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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-
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
Structure of the Project for Welfare in APEC
Meeting
at
Thailand
Japan
Child Centered:
from
Product Approach
To
Process Approach
APEC
Each Economy
Textbook
Videos
Knowledge
Bank
Specialists
Group of Teachers
Group of Teachers
Group of Teachers
Group of Teachers
Developing Communicators for
APEC welfare!
APEC HRD Edu-net KNOWLEDGE Bank
Developing Knowledge Network
Ecnomoy
Ecnomoy
Ecnomoy
Ecnomoy
Ecnomoy
Ecnomoy
Economy
Economy
Economoy
Ecnomoy
Ecnomoy
Ecnomoy
Ecnomoy
Ecnomoy
Ecnomoy
Economy
Economy
Economoy
Economy
Economy
Economy
Collaborative Studies on Innovations for Teaching and
Learning Mathematics in Different Cultures (III)
Lesson Study focusing on Mathematical Communication-
Developing Human Network
Procedure of the Project 2008
Each economy
started to share
the ideas on
movement of
Lesson Study
January, 2008
Japan as a host
1
Each economy
challenged to develop
Teaching Approaches 2
Each
for Mathematical
Communication via. Economy
Lesson Study by
involving school
teachers
Encourage to
use developed
TA for MC and
videos for LS
Movement by 4
Teachers in
Each
each economyEconomy
Each economy
shared the
results of
Lesson Study
August, 2008
3
Thailand as
a host
13 economies
We want to enhance the Educational Improvement in
each economy
16 economies
How many are there the unit squares?
Mathematical
Thinking
enabling us
looking at the
world differently.
By D. Tall
Counting: One, Two, Three,….
↓
Adding:
8+9+10
↓
Multiplying:
3x9
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
Pedagogical
Content Knowledge
How can we develop students’
centered leaning?
Pedagogical
Knowledge
Lesson Study
For Developing
Classroom
Communication
Content
Knowledge
Developing Pedagogical Content Knowledge
Plan
Research Lesson
Reflection
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
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?
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)
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)
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)
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.
Working Group 1
Kanazawa day 1.
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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.
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.
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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.
Mathematical Communication
Working Group 3
Kanazawa day 1
Communication & National
Curriculum
Communication & National
Curriculum
• 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.
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
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
Approaches
Authentic Teacher Education Materials
Approaches
• Access to rich mathematical tasks
• Opportunities to develop the abilities in the
development of such tasks.
Approaches
• The use of video and technology to show
the implementation of such tasks.
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.
Example
• Communication within the context of
mathematical thinking and learning.
Example: Grade 3 Area (Taiwan), the role
of textbooks.
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.
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?
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