anticipating, monitoring, selecting, and sequencing During planning, considering how students might be prompted to recognize mathematical relationships between responses A classroom culture with explicit supports for student discourse. After talking about the bullet points on this slide, have groups discuss their sequencing and how they would use the papers they selected to connect mathematical ideas. Share out from as many groups as there is time for.

The Five Practices Model Closure Essential Question: How do we deliver instruction so that our students develop a deeper mathematical understanding? ”Planning is a premier teaching skill - one that has a significant impact on the quality of students' instructional experience in the classroom.” Stigler and Hiebert 1999

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