2022/5/25

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

Objectives of Mathematics Education

Universityof Tsukuba
JapanUniversityof Tsukuba
Japan

Reference

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

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 MathStudy with your friends: Mathematics for Elementary
School, Gakko Tosho (2005, 2011, 2016, 2020 editions)

Reflection

SEA-BES: CCRLS for Mathematics
Terminology
to explain
conceptual
difference andtask sequence
to designlesson

112

Various Teaching Approaches for Teaching Math.
How different? When we prefer it?

Math.
CritiqueMathematics is the subjectfor overcoming contradiction

Math. Value &Attitude

Math. Thinking

Students do Math. like
Mathematician without Teachers

Students Agency inGeneral

AuthenticMath. Act.
Oriented

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

Universityof Tsukuba
Japan

How many ways ofsolution?
How manyanswers?

DialecticApproachIs it an openended task?

Designing up to overcoming contradiction

Problem Solving Approach

Shift to Designing Task-sequence.
students use what they learned

Mathtreats
onlytrue.

Universityof TsukubaJapan• If we see it just a task, it is…..

Done by teachers whowell Know
Mathematical Activity

Various meaning ofopenness.
➢ For students➢ For mathematics

Problem
For students, any task is open as long as
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.

3

Couse of Study by MEXT, JAPAN (2017)

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

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

Part II: Fraction andProportionality

Part I： Number of Operations

AppreciationʻTeaching Mathematics to Develop Mathematical Thinking as
Higher Order Thinking: How do you teach? Why?ʼ III441

2022/5/25

Why students produced various ways ofsolutions?
If we read previous pages…
Task 2

Task 1

They only used what they already learned.
Various ways of solutions are related with which learned do they use.

• If we see it just a task, it is…..
Task 3

Task 4
Whowillposetask 2?

What welearn fromthis task
sequence?

In mathematics, we seek
general idea66

Task 2

Task 1

Task 4• If we see it just a task, it is…..
Task 3

Task 2

Task 1

Task 4

7

Universityof TsukubaJapan• If we see it in the task sequence• If we see it just a task, it is…..
Task 3

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

Universityof TsukubaJapan• If we see it in the task sequence

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

7

Which idea isUseful?

Which idea is more general?

55Which idea isapplicable?

Universityof TsukubaJapan• If we see it in the task sequence• If we see it just a task, it is…..
Task 3

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

Universityof TsukubaJapan• If we see it in the task sequence

See it only as a task or see it in the task sequence882

2022/5/25

Task 2

Task 1

Task 4• If we see it just a task, it is…..
Task 3

Task 2

Task 1

Task 4

99

Universityof TsukubaJapan• If we see it in the task sequence• If we see it just a task, it is…..
Task 3

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

Universityof TsukubaJapan• If we see it in the task sequence

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

10

10• If we see it just a task, it is…..
Task 3

Task 2

Task 1

Task 4Which activity, you would liketo teach? For that, how do you
use or change this task

11

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

Universityof TsukubaJapan• If we see it in the task sequence

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

Universityof TsukubaJapanOpen A. originated teaching practice in the Secondary School of UT before WWII and the national textbook waspublished 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 Nohoda (1983)

Nohoda, N. (2000).
Teaching of OpenApproach Methods inJapanese Classroom. In
Proceedings of theconference of IGPME.
➢ Open for students➢ Open for mathematics➢ Open for teachers1112123

2022/5/25

Various Teaching Approaches for Teaching Math.
How different? When we prefer it?

Math.
CritiqueMathematics is the subject
for overcoming contradiction

Math. Value &Attitude

Math. Thinking

Students do Math. like
Mathematician without Teachers

Students Agency inGeneral

AuthenticMath. Act.
OrientedUniversityof Tsukuba
Japan

Done by teachers whowell Know
Mathematical Activity

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.

134