2022/5/19

Mathematics Education to Develop Students Agency:

Universityof Tsukuba
JapanPart III: 1. Problem Solving Approach

Masami Isoda
PhD/Prof, h.c.PhD (KKU), h.c.Prof(USIL)
Director of CRICED, University of Tsukuba, Japan

Model Curriculum SEA‐BES: CCRLS for Math

Motto of thecourse: By using
what welearned, we
continue
furtherlearning

Mathematical Thinking : What it isLesson Study : Design
Approaches based oncontent of teaching

Lesson 3. Problem Solving Approach and Task Sequence

11Universityof Tsukuba
Japan

Mathematics Education to Develop Students Agency:
Problem Solving Approach, Shape & Figure, Measurement, and Pattern & Data

Part II: Fraction andProportionality
Part III: Problem Solving Approach, Shape &Figure, Measurement, and Pattern & Data

Terminology
to explain
conceptual
difference andtask sequence
to design
lessonStudy with your friends: Mathematics for Elementary
School, Gakko Tosho (2005, 2011, 2016, 2020 editions)

Review

Mathematical Thinking : What it is

SEA‐BAS: CCRLS for Mathematics

Model Curriculum SEA‐BES: CCRLS for Math

Part I： Number of Operations

Lesson Study : Design
Approaches based oncontent of teachingʻTeaching Mathematics to Develop Mathematical Thinking asHigher Order Thinking: How do you teach? Why?ʼ III221

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Objectives of Mathematics Education

Universityof Tsukuba
Japan

Reference

Review

Couse of Study by MEXT, JAPAN (2017)

Reflection

Couse of Study by MOE, JAPAN (Shimada, 1956)
Katagiri (1987): Attitude, Way of Thinking, and Ideas in content
Isoda & Katagiri(2012) Mathematical Thinking

Appreciation
Acquisition

3

Various Teaching Approaches for Teaching Math.
Objective oriented
How different? When we prefer it?
Mathematics is the subject
for overcoming contradiction

Done by teachers whowell Know
Mathematical Activity

Math.
CritiqueMath. Value &AttitudeMath. Thinking

Students do Math. like
Mathematician without Teachers

Students Agency inGeneral

Authentic
Math. Act.
OrientedUniversityof TsukubaJapan

DialecticApproach
Designing up to overcoming contradiction

Problem Solving Approach

Shift to Designing Task‐sequence.

Problem
For students, any task is open as long as
students use what they learned
Mathtreats
onlytrue.

Designing Task only
Change the task to Open‐Ended

Open Approach

Shift it to Students Centered

Exam.
Injection Approach
Teacher Centered
Oriented
Done by teachers who do not design task and lesson by themselves
Approaches should be selected by teachers depending on what students we would like todevelop. Good teachers can manage various
approaches and control them as their
Reviewpreference because they know these as parameters depending on the objective of the class.

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See it only as a task or see it in the task sequence• If we see it just a task, it is…..

Universityof Tsukuba
Japan

Review
How many ways ofsolution?
How manyanswers?
Is it an open‐ended task?
Various meaning ofopenness.
 For students
 For mathematics

55Task 3

Why students produced various ways ofsolutions?
If we read previous pages…

Task 2

Task 1

Universityof Tsukuba
Japan• By using what students learned

See it only as a task or see it in the task sequence
Review:• If we see it in the task sequence,
revised

They must challenge it what they already learned: Various ways ofsolutions must be appeared if they learned well on the appropriate task
6sequence if the textbooks are developed for Student Agency

632022/5/19• If we see it in the task sequence,
Task 3

Task 4

Whowillposetask 4?
What welearn fromthis tasksequence?

Which idea isapplicable?
Which idea isUseful?

Which idea is more general?
In mathematics, we seek
general idea

Universityof TsukubaJapan• By using what students learned

See it only as a task or see it in the task sequence7

7

If Student Agency: Learned how toTask 3

Task 2How can we develop
students who will posetask 4 by and forthemselves?
Task 1

Task 4

Universityof TsukubaJapan• By using what students learned

See it only as a task or see it in the task sequence

Repetition of Open Approach develop the students who try to use what they learned.

Repetition of appropriate task sequence develop Math. Thinking., Val., & Atti. 884

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Let’s see the lesson study video, again.

Universityof Tsukuba
JapanPlease visit the past lessons inPart I. Number and Operations: Lesson 2~10

Let see the following (Second Grade) up to 12:27
https://www.youtube.com/watch?v=7TY_SHTgmFQ
6:48 S. ‘there is something wrong’
6:50 T. ‘What? Is there something wrong?’
6:51 S. ‘It is correct’ (not in English subtitle but in Japanese)

6:52 Others ‘backwards’ ‘I got it, not in order’ Why could he say ‘wrong’? Why did he choose the term ‘wrong’?
 Why others understand it immediately?

Why they could?

Review of Part I
99Let’s see the lesson study video, again.

Universityof Tsukuba
Japan

Please visit the past lessons inPart I. Number and Operations: Lesson 2~710105

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Why they could? A year ago…

Universityof Tsukuba
Japan1111Task sequence on the textbook
Part I. Number and Operations: Lesson 2~10

Universityof TsukubaJapanIf we make it in order,
it becomes beautiful.
Task 1

Beautiful?

Task 2

Beautiful!
Repetition by using what students learned.

1262022/5/19

Task sequence on the textbook
Part I. Number and Operations: Lesson 2~10

Universityof Tsukuba
Japan

13

13

Task sequence on the textbook
Part I. Number and Operations: Lesson 2~10

Universityof Tsukuba
Japan

Repetition of appropriate
task sequence develop
Mathematical Ideas, Ways ofThinking, Values & Attitude.

14147

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In Japan, Open A. is a part of Prob. Solv. A.

Universityof Tsukuba
JapanOpen A. originated teaching practice in the Secondary School of UT before WWII and the national textbook
was published in 1943. Shimada, S. rebirthed it the Open‐Ended A. Project at the end of 1960s and published
the book (1976).
1) Theorization: Nohoda, N. wrote the PhD thesis in 1983.
2) Extension: Sawada, T. lead the project for the problem sequence developped by students.
3) Spread to the World: Becker, J. published English translation of the book in 1996 in USA.

Problem Sequence in Nobuhiko Nohoda (1983)

Nohoda, N. (2000).
Teaching of OpenApproach Methods inJapanese Classroom. InProceedings of theconference of IGPME.
 Open for teachers Open for students
 Open for mathematics

In Japan, Open Approach became a part of Problem‐solving approach in 1990s.
Currently, there is a research group of Takeshi Miyakawa on Study and Research
Paths (SRP) on Anthropological Theory of the Didactic (ATD), French Didactics.
15

15

Various Teaching Approaches for Teaching Math.
Objective oriented
How different? When we prefer it?
Mathematics is the subject
for overcoming contradiction

Done by teachers whowell Know
Mathematical Activity

Math.
CritiqueMath. Value &Attitude

Math. Thinking

Students do Math. like
Mathematician without Teachers

Students Agency inGeneral

AuthenticMath. Act.
OrientedUniversityof Tsukuba
Japan

DialecticApproach
Designing up to overcoming contradiction

Problem Solving Approach

Shift to Designing Task‐sequence.

Problem
For students, any task is open as long as
students use what they learned
Mathtreats
onlytrue.

Designing Task only
Change the task to Open‐Ended

Open Approach

Shift it to Students Centered

Exam.
Injection Approach
Teacher Centered
Oriented
Done by teachers who do not design task and lesson by themselves
Approaches should be selected by teachers depending on what students we would like todevelop. Good teachers can manage various approaches and control them as theirpreference because they know these as parameters depending on the objective of the class.

168