MODULE 5 – COMMUNICATION This module focuses on the role of communication in the mathematics program. The language of mathematics is used to communicate relationships and make sense of the world. Students learn through communication with their peers and their teacher. Through discussion, teachers gain insight into the thinking of their students and are better equipped to design effective instruction. Internal dialogue is also a critical component of understanding. Materials: BLM 5.1, chart paper, markers, six Question and Prompt cards (copied from pp. 6.15–6.18 of the Guide) Looking Back (based on Module 4) Have participants share materials they normally use when planning their mathematics program. Ask participants, divided into small groups, to discuss changes they are making in their program in order to implement guided mathematics, shared mathematics, and independent mathematics. Getting Started 10 min Introduction #1 - 3 Have participants create a mind map about communication in the mathematics program. Ask them to record Communication and Mathematics in the centre of a sheet of chart paper, and to record ideas related to the topic using graphics, diagrams, pictures, and words. Ask groups to share their mind maps with the whole group. 1 Module 5 – Communication KEY MESSAGES At the heart of mathematics is the process of setting up relationships and trying to prove these relationships mathematically in order to communicate them to others. 5 min #4 - 8 The secret to successful teaching is being able to determine what students are thinking, and then use that information as the basis for instruction. Through skilfully led discussion, teachers will gain insight into student understanding and students will build understanding and consolidate learning. Students’ writing about their mathematical learning will also reveal and consolidate understanding but must be prefaced by many oral opportunities. Whether students are talking or writing about their mathematical learning, the most valuable question that a teacher can ask of them is, “How did you know?” 2 Module 5 – Communication Working on It 20 min Promoting Opportunities for Communication #9 - 12 Fostering students’ communication skills is an important part of the teacher’s role in the mathematics classroom. Teachers need to be aware of the many kinds of opportunities that exist in the classroom for helping students communicate. Ask participants to read the list of bulleted statements on p. 6.4 of the Guide. Arrange participants in groups of four to six. Have the groups create a graphic organizer on chart paper and organize into categories ideas from the list on p. 6.4. Ask participants to record an additional example of an opportunity for communication in each category. Ask groups to share their graphic organizers with the large group. Discuss similarities and differences. 3 Module 5 – Communication Oral Communication Teachers can promote students’ communication skills by providing models of good communication, such as: 20 min #13 - 22 Helping students develop skills in problem solving by demonstrating the thinking process for solving a problem and modeling this process in oral dialogue; Having student volunteers explicitly demonstrate what good communication would, and would not, sound like; Using prompts and questions that help students expand on their oral responses; Modeling prompts and questions that can be used by students as they work together; Encouraging students to use 'think time' before they communicate; Encouraging concrete representation as a basis for communicating mathematical understanding. Use a jigsaw strategy (see Module 1, p. 4) to help participants explore strategies for fostering oral communication. Arrange participants in home groups of six. Ask participants to number themselves from 1 to 6 to identify their expert group number. Assign a different strategy from pp. 6.6–6.7 to each expert group. Ask participants to record information on copies of BLM 5.1 when they work in the expert groups. Have participants return to their home groups to share their findings. Participants can complete other sections of BLM 5.1 as they listen to information shared in their home groups. 4 Module 5 – Communication Questions and Prompts for Promoting Communication The questions and prompts teachers use will vary to reflect the purpose of the communication they wish to elicit from students. At different times, teachers ask students to: 20 min #23 - 27 Retell; Predict, invent, or problem solve; Make connections; Share their representations of mathematical situations; Reflect on their work; Share their feelings, attitudes, or beliefs about mathematics. Have participants work in groups of four to solve the problem below. Ask two participants in each group of four to play the role of ‘student’ and two participants to play the role of ‘teacher’. Ask the ‘students’ to solve the problem. Next, have the ‘teachers’ use the Question and Prompt Cards (copied from pp. 6.15–6.18) to help them support their ‘students’ as they solve the problem. TWO MACHINES, ONE JOB Ron’s Recycle Shop was started when Ron bought a used paper-shredding machine. Business was good, so Ron bought a new shredding machine as well. The old machine could shred a truckload of paper in 4 hours. The new machine could shred the same truckload in only 2 hours. How long would it take to shred a truckload of paper if Ron ran both shredders at the same time? (See possible strategy on p. 7.) – Van de Walle, Elementary and Middle School Mathematics: Teaching Developmentally, Fourth Edition, 2001, Pearson Longman, p. 18 In a large group, ask participants to describe their experiences as students and as teachers during the problem-solving situation. 5 Module 5 – Communication Promoting Written Communication Talk, then write Model the writing process Use strategies that promote written communication Provide authentic writing tasks Ask participants to number themselves from 1 to 5. Organize participants in their number groups. Explain that each group is responsible for studying three strategies for promoting written communication. Ask the groups to record their ideas on chart paper. 20 min #28 - 30 Group 1 – Mind Mapping, Model Writing, Shared Student Writing (pp. 6.9–6.10) Group 2 – Think-Talk-Write, Thinking Windows, Place Mat (pp. 6.10–6.11) Group 3 – Procedural Writing, Graphic Organizers, Word Wall (pp. 6.11–6.12) Group 4 – Strategy Wall, Journals/Logs, Picture Books (pp. 6.12–6.13) Group 5 – Poster Projects, Problem Posing, Creative Writing (pp. 6.13–6.14) Ask groups to present their work to the whole group. 6 Module 5 – Communication Reflecting and Connecting 10 min In Your Classroom Encourage participants to think about #31 communication as they plan their math lessons in the next few days. Ask them to focus specifically on the prompts and questions they use to help students communicate. Ask them to be prepared to share their thoughts about communication in the mathematics program at the next session. For Next Time Ask participants to read Chapter 7 – Classroom Resources and Management. Possible Strategy for “Two Machines, One Job” (p. 5) Since the old machine shreds a truckload of paper in 4 hours, it would shred ¼ truckload in 60 minutes. Since the new machine shreds a truckload of paper in 2 hours, it would shred ½ truckload in 60 minutes. With both machines running, they would shred ¾ truckload in 60 minutes. If the two machines, running together, shred ¾ truckload in 60 minutes, they shred ¼ truckload in 20 minutes. Therefore, it would take 80 minutes to shred a truckload. 7