Developing Mathematical Discourse in the Secondary Classroom, Facilitator Handbook

Developing Mathematical Discourse in the Secondary Classroom

Professional Development Facilitator Handbook -SAMPLER- Developing Mathematical Discourse in the Secondary Classroom, Facilitator Handbook

Pearson School Achievement Services Developing Mathematical Discourse in the Secondary Classroom Facilitator Handbook

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ISBN 119582

Facilitator Agenda Developing Mathematical Discourse in the Secondary Classroom

Section Time Agenda Items

Introduction 35 minutes Slides 1–4 Introduction and Welcome Agenda Activity: Telephone Math Outcomes 1: Mathematical Communication 55 minutes Slides 5–11 Section 1 Big Questions Discourse Think Aloud Communication Standards in Mathematics Activity: Mathematical Practices in Famous Trios Definition of Mathematical Discourse Activity: I Spy Small-Group and Whole-Class Discussions Video: The Role of Mathematical Discourse in the CMP2 Classroom Phases of a Classroom Discussion Revisit the Section 1 Big Questions Break 15 minutes 2: Discourse around a Rich Problem 55 minutes Slides 12–15 Section 2 Big Questions All-Sports Ticket Survey Problem The Teacher’s Role and the Student’s Role in Classroom Discourse Revisit the Section 2 Big Questions 3: Get Students Talking 60 minutes Slides 16–21 Section 3 Big Questions Recognizing the Concerns of Teachers Overcoming Obstacles Activity: Blogging Establishing Ground Rules with Students Video: Classroom Conversation: A Way to Begin Participate in a Classroom Conversation Activity: Participate in a Classroom Conversation

Revisit the Section 3 Big Questions Lunch 30 minutes Section Time Agenda Items

4: Going Deeper: Strategies That Promote 95 minutes Slides 22–28 Productive Mathematical Discourse Section 4 Big Question Effective Questioning Choosing Effective Questions Activity: Choosing Effective Questions Classroom Strategies for Mathematical Discussions Classroom Video Observation Video: Sharing Gas Costs Reflect: Something Old, Something New Revisit the Section 4 Big Question Break 15 minutes 5: Teaching for Mathematical Proficiency 50 minutes Slides 29–33 Section 5 Big Question Standards for Mathematical Practice Card Sort (SMP Card Sort) Activity: SMP Card Sort—Part 1 Activity: SMP Card Sort—Part 2 Self-Evaluation Revisit the Section 5 Big Question Reflection and Closing 10 minutes Slides 34–40 Do Now! Outcomes Review Closing Evaluation References Total 6 hours

Preparation and Background Workshop Information Big Understandings  Discourse describes the ways in which students represent, think, talk, agree, and disagree; the way students exchange ideas and what the ideas entail; and it is shaped by the tasks in which students engage, as well as by the nature of the learning environment (NCTM 1991).  Mathematical discourse is more effective when “students try to communicate precisely to others” (NGA Center and CCSSO 2010, 7). Effective discourse happens when “students justify their conclusions, communicate them to others, and respond to the arguments of others” as a way to construct mathematical understandings (NGA Center and CCSSO 2010, 6).  Teachers encourage meaningful mathematical discourse by presenting worthwhile and engaging mathematical tasks that require students to make sense of the problem, explain its meaning, and persevere in solving it, and “identify correspondences between different approaches” (NGA Center and CCSSO 2010, 6).  Teachers can orchestrate productive mathematical discussions by anticipating student responses, monitoring students during the task, selecting and sequencing students to present their work, asking effective questions, and connecting student responses to key mathematical ideas (Smith and Stein 2011, 8).  Productive mathematical discourse takes time and practice to become an effective learning tool and involves various teaching actions. Teachers develop their orchestration skills through careful planning and introducing new strategies over the course of time (Bay- Williams and McGatha 2014, 78).

Big Questions  What is the definition of mathematical discourse?  What does effective mathematical discourse look like in the classroom?  How can teachers use rich mathematical problems to promote purposeful mathematical discourse among students?  What are the instructional implications for productive mathematical discourse associated with student proficiency?  How can teachers create a classroom environment that encourages students to communicate openly and appropriately with their peers?  How can teachers initiate productive mathematical discourse associated with student proficiency?  What strategies can teachers use to elicit deeper mathematical conversations and productive discourse among students?  How do the mathematical practices provide a teaching framework that leads to productive mathematical discourse associated with student proficiency?

Outcomes  Define rich mathematical discourse.  Identify opportunities during instruction that allow for rich mathematical discourse.  Develop strategies for promoting mathematical discourse in a variety of classroom situations.  Describe the importance of developing students’ mathematical language skills.  Demonstrate how to use effective questioning techniques to engage students in rich mathematical discourse.

Section 2: Discourse around a Rich Problem (Slides 12–15) Time: 55 minutes Big Questions  How can teachers use rich mathematical problems to promote purposeful mathematical discourse among students?  What are the instructional implications for productive mathematical discourse associated with student proficiency? Training Objectives  Experience solving a rich mathematical problem from a student’s perspective.  Engage in mathematical conversations with colleagues.  Distinguish the roles of the teacher and the students during mathematical discussions. Materials per Section  Participant Workbook  Chart paper  Markers  Companion guide for All-Sports Ticket problem (AllSportsTicket.doc)

Topic Presentation Points Presentation Preview

Section 2 Big Questions  Display Slide 12.  Explain to participants that in this section of the workshop, they will discover the answers to the question on this slide. o How can teachers use rich mathematical problems to promote purposeful mathematical discourse among students? o What are the instructional implications for productive mathematical discourse associated with student proficiency?

PW: Page 11

All-Sports Ticket Survey Problem  Display Slide 13.  Present the All-Sports Ticket Survey problem as an opportunity for rich discussion.  The companion guide with details for solving the problem and finding solutions can be found in the Additional Resources folder (AllSportsTicket.doc).  Model best practices while facilitating the task. o Introduce the problem. PW: Pages 12–13 o Have participants work on the task in small groups. o Have participants discuss the task with their small groups while you walk around and ask questions. Some example questions are below. More questions can be found in the companion guide. – Describe all the variables in this problem (price, number of parents, revenue). – Which quantities are cumulative? How do cumulative quantities help you with this problem? – What forms of functions can be used to model the data for this problem? – Which functional model will best answer the question the problem asks? o Select participants to share work so that multiple solution strategies are presented. o Sequence participants’ presentations of their solution processes from least sophisticated to most sophisticated. o Discuss multiple representations. o Discuss the need to communicate precisely to solve the problem. o Discuss linear versus quadratic relationships and compare representations of both. o Summarize the mathematics using specific terms. State explicit concepts.

The Teacher’s Role and the  Display Slide 14. Student’s Role in Classroom  Debrief the All-Sports Ticket problem by identifying and discussing Discourse the teacher’s role in presenting a mathematical task. o Reflect on examples that occurred during the problem-based task to promote productive mathematical discussion. o Instruct participants to use the graphic organizer in the Participant Workbook to write down reflections. o Ask participants: Which mathematical discussions PW: Page 14 went well? Why?  Identify and discuss the participant’s role (from a student’s perspective) in working collaboratively to solve the problem.  Ask participants to take a few moments to reflect on the experience they just had in their role as a student.  Again, have them use the graphic organizer to write down their reflections from a student’s perspective.  Use the following questions as a guide to facilitate a whole-group discussion. o Did you find it helpful to have a chance to think about the question yourself before it was discussed in your group? o How far did your group really think together, or did you tend to follow independent lines of thought? o Did you listen to, share ideas with, and consider the alternative views of everyone in the group? o Did you build on one another’s ideas to construct chains of coherent reasoning? o Did you feel able to share your ideas without fear of embarrassment of being wrong? Did anyone feel uncomfortable or threatened? If so, why? o Did your discussion stay “on task,” or were you “wandering”?  Invite participants to reflect back on Standards for Mathematical

Topic Presentation Points Presentation Preview Practice 1, 3, and 6 (SMP1, SMP3, and SMP6).

 Summarize and give purpose to the activity by asking: “What are the instructional implications for productive mathematical discourse associated with student proficiency?” o Probe participants by asking them to identify what they did specifically that aligns with SMP1, SMP3, and SMP6.

Revisit the Section 2 Big  Display Slide 15. Questions  Before moving on to Section 3, review the Section 2 Big Questions. Invite participants to share what they have learned so far. o How can teachers use rich mathematical problems to promote purposeful mathematical discourse among students? o What are the instructional implications for productive mathematical discourse associated with student proficiency?