1. APEC-Tsukuba International Conference At Tokyo and Kanazawa, Dec., 8-15, 2007 APEC HRD Project. 02-2008 Collaborative Studies on Innovations for Teaching and Learning Mathematics in Different Cultures (III) -Lesson Study focusing on Mathematical Communication-

2. Background and Aims Priority area of the third APEC Education Ministerial Meeting “Stimulating Learning in Mathematics and Science”. Supporting Challenges of Each Economies through Lesson Study

3. APEC Structure of the Project for Welfare in APEC Meeting at Thailand Japan Each Economy Specialists Group of Teachers Textbook Videos Knowledge Bank Child Centered: from Product Approach To Process Approach

4. Developing Communicators for APEC welfare! APEC HRD Edu-net KNOWLEDGE Bank Developing Knowledge Network Ecnomoy Economy Ecnomoy Economy Ecnomoy Economy Ecnomoy Economoy Ecnomoy Economy Ecnomoy Economoy Economy Collaborative Studies on Innovations for Teaching and Learning Mathematics in Different Cultures (III) Lesson Study focusing on Mathematical Communication- Developing Human Network

5. Procedure of the Project 2008 2 3 Each economy started to share the ideas on movement of Lesson Study January, 2008 4 Each economy shared the results of Lesson Study August, 2008 Thailand as a host Japan as a host 1 Each economy challenged to develop Teaching Approaches for Mathematical Communication via. Lesson Study by involving school teachers Each Economy Encourage to use developed TA for MC and videos for LS Movement by Teachers in each economy Each Economy

6. We want to enhance the Educational Improvement in each economy 13 economies 16 economies

7. How many are there the unit squares? Counting:One, Two, Three,…. ↓ Adding:8+9+10 ↓ Multiplying: 3 x 9 Mathematical Thinking enabling us looking at the world differently. By D. Tall

8. If there is not Lesson Study? If we introduce Lesson Study? A U.S. teacher said, “Before Lesson Study, we had talked about multiple intelligences, constructivism and so on, but never talked about the contents of teaching. In the Lesson Study project, we began to talk about the subject matter, why we teach it, how we teach it and what students learn from the lesson” by Catherine Lewis

9. Pedagogical Content Knowledge

10. How can we develop students’ centered leaning? Lesson Study For Developing Classroom Communication Pedagogical Knowledge Content Knowledge Developing Pedagogical Content Knowledge Research LessonPlanReflection

11. Why do we focus on mathematical communication? Dec. 9. First day: Representation and Communication Keynote Lectures Tadao Nakahara, Kozo Tsubota, Koeno Gravemeijer Research Lesson: Kozo Tsubota, 6th grade, Considering How to Use Ratio. Panel Discussion about Lesson Working Group and Lectures, Report Back from WG Dec. 10. Second day: Communication, Argumentation and Reflection Keynote Lectures Hiroshi Nemoto, Hiroshi Tanaka, Guershon Harel Research Lesson: Hiroshi Tanaka, 5 grade. Panel Discussion about Lesson Working Group and Lectures, Report Back from WG Closing Remarks Shizumi Shimizu

12. Why do we focus on mathematical communication? On your national curriculum document (including the general document of whole curriculum), how does it enhance communication or mathematical communication for students? –What are your components of mathematical communication to develop? When you consider the classroom communication, what kinds of components you want to integrate on the words of communication for developing mathematical thinking? –What kinds of approach will you prefer to develop the communication in classroom? What is your model teaching approach (or your teaching strategy) to enhance classroom communication in mathematics?

13. How can we develop? Representation and Communication Panel Discussion about Lesson Chair: Yasuhiro Hosomizu (Univ. of Tsukuba) Panelist: Marcela Santillan Nieto (Mexco), Tran Vui (Vietnam) Cheng Chun Chor Litwin (Hong Kong) Kozo Tsubota, Yoshikazu Yamamoto(Univ. of Tsukuba) Working Group and Lectures APEC specialists; WG on what are Representation and Communication in this lesson for considering how to develop the lesson. Japanese participants; Lectures Report Back from WG Reporter: Wang Shangzhi (China), Mangoo Park (Korea), Monica Miyagui (Peru)

14. Reflection and Argumentation Panel Discussion about Lesson Chair: Max Stephens (Australia) Panelist: Arturo Mena (Chile), Satoshi Natsusaka, Takao Seiyama, Hiroshi Tanaka (Univ. of Tsukuba) Working Group and Lectures APEC specialists; WG on what are Reflection and Argumentation in this lesson for considering how to develop the lesson. Japanese participants; Lectures Report Back from WG Reporter: Su Chun Lin (Chinese Taipei), Madihah Khalid (Brunei Darussalam), Francisco Cerda Bonomo (Chile)

15. How can we develop? Argumentation and Reflection Panel Discussion about Lesson Chair: Max Stephens (Australia) Panelist: Arturo Mena (Chile) Satoshi Natsusaka, Takao Seiyama, Hiroshi Tanaka (Univ. of Tsukuba) Working Group and Lectures APEC specialists; WG on what are Reflection and Argumentation in this lesson for considering how to develop the lesson. Japanese participants; Lectures Report Back from WG Reporter:Su Chun Lin (Chinese Taipei), Madihah Khalid (Brunei Darussalam),Monica Miyagui (Peru)

16. Kanazawa Day 1: Representation On your national curriculum document (including the general document of whole curriculum), how does it enhance communication or mathematical communication for students? 20 min. What is your model teaching approach (or your teaching strategy) to enhance classroom communication in mathematics? 90 min. Lesson Study Status 15 min. Report Back Session 15 min.

17. Working Group 1 Kanazawa day 1. GROUP 1 DISCUSSION REPORT National Curriculum. How does it enhance communication for students In some national curriculums stated that the mathematics communication is an important process that need to be developed beside the contents (BRU, THA, SIN). Some types of representations mentioned in their curriculums such as: Concrete, Real world, Symbolic, ICT, Diagram. The evaluation, exam also change to support the communication in the classroom: Presentation, Portfolio. The nature of classrooms requires communication. This is a professional skill of teachers of all subjects not only mathematics (speak, explain, prove...). But they do not use the term "communication" in the curriculum. Communication is considered as a professional skill of classroom teachers. Sometime students can solve the problems but feel difficult to explain, they use symbols, writing the solution. To enhance the communication effectively, the curriculum of some economies have innovations in assessments such as rubric assessment, clarification, representation, journal writing, visualization and model drawing (BRU, THA, SIN). Some curriculums still emphasize in content knowledge but not pedagogy (CHI, VIE). The communication needs to be improved. Nothing talked about communication in some curriculum, there is a general description but not in detailed (HOL, VIE, TAI), the communication happens in contextual problem, open ended questions, productions of students.

18. Working Group 1 (cont.) Kanazawa day 1. Teaching approach to enhance classroom communication in mathematics It is difficult to define what is the appropriate teaching approaches (problem solving, investigation, inquiring, discovering) in our countries to enhance communication. We can define some characteristics or principles of a teaching approach supporting communication. Characteristics: What students should know not what teachers know; Students: real interest, appreciate the students' thinking; Teachers really want to know: how students thinking; Sometime we underestimate student ability and overestimate the teacher's explaining; Students explain their own ideas; How can the teacher get students involve in discussion and explanation. The kinds of tasks: Challenging, solutions at different levels, students engage in the lesson. Create a trust to students and parents. Communication in mathematical classes is quite normal. The communication decreases from primary level to high school level because of a lot of content knowledge need to be covered.

19. Working Group 1 (cont.) Kanazawa day 1. The ability of discussion, communication need to be encouraged. Reflection: Verify their own understandings. Some students know how to do thing but do not know how to reflect it. Teachers should create situations for students' reflection. That view relates to the causality. Students know how to show the causality for the thing happens. Status of Lesson study project in countries BRU: Would like to implement lesson study. The lesson study project supported by the MoE this year, until now 2 schools involved with lesson study but not many teachers. This year the project will focus on coomunication and make sure that the representation, reflection, argumentation happen. TAI: We will ask the government to approve the project. Until now there are three researchers involved with the project. Lesson study will be implemented at primary schools. CHI: Just have known lesson study from 2005. But the MoE gives a strong support to implement it in the classrooms quickly and has a cooperation with JICA. VIE: The lesson study has been implemented in three schools in Hue City. We has a research proposal in two years for lesson study in another 5 provinces. There will be about 30 classroom teachers involving this project. SIN: Implemented whole school approach with all subjects using the lesson study cycle. Teachers are trained by consultants on lesson study. Positive feedbacks, powerful tool for staff development. Will involve more teachers to go through the cycle: plan - do - see. THA: Four schools involved with lesson study project, whole school approach two years ago. Very positive impact from schools.

20. Mathematical Communication Working Group 3 Kanazawa day 1

21. Communication & National Curriculum

22. In Hong Kong, communication often refers to students working in groups and interaction among students. In Malaysia, the rhetoric is present but how it is used to learn mathematics is not clear. Modes of communication are suggested. In Taiwan, one of the five strands is Connection of which communication is a component. Common opinion is that targets like communication is not clear and concrete enough for teaching and assessment. It is similar in Thailand and Brunei.

23. Communication & National Curriculum In Singapore, students are expected to communicate their solution methods because of the format of the national examination. In Chile, it is similar but to a smaller extent In Honduras, JICA projects introduced Japanese textbooks which focus on communication. In Peru,.. In Mexico, mcq practice

24. Approaches Given the context – culture, examination system, teacher beliefs and mathematical knowledge, large class size – we suggest some approaches to help participating economies implement communication, representation, reflection, and argumentation in the teaching and learning of mathematics

25. Approaches Authentic Teacher Education Materials

26. Approaches Access to rich mathematical tasks Opportunities to develop the abilities in the development of such tasks.

27. Approaches The use of video and technology to show the implementation of such tasks.

28. Approaches The use of lesson study to show an even more authentic implementation of such tasks. Lesson study also has the potential for teacher development in mathematical knowledge, pedagogical knowledge and pedagogical-content knowledge.

29. Example Communication within the context of mathematical thinking and learning. Example: Grade 3 Area (Taiwan), the role of textbooks.

30. Example Communication required in national examination e.g. about 50% of the national test at Grade 6 in Singapore requires extended explanation of solution method, and about 20% of the national tests at Grades 4 and 8 require also require explanation of solution method.

31. PSLE 2006 At 09 00, a lorry started from Town X and traveled towards Town Y. at a speed of 55 km/h for the whole journey. At 11 00, a car started from Town Y and traveled towards Town X. The speed of the car remained the same until it passes the lorry at 13 00. At this point, the lorry had traveled 5/9 of the journey. After passing the lorry, the car decreased its speed by 8 km/h and traveled at the new speed for the remaining journey. At what time did the car reach Town X?

32. Kanazawa Day 2: Argumentation and Reflection What is your model teaching approach (or your teaching strategy) to enhance classroom communication in mathematics? 80 min. Report Back Session 15 min. Report Back from Specialist Session About Kanazawa