CRICED, University of TsukubaFirst Announcement (ver5)

APEC - Tsukuba
International Conference on Innovative Teaching Mathematics
through Lesson Study (II)- Focusing on Mathematical Thinking December 2 – December 7, 2006
Tokyo & Sapporo, JAPANA conference on the APEC project:“Collaborative Studies on Innovations for Teaching and Learning Mathematics in
Different Cultures (II) - Lesson Study focusing on Mathematical Thinking -”General Introduction
At the third APEC Education Ministerial Meeting held on 29-30 April 2004 in Santiago,
the ministers defined the four priority areas for future network activities. “Stimulating
Learning in Mathematics and Science” is one of the four priority area. Based on thispriority, the APEC project “A Collaborative study on innovations for teaching andlearning mathematics in different cultures among the APEC Member Economies” wasapproved by APEC Member Economies in August 2005. The project held meeting inlast January 2006 at Tokyo in Japan and last July 2006 at Khon Kaen in Thailand. The
project was managed by the Center for Research in Mathematics Education (CRME) in
Khon Kaen University and the Center for Research on International Cooperation in
Educational Development (CRICED) in University of Tsukuba. The result will be seenon the website: http://www.criced.tsukuba.ac.jp/math/apec2006/
Based on the success, the specialists from APEC economies decided to continue theproject more four years in relation to following topics: Mathematical Thinking (year2007), Communication (year 2008), Evaluation (year 2009), and Generalization (year2010). The first three topics are selected in relation to three Lesson Study processes,
Plan (for Mathematical Thinking), Do (for Communication) and See (for Evaluation).
The result of each year will be based for the following year project. In the final year,
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Generalization will be set for the benefit of all subjects in education.
For year 2007, the APEC project “Collaborative Studies on Innovations for Teachingand Learning Mathematics in Different Cultures (II) - Lesson Study focusing onMathematical Thinking-” is accepted in May 2005 and approved at October 6, 2006.
Mathematical Thinking is necessary ability for science, technology, economical life anddevelopment.
With Lesson Study approaches, the project aims to1) Collaboratively share the ideas and ways of mathematical thinking which isnecessary for science, technology, economical life and development on the APEC
member economies, and
2) Collaboratively develop the teaching approaches on mathematical thinking throughLesson Study among the APEC member economies.
As the goal of project, we would like to publish the report (or book) with CD-roms
including the video of good teaching practices for developing mathematical thinking forteacher education in APEC economies and the world. In order to achieve the goals of
the project, activities will be implemented in four phases
Phase I, A workshop and a Lesson Study meeting (a kind of workshop for specialists)
among key mathematics educators from APEC member economies hosted by Center for
Research on International Cooperation in Educational Development (CRICED),
University of Tsukuba, Japan will be organized in order to share the idea and ways ofmathematical thinking on curriculum level and teaching level (at Tokyo & Sapporo,
December 2006).
Phase II, Each co-sponsoring APEC member economy will engage in the Lesson Study
project for developing some topics of mathematical thinking (February-July 2007).
Phase III, An International Symposium and a Lesson Study meeting (a kind ofworkshop for general teachers) will be organized in order to share teaching approaches
for developing mathematical thinking by economies. The symposium will be hosted byCenter for Research in Mathematics Education (CRME), Faculty of Education, Khon
Kaen University, Thailand (at Khon Kaen, August 2007).
Phase IV, The professional development for school mathematics teachers will be
conducted based on the obtained - best practice and learned-innovation(August-September 2007).
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Specialists from member economies
The project and the meetings are planned for all APEC economies’ welfare. The project
itself has been carried out by the specialists from member economies who participatedin the past two meetings at Tokyo in last January 2006 and Khon Kaen in last June 2006,
and at the same time it opens for new delegates who are recommended by all economies.
From the project side, the specialists of the last meetings in Appendix 2 will berecommended to participate the meeting for the continuation of the project.
In the case of economies recommending new specialists, please consider following
conditions of specialists for developing the products of the project.
Specialist;
・ is expected to be a researcher of mathematics education,
・ is working in the Ministry of Education or academic institutions including
universities and teachers’ colleges,
・ has an experience of research in classroom at elementary school level,
・ knows and feels interested in Lesson Study movements,
・ is interested in the conference,
・ will engage in Lesson Study and develop teacher education program ineach economy in the project.
・ must participate in both meetings in Japan and Thailand
・ will present his/her reports both in Japan and Thailand
For the convenience, the list of specialists participated in the past meetings in Januaryand June 2006 will be attached to this document.
Please let us know the specialists who are recommended from economies with theformat (Appendix 1) that attached last pages of this document until October 30, 2006.
For sharing the welfare to improve the quality of education through the Lesson Study, it
is very welcome the member economies will support travel grants for a number ofdelegates. Organizing committee will consider the ways to support one specialist fromeach economy by the APEC grant or the grant from Japan but the committee has to saythat there is limitation. Depending on the APEC policy, the travel cost of one specialist
from each APEC eligible member economy (Chile, China, Indonesia, Malaysia, Mexico,Papua New Guinea, Peru, Philippines, Russia, Thailand, and Vietnam) should be
supported by APEC grant. Economies who can dispatch by the self-grant will berecommended using self-grants for their participations.
The ways of support will be estimated after the specialists nominated from the eacheconomy until October 30, 2006. If the number of delegates is larger than the limitationof the grant, organizing committee will trying to find the ways based on the APEC
policy. The way of invitation will be informed participants until October 31, 2006.
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The project is approved for all APEC welfare. The specialists supported by the APEC
grant or the Japanese grant will be requested to present their report. In case more than
two specialists in an economy expected to contribute, organizing committee
recommends them integrating their report into one report.

Ways of Publications based on APEC Policy
The results of Phase I and Phase III will be published as proceedings of meetings. For
the welfare for APEC economies, all results including videos which will be presented in
the meeting are going to be opened on the website:
http://www.criced.tsukuba.ac.jp/math/apec2007/
At the same time, depending on APEC EDNET policy, these results will be opened on
the Knowledge Bank on APEC EDNET.
Based on the result of meetings, we are planning to develop a teacher education
textbook for developing mathematical thinking.

Questions for Discussion in the Meeting of Phase I in Japan
We focus on mathematical thinking as for teaching contents in elementary1 schoolclassrooms. It is necessary components for analyzing subject matter and planning thelesson with the specified aim. Here, we pose three questions which will be discussed at
the meeting in Japan. Every specialist is expected to present their report in relation tothese three questions with examples.
Question 1: How mathematical thinking is defined in your curriculum documents
and your lesson?
From the view point of Lessons Study, Mathematical Thinking should be developed
through lessons. It is defined by the curriculum and embedded in the aim of each lesson.
Thus, curriculum documents of each economy would be the clearest resources foranalyzing what mathematical thinking is in each economy.
In Japanese curriculum, mathematical thinking has been enhanced for clarifying thequality of activity from 1951 for secondary school and 1953 for elementary and middle
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It may be until 12 or 13 years old.

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school.
In Japanese curriculum documents, mathematical thinking is defined withmathematizing activity and it has three components to be taught: the ability of ‘see as’,‘ways of thinking’, and ‘appreciation of its significance’. On evaluation standards inJapan, there are four categories: Attitude, Mathematical Thinking, Representation andUnderstanding. Each category is related with each other. Mathematical Thinking isbased on mathematical attitude, done with mathematical representation and necessary
for understanding. The order of these four categories itself resembles the process of
thinking but it is not specific to mathematics because there are similar conditions
existed in other academic subjects.
The Ministry of education, Japan, recommended teachers to have decision making
conditions for teaching in the process of a lesson based on the observation conditions
developed from these four categories. In lesson planning at the first part of Lesson
Study process, teachers analyze subject matter and expect students’ responses. In thisprocess, teachers plane the ways of decision with four categories. Thus, the Ministry
recommended teachers to describe these four categories with specific mathematicalconceptions which appear in specific lesson.
OECD PISA and NCTM standard are the considerable documents for ourcommon understanding before the meeting.
In the Tokyo meeting on last January 2006, Jan de Lange described the meaning ofmathematical literacy with necessary competency for living in OECD PISA.
http://www.criced.tsukuba.ac.jp/math/apec2006/proceedings
In OECD PISA (2003), mathematical literacy and key competencies of mathematics
were defined with interesting problems: reasoning, argumentation, communication,modeling, problem-solving, reproduction and connection.
http://www.pisa.oecd.org/dataoecd/1/60/34002216.pdf
In NCTM Standard (2000), there were five content standards and five process standards
are described with illuminating examples. Process Standards are as the following:
Problem solving, Proof and reasoning, communication, connection and representation.
http://standards.nctm.org/
Both frameworks are not curriculum documents themselves which specify teachingcontents in grades and orders such as the national curriculum standards of Japan and
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meaning is not the same even if they use same words.
Question 2: What is your key window for considering mathematical thinking?
Mathematical thinking is open ideas. Thus, it is very difficult to discuss its development
without having a window to discuss.
When we focus on each lesson, we easily focus on specific knowledge and skills(Understanding), and easily forget to develop Attitude, Mathematical Thinking andRepresentation. Japanese middle-school curriculum documents enhance a dynamic
learning activity with the following three features of mathematics. First feature isreorganization through mathematization by reflective thinking. Second feature isacquisition and using mathematical concept on ideal world (existing expected
harmonized world). Third feature is learning how to learn, develop and use mathematics
in previous two types of learning. All three features are necessary perspectives forplanning a lesson and learning how to learn, develop and use mathematics is a kind ofmathematical thinking specially recommended in the classroom. Thus, learning how tolearn itself is an important key window.
A very basic process of thinking was described by John Dewey (1910) with theimportance of reflective thinking. Reflective thinking is a key window to develop
mathematics such as mathematization (e.g., Hans Freudenthal, 1973)
The methods of developing mathematics was well-known by the work of George Polya(1957) in ‘How to solve it’ It shows the strategies of mathematics and we candistinguish a variety of mathematical thinking by his perspectives. His idea is a key
window shared in the world. ‘Thinking mathematically’ by John Mason, Leone Burton
and Kaye Stacey (1982) is a good resource for teacher education. Letting people know
the way to develop mathematics itself is necessary for teaching mathematical thinking.
Mathematical thinking has been using to describe in the context of problem solving. It isa window as well as other windows. For example, from the view points ofrepresentation, the permanence of the equivalence of form is a way of expansion ofmathematical form which is trying to keep the mathematical structure. Representation is
also a key window.
Alan H. Schoenfeld is well known by his cognitive research on problem solving. He
suggested Vygotskian perspective to develop mathematical thinking as internalized
communication and the importance of belief (value) systems for thinking
mathematically. From his perspective, the ways of communication is necessary for
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developing mathematical reasoning. In this case, communication is a key window.
Belief, Value and Attitude (including the affective domain) are also studied in cognitive(Douglas B. McLeod) or cultural context (Alan Bishop). These are a driving force ofmathematical thinking . Then, these domains will be also key windows.
There are a number of researches which focus on special ways of reasoning. Induction
and Analogy is well known by George Polya. Analogy is discussed with the knowledge
development on the embodied cognition by George Lakoff and Rafael Nunez (2000)
that is a framework to develop knowledge with hands-on activity such as dragging on
the computer. Abduction is a kind of reasoning by Charles Sanders Peirce. Historically,
Analysis is a kind of reasoning against proof (integration). Generalization process is
described by Dorfler. W. Each way of reasoning will be also a key window.
There are a number of windows. Each window has specific range for describing object.
Please consider our target of the meetings is sharing the framework to develop student’s
mathematical thinking by teachers in classrooms.
Question 3: How can we develop mathematical thinking through the lesson?
In the problem solving approach for mathematics teaching such as Open-ended
approach, students meet an unknown problem which can be solved with known
mathematics. Students represent their ideas by themselves and discuss each others.
Solvable or approachable unknown problem for students is an important condition ofproblem in a lesson. Even if most of mathematics problems for mathematicians are very
difficult to solve in a year, it will be solved based on something already known.
In the process of communication, there is necessary to share the norms such as ideas
could be explained what students already learned. It is a kind of learning how to learn inmathematics because it follows the deductive ways of reasoning specialized inmathematics. The communication in mathematics sometimes resembles the debate inSociety but in mathematics everyone cannot decide the validity of ideas without sharing
presupposition in community and can not decide it by the majority. But sometimes,
authorized teachers teach everything without communication.
There are a number of didactical suppositions which must be useful for Lesson Studyfor developing mathematical thinking. Clarifying these suppositions based on authentic
mathematical activity with example is useful for teachers to develop the lesson. Without
examples, every teacher may agree the importance of these suppositions but difficult tounderstand real meaning in his/her teaching process and impossible to develop his/her
lesson for implementing based on them.
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In the case of Japan, these didactical suppositions are integrated as various teachers’
theories of mathematics education with the results of Lesson Study. Problem Solving
approach and Open Approach are models of Japanese teachers’ theories.
The format of the report of workshop
The number of pages is 4 or 5 pages, at most 10 pages. The format of your report isPME format. http://www.pme30.cz/doc/PME30Template.rtf
The report is expected to include your claims for mathematical thinking with examples.
The report must be written based on your academic back ground because it will appear
the proceedings of meeting. But the meeting itself is not the chance of your researchpresentation. Your paper is aimed to use for discussion documents for each other inworkshop against three questions. All specialists expected to read all reports before themeeting. The deadline of the submission of your report is November 24, 2006. We will
put your report on the web site which can be seen by the specialists. After the workshop
you may have a chance to rewrite for proceedings. Proceedings are open for anyone.
Please consider that the final goal of the project is developing a teacher education
textbook. Teachers do not have a chance to share your original academic ideas but havea chance to develop good lessons based on your ideas.
It is necessary to give your answers against the three questions. It is necessary toinclude some examples.
If you could include the example of lesson with video, it is welcome. The format ofwriting with video is explained in followings;
http://www.criced.tsukuba.ac.jp/math/apec2006/progress_report/General/Conclusion.pdf
http://www.criced.tsukuba.ac.jp/math/apec2006/progress_report/Specialist_Session/Isoda.pdf

You are expected to report your result of Lesson Study with your video at Thailand
session in August, 2007 at Phase III.
The format of the lecture papers in open symposium
The format of the paper is PME format with no limitation of the number of pages.
Integrated issues of the trends of research, the curriculum developments in relation tomathematical thinking or teachers’ theories for planning lessons to develop
mathematical thinking are expected.

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Structure of Meeting in Tokyo and Sapporo, December 2-7, 2006
The aims of Phase I, first meetings are to share the ideas against the three questions andto know the lessons which develop mathematical thinking. APEC-Tsukuba meetings
have three components:
First component is open symposium; in December 3 and 4
Lectures and a panel for sharing ideas of mathematical thinking to develop
lessons by teachers
Second component is workshop; in December 5-7
Workshop to develop a collaborative framework for Lesson Study to develop
mathematical thinking
Third component is Lesson Study Meeting; in December 2, 5 and 6.
Sharing examples of Lesson Study to develop mathematical thinking
Schedule of APEC - Tsukuba meetings
Following are schedule of APEC – Tsukuba meetings in Tokyo & Sapporo. Titles oflectures are tentative.
December 1 FRI - 2 SAT Morning: Arrival days of Participants
In December 1 evening and 2 morning: “Symposium to develop excellent students in
Mathematics” will be held.
December 2 SAT. Afternoon: First day of APEC Program from the noon.
APEC Lesson Study Meeting: For sharing examples to develop mathematical thinking.
Elementary School of University of Tsukuba will be held.
December 3 SUN: Second day of APEC Program
APEC-Tsukuba International Conference: Tokyo Open Symposium with lectures
Opening, keynote lectures and lectures.
December 4 MON Morning: moving to Sapporo
December 4 MON Afternoon: Third day of APEC Program
Sapporo Open symposium: One Panel and one Lecture
December 5 TUE and 6 WED: Forth and Fifth days of APEC Program
Workshop (morning) and Lesson Study (afternoon) in Elementary School
December 7 THU: Seventh day of APEC Program
Workshop and Closing,
Moving to Tokyo at night.
December 8 FRI: Departure day

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Venues of APEC - Tsukuba Conference in Tokyo and Sapporo
The meetings will be held following places:
Dec. 1 FRI: JICA INSTITUTE FOR INTERNATIONAL COOPERATION
http://www.jica.go.jp/english/contact/ific/index.html(Included accommodation in Tokyo)
Dec. 2 SAT: Attached Schools, University of Tsukuba at Tokyo
http://www.gakko.otsuka.tsukuba.ac.jp/map.jpg
Dec.3 SUN: JICA INSTITUTE FOR INTERNATIONAL COOPERATION
http://www.jica.go.jp/english/contact/ific/index.html
Dec 4-8 MON-FRI: JICA SAPPORO INTERNATIONAL CENTER
http://www.jica.go.jp/branch/hics/jimusho/hics.html#map(Included accommodation in Sapporo)

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Important Information for Participants at APEC-Tsukuba ConferenceFirst Announcement will send:
October 11, 2006
Contact URL: http://www.criced.tsukuba.ac.jp/math/apec2007
Dead line of the nomination of specialists from member economies:
October 30, 2006
Contact address: apec@criced.tsukuba.ac.jp
Invitation letter, Information of Trip and Second Announcement will be sent:
October 31, 2006
Contact address: apec@criced.tsukuba.ac.jp
Contact URL: http://www.criced.tsukuba.ac.jp/math/apec2007
Dead line of the submission of paper:
November 24, 2006
Contact address: apec@criced.tsukuba.ac.jp
All Papers for Discussion will be on the website:
November 27, 2006
Contact URL (to be announced to specialists)
Final Announcement will be on the website:
November 30, 2006
Contact URL: http://www.criced.tsukuba.ac.jp/math/apec2007
Arrival days of Participants
December 1 FRI - 2 SAT Morning

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List of Correspondence of the Conference
Conference Host:
Organized by
Supported by

University of Tsukuba
Ministry of Education, Japan
Japan International Cooperation Agency (JICA)
Hokkaido University of Education
Japan Society of Mathematical Education (JSME)Japan Society of Science Education (JSSE)

Organizing Committee
Chair: ISODA, Masami
Associate Professor of Mathematics Education,
Center for Research on International Cooperation in Educational Development
University of Tsukuba, 305-8572 Japan
isoda@criced.tsukuba.ac.jp, Tel: +81-29-853-7286, Fax: +81-29-853-7288
Tokyo session organizer:
SHIMIZU, Shizumi
Associate Professor of Mathematics Education,
Graduate School of Comprehensive Human Science
University of Tsukuba, 305-8572 Japan
Sapporo session organizer:
OKUBO Kazuyoshi
Professor of Mathematics Education
Hokkaido University of Education at Sapporo
002-8502, Japanokubo@sap.hokkyodai.ac.jp
Organizing Committee:
BABA Takuya, Associate Professor, Hiroshima University
SAITO Noboru, Professor, Naruto University of Education
HATTORI Katunori, Professor, Naruto University of Education
YOSHIDA Minoru, Professor, Shinshu University
NINOMIYA Hiroyuki, Associate Professor, Saitama University
Supporting Members:
OHARA Yutaka, Associate Professor, Naruto University of Education
CHINO, Kimiho., AOYAMA, Kazuhiro., YAHARA Hiroki
Researchers, Mathematics Education and Informatics
Center for Research on International Cooperation in Educational Development
University of Tsukuba
General Contact Address
Center for Research on International Cooperation in Educational Development
University of Tsukuba, 305-8572 Japan
apec@criced.tsukuba.ac.jp, Tel&Fax: +81-29-853-6573
APEC Project Overseers
Suladda Loipha, Khon Kaen University, Thailand
Maitree Inprasitha, Khon Kaen University, Thailand
Masami ISODA, University of Tsukuba, Japan
Shizumi Shimizu, University of Tsukuba, Japan
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Appendix A
Specialists from the Economy
Please fill and send it back through the economy (government) by e-mail.
* Specialists will be already participated specialists of the both meetings on last
January in Tokyo and last July in Thailand (see Appendix 2), or new persons
who are recommended by the economy.
**The specialist written on 1) will be supported by the APEC project grant or
the Japanese grant. From the project side, the specialists of the last meetings
will be recommended for the continuation of the project.
***There is no limitation of the number of specialists who are recommended byeach economy with self-grant.
1)
Names(First Middle Last)

Title

EconomyAffiliation(Institution)e-mailTel/Fax
2)
Names(First Middle Last)

Title

EconomyAffiliation(Institution)e-mailTel/Fax
3)
Names(First Middle Last)

Title

EconomyAffiliation(Institution)e-mailTel/Fax

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Appendix B
LIST of Specialists (Experts)
on the both meetings at Tokyo, last January and at Kohn Kaen, last June.

NAME

economyAFFILIATION

Max Stephens

Australia

University of Melbourne

m.stephens@unimelb.edu.au

Grecia Gálvez

Chile

Ministerio de Educación

grecia.galvez@mineduc.cl

E-mailMarsigit

Indonesia

The State University of Yogyakarta

marsigitina@yahoo.com

Frederick Leung

Hong Kong

University of Hong Kong

frederickleung@hku.hk

Lim Chap Sam

Malaysia

University of Science Malaysia

cslim@usm.my

Masami Isoda

Japan

University of Tsukuba

isoda@criced.tsukuba.ac.jp

Shizumi Shimizu

Japan

University of Tsukuba

ssimizu@human.tsukuba.ac.jp

Kazuyoshi Okubo

Japan

Hokkaido University of Educationokubo@sap.hokkyodai.ac.jp
SapporoSoledad A. Ulep

Philippines

Yeap Ban Har

Singapore

University of Philippines

soledad.ulep@up.edu.phNational Institute of Educationbhyeap@nie.edu.sg
Research

Suladda Loipha

ThailandKhon Kaen University

suladda@kku.ac.th

Maitree Inprasitha

ThailandKhon Kaen University

inprasitha@hotmail.com

Akihiko Takahashi

USA

DePaul University

takahash@mac.com

VietnamHue University

tranvui@yahoo.com

Tran Vui

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