Welcome to Module 5

1. Welcome to Module 5 Communication

2. Getting Started Create a mind map. Record Communication and Mathematics in the centre of the map. Use graphics, diagrams, words, pictures, etc., to show your ideas on this topic. Communication and Mathematics

3. Getting Started Share... your mind map.

4. Key Messages At the heart of mathematics is the process of identifying relationships and trying to present these relationships mathematically in order to communicate them to others.

5. Key Messages The secret to successful teaching is being able to determine what students are thinking, and then use that information as the basis for instruction.

6. Key Messages Through skillfully led discussion, teachers will gain insight into student understanding and students will build understanding and consolidate learning.

7. Key Messages Students’ writing will also reveal and consolidate understanding but must be prefaced by many oral opportunities.

8. Key Messages How do you know? Whether students are talking or writing about their mathematical learning, the most valuable question that a teacher can ask of them is “How do you know?” There are 6.

9. Working on It Promoting Opportunities for Communication

10. Promoting Opportunities for Communication 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 to communicate.

11. Promoting Opportunities for Communication Read the list of opportunities for communication on p. 6.4. In groups of four to six, create a graphic organizer on chart paper and organize into categories the ideas from the list. - What kind of graphic organizer will you use? - What categories will you use? In each of your categories, add another example of an opportunity for communication.

12. Promoting Opportunities for Communication Share with the large group. Discuss similarities and differences.

13. Working on It Oral Communication Teachers can promote students’ communication skills by providing models of good communication.

14. Oral Communication Help students to develop skills in problem solving by demonstrating the thinking process for solving a problem and modeling this process in oral dialogue.

15. Oral Communication Have student volunteers explicitly demonstrate what good communication would, and would not, sound like.

16. Oral Communication Can you think of another way to show that? Use prompts and questions that help students expand on their oral responses.

17. Oral Communication Here’s my strategy for getting more points… Model prompts and questions that students can use as they work together.

18. Oral Communication If I go there, then she will be able to jump me. Hmmm… Encourage students to use ‘think time’ before they communicate. I’m going to move to H,8

19. Oral Communication Encourage concrete representation as a basis for communicating mathematical understanding.

20. Oral Communication Form six expert groups. In your expert group: Read about a strategy for fostering oral communication (pp. 6.6 - 6.7). Record your ideas on BLM 5.1: - What is the strategy? Give an example of what it might sound like. - When could the strategy be used appropriately?

21. Oral Communication Return to your home group.

22. Share your thoughts. and record them on BLM 5.1

23. Questions and Prompts for Promoting Communication The questions and prompts that teachers use will vary to reflect the purpose of the communication they wish to elicit from students. At different times teachers ask students to:

24. Questions and Prompts for Promoting Communication • Retell; • Make connections; • Reflect on their work;

25. Questions and Prompts for Promoting Communication • Predict, invent, or problem solve; • Share their representations of mathematical situations; • Share their feelings, attitudes, or beliefs about mathematics.

26. A Problem to Solve… Form groups of four consisting of two ‘students’ and two ‘teachers’. The ‘students’ solve the problem. The ‘teachers’ use the Question and Prompt cards to help support their ‘students’ as they solve the problem.

27. A Problem to Solve… Two Machines, One Job Ron’s Recycle Shop opened when Ron bought a used paper-shredding machine. Business was good, so he added a new shredding machine. 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? - Van de Walle, Elementary and Middle School Mathematics: Teaching Developmentally, Fourth Edition, 2001, Pearson Longman, p. 18

28. Promoting Written Communication Talk, then write Provide authentic writing tasks Model the writing process Use strategies that promote written communication

29. Promoting Written Communication Number yourselves from 1 to 5, and reorganize into your number groups. Each group is responsible for explaining three strategies for promoting written communication to the large group. Record your group’s ideas on chart paper for sharing.

30. Promoting Written Communication • Mind Mapping, Model Writing, Shared Student Writing, • Think-Talk-Write, Thinking Windows, Place Mat, • Procedural Writing, Graphic Organizers, Math Word Wall • Math Strategy Wall, Class Journals/Logs, Math Picture Books • Poster Projects, Problem Posing, Creative Writing

31. Reflecting and Connecting In your classroom… Think about communication as you plan your math lessons. What prompts and questions will you use to help students communicate? Be prepared to share your discoveries at the next session.