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)