2021/3/23
PPT for Lesson 5 on SEAMEO School Network by Isoda, Masami. Prof/PhD, CRICED, University of Tsukuba, Japan: ©Masami Isoda

What didnʼt you learned yet?
Free Program for SEAMEO School Networkfrom the University of Tsukuba, Affiliate Member of SEAMEO

Number• Existence andnecessity• OrderTeaching Mathematics to Develop Mathematical Thinking as Higher Order Thinking:

How do you teach? Why?

Lesson 5: What is addition?

Larger orSmaller
Greater or Less
• Operations

Isoda, Masami. Prof., Faculty of Human Sciences
Director of CRICED, The University of Tsukuba, Japan
With collaborations ofHow do you explain by using your terminology?
Translation between different representations!

ReviewIn Japan:
Make sense (understandmeaning)
Think about how to
calculate/operate/find theeasier way to answer
Acquisition of proficiency

Altogether toIncreaseVS
Increase to
Altogether

Try to teach how to extend
the number

Story Problems
Mathematical Modeling
Altogether Situation A, B, C, …
Concrete Object
Explanation with blocks
manipulative
Semi Concrete Object

Nguyen Chi Thanh, TEH Kim Hong and Wahid Yunianto
Adopting a 21stCentury Curriculum

Revitalizing
Teacher Education

Math expressionAddition: operation

Explanation by sentences

Math sentence
addition

Explanation of the task sequence

Learning How to Learn from repetition of similar tasks by using what already learned.

Review

Task sequence for preparation of future learning.

Do you have all three tasks inyour textbook?

Review

Why we need the line up the cards?

Reflection

How children get the answer?

3Addition situation for different set

Acquisition

HOTS isMath. T.

Curriculum Standards: SEABES-CCRLS( by SEAMEO-RECSAM (Mangao, Ahmad, Isoda; 2017)

What is addition?

Review

Additional sentence to explain manipulation of concrete and semi-concrete object at the beginning.

Translation from addition expression to story problem

Appreciations

Addition is a binominal operation

On situations: It is the object for addition.
• Altogether, Increase, Different Sets: the ways of translations and conceptualization• It can be answered by counting.
• If counted, it is not the answer of addition but the answer of counting.
On the world of number: not denominated number/not quantity• Number(Existence/ necessity, set/cardinal), Order, Operation• Addition is a binominal operation;
It cannot be answered by counting but answered by memorized calculation such as composite ofnumbers.

• Operation put the structure into Number Set!
Equivalence class:4~(2+2), 4~(1+3). 4~(3+1)(2+2)~(1+3)? (1+3)~(3+1)?
Commutativity, Associativity• Addition is the inverse operation of subtraction.

11Gakko Tosho has the copyright of the Textbooks in English on this ppt.

2021/3/23
PPT for Lesson 5 on SEAMEO School Network by Isoda, Masami. Prof/PhD, CRICED, University of Tsukuba, Japan: ©Masami Isoda

Why we teach number on this sequence?

Letʼs see the class of grade 1-second month
by Mr. Takao Seiyama, Elementary School at U.T.

Number• Existence andnecessity• Order• Operation put the structure into Number Set!
Equivalence class:4~(2+2), 4~(1+3). 4~(3+1)(2+2)~(1+3)? (1+3)~(3+1)?
Commutativity, Associativity• Why children can answer the reason why?
From the video, can you find what children learned before?
What task sequence did you imagine to develop children who are able
to answer the reason why?
What activity after the video you will imagine?

Larger orSmaller
Greater or Less• Operations

In Japan:
Make sense (understandmeaning)
Think about how to
calculate/operate/find theeasier way to answer
Acquisition of proficiency

References
Altogether toIncreaseVS
Increase toAltogether

Try to teach how to extend
the number16Letʼs see theclass of grade 1second month by
Mr. Takao
Seiyama,Elementary
School at U.T.

•

From thevideo, can you
find whatchildrenlearnedbefore?

•What task
sequence did
you imagine todevelopchildren who
are able toanswer thereason why?

•

What activity
after the video
you will
imagine?

ReferencesMasami Isoda, Raimundo Olfos edited (2020). Teaching Multiplication with Lesson Study: Japaneseand Ibero-American Theories for International Mathematics Education. Cham, Switzerland: Springer.
(Open Access)
Masami Isoda, Aki Murata (2020). Study with your friends: Mathematics for Elementary School (12vols.). Tokyo, Japan: Gakko Tosho.

Masami Isoda, Aki Murata, Aida Yap (2015). Study with your friends: Mathematics for Elementary
School (12 vols.). Tokyo, Japan: Gakko Tosho.
Masami Isoda, David Tall (2019). Mathematics for Junior High School (3 vols.). Tokyo, Japan: GakkoTosho.
Dominador Dizon Mangao, Nur Jahan Ahmad, Masami Isoda edited (2017).SEAMEO basic education

standards (SEA-BES): Common core regional learning standards (CCRLS) in mathematics andscience. Penang, Malaysia: SEAMEO-RECSAM, http://www.recsam.edu.my/sub_seabes/images/docs/SEAMEO-ASEAN-Curriculum-SEABES-CCRLS-Standards.pdf

Maitree Inprasitha, Masami Isoda, Patsy Wang Iverson, Ban Har Yap (2015). Lesson Study:
Challenges in Mathematics Education. New Jersey, USA: World Scientific
Masami Isoda, Shigeo Katagiri (2012). Mathematical Thinking: How to develop it in the classroom.
New Jersey, USA: World Scientific

TEH Kim Hong, ISODA Masami, GAN Teck Hock (in printing). Mathematics Challenges for Classroom
Practices at the Lower Primary Level. Penang, Malaysia: SEAMEO-RECSAMISODA Masami, TEH Kim Hong, GAN Teck Hock (in printing). Mathematics Challenges for Classroom
Practices at the Upper Primary Level. Penang, Malaysia: SEAMEO-RECSAMGAN Teck Hock, ISODA Masami, TEH Kim Hong (20augi21). Mathematics Challenges for Classroom
Practices at the Lower Secondary Level. Penang, Malaysia: SEAMEO-RECSAM

Gakko Tosho: Study with your friends:
Mathematics for Elementary School SeriesChildren could explain the reason why because...

Can you imagine the ways how children are going to learn subtraction?

Primary School Textbook
2001 Curriculum2005 Japanese Edition
2005 English Edition↓
2010Thai Ed.

2005 Edition

10 Editions

2010 Edition

Children find anotherbeautifulstructure/pattern ofnumbers by using
equivalence class onaddition

Junior High S. Textbook
2012 Curriculum2016 Japanese-Edition
2019 English-Edition2020 Indonesian-Edition
202X Thai Ed.

4 Editions

Isoda, M., Tall, D. (2019). Junior High School
Mathematics Textbook, Gakko Tosho

4 Editions

NEWEST EDITION
The World of Number as
Addition StructureOperation
Equivalent Class
How many classes?

2012 Mexico Ed.
2019 Chile Pro. Ed.
2011 Curriculum2011 Japanese Edition
2011 English Edition↓
2019 Papua N.G. Edit.
2020 Indonesian Edi.
2020 Chile Ed.
2015 Japanese-Edition
2015 English-Edition2020 Curriculum2020 Japanese Edition2020 English Edition
1522Gakko Tosho has the copyright of the Textbooks in English on this ppt.