2021/4/19

How each task chose the number and set the task sequence.

Free Program for SEAMEO School Networkfrom the University of Tsukuba, Affiliate Member of SEAMEO

Teaching Mathematics to Develop Mathematical Thinking as Higher Order Thinking:

How do you teach? Why?

What is the number?
We usually teach:

How do you teach?
Make sense?
Acquisition of proficiency?

• Existence and necessity

For what?
Number sense?

Cardinal (Set) Number

Lesson 9: How to extend addition?
• Order/Larger or Smaller/
Greater or Less

Isoda, Masami. Prof., Faculty of Human Sciences
Director of CRICED, The University of Tsukuba, JapanHow do we teach the number more than ten.

With collaborations ofNguyen Chi Thanh, Erlina Ronda and Aida Yap
Adopting a 21stCentury Curriculum

Review• Operations

Revitalizing
Teacher Education

How do we teach addition more than ten.

Using what you already knew on the past 8 lessons!

Extend the number by using the idea of the base ten placevalue system: Permanence of Form, Analogical Reasoning
based on what children already learned
New way to represent cardinal number for BTPVSNew way of representation of ordinal number for BTPVSIn Japan:
Make sense (understandmeaning)
Think about how to
calculate/operate/find theeasier way to answer
Acquisition of proficiency
Try to teach how to extend
the number

Why the number table begin from 0?
Whatʼs new? Why here?
Why children
have to put 0
in here?

Why we need
the line ofnumber in here?
Necessity of using 0 as for showing place value

What is the representation/model for the base ten place value system

How children shift
new way of counting?

Which number is really base ten place value system?

Terminology!

Grouping for 10Forwhat?

Idea of Set and Unit,
Number, Arabic digit,
Numeral, Concrete object,BA
Semi-concreteobject,
Denominated number,Base ten system, Baseten place value system Participants
need toconsider whatʼsnew.

Count by 10 Participants of this program are able toimagine the ways of learning from the pastprocess of learning.

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

When we should teach count by two and five, here?
Why we need the line of number, here?
HOTS isMath. T.

Thoseterminology
distinguishtasks andexplain task
sequence
for thepreparationof futurelearning.

3
Review

Necessity of regrouping/rearrangment
under base tenplace value
system to show
(cardinal)
numberWhy 28 instead of 21?
Where and when didchildren learn it?

For
what?
Number can beseen under thevarious units byusing attribute ofconcrete object onsituations.
It is a preparation ofmultiplication.

2021/4/19

By using what children learned!
Task sequence for preparation of future
Number• Existence andnecessity• Order
Larger orSmaller
Greater or Less
• Operations

Review

References

In Japan:
Make sense (understandmeaning)
Think about how tocalculate/operate/findthe easier way to answer
Acquisition of proficiency
Try to teach how toextend the number

13

Whatʼs new? Letʼs explain task sequence by using terminology.

Mathematical
Sentence is given.
Think about how to
calculate/operate

Make 10 by decomposite of augend.
And then, composite.

Make 10 by decomposite of addend.
And then, composite.

De-compositeaugend method

Composite-addend
methodGakko Tosho: Study with your friends:
Mathematics for Elementary School Series

2010 Edition

2005 Edition

Why this order: 9+4→３＋９→８＋６？

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

4 Editions

NEWEST EDITION

How do you explain by using terminology?
Think about
how toMade 10
De-compositeof Augend
Composite of
AddendPrimary School Textbook
2001 Curriculum2005 Japanese Edition
2005 English Edition↓
2010
Thai Ed.

10 Editions

Addition iscomposite ofnumbers

Counting by using
BTPVS.

StoryProblems

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

4 Editions

Addition situation
Altogether
Increase2012 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
14

References

World of addition: Beautifulness of pattern (structure)
Math expression
Think about how to calculate?
Using blocks for BTPVSMath sentence
addition

Masami 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 ScientificProceduralization
Beautifulness ofadditions

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