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 10: How to extend Subtraction• 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 ofAida Yap and Maitree Inprasitha
Adopting a 21stCentury Curriculum

Review• Operations
How do we teach addition more than ten?

Revitalizing
Teacher Education

How do we teach subtraction 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 0in 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 10For
what?

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:
10 is a unit
for counting

Necessity of regrouping/rearrangment
under base tenplace valuesystem to show
(cardinal)
number 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 andexplaintask
sequence
for thepreparationof futurelearning.

Why 28 instead of 21?
Where and when did
children learn it, already?

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

3Review1

2021/4/19

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

Think about how tocalculate/operate(Set/Cardinal)Number up to 10: Counting unit is one, compose & de-compose, and beautiful
pattern by arrangement

Bar for 10 blocks

Extension to unknown(Set/Cardinal)Number more than 10: Counting unit is one & ten, and composite & decomposite, and beautiful pattern by arrangement, line and table of numbers (start from 0)
Integration new on unknown with known

Integration new on unknown with known
A theory for conceptual change for learning trajectory: (Isoda, 1991;Isoda&Olfors, 2021)

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

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

De-compositeaugend method

De-compositeaddend method

Why this order: 9+4→３＋９→８＋６？

A theory for conceptual change for learning trajectory: (Isoda, 1991;Isoda&Olfors, 2021)

Open Access

Open Access

Learning
newthings byusing
learnedLearning
newthings byusing
learned

Could you explain the learning process for extension ofsubtraction more than 10 by using terminology?
Learned:
Subtraction
situation
 left difference
Subtraction wasde-composite ofnumbers

Counting back byusing BTPVS.
MathematicalSentence is given.
Think about how to
calculate/operate

Use 10s on minuend
for subtraction andadd remaining.
SubtractionAddition method

Use 1s on minuend byde-composing
subtrahend andsubtract remaining
from 10s on minuend
Subtractionsubtraction method

Bar for 10 blocks

Extension to unknown(Set/Cardinal)Number more than 10: Counting unit is one & ten, and composite & decomposite, and beautiful pattern by arrangement, line and table of numbers (start from 0)

Try to teach how toextend the number

Mathematical
Sentence is given.

(Isoda, 1991; Isoda&Olfos 2021)(Set/Cardinal)Number up to 10: Counting unit is one, compose & de-compose, and beautiful
pattern by arrangement

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

Counting by using
BTPVS.

Extension and Integration (MOE-JP, 1968)
Conceptualization and Procedualization(Isoda, 1991; Isoda&Olfos 2021)

Whatʼs new? Change the meaning of addition! How?
Learned:Addition situation
 Altogether
 Increase
Addition wascomposite ofnumbers

Extension and Integration (MOE-JP, 1968)
Conceptualization and Proceduralization

Review

References10s or 1s, whichpart is easier toreduce at first.

Why this order: 12 - 9→11-3→14 - 6？

17

How do you explain by using terminology?

StoryProblems

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

Gakko Tosho: Study with your friends:
Mathematics for Elementary School Series

2010 Edition

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

2005 Edition10 Editions

 Think about howto Use 10s or 1s onminuend Subtractionaddition method
 Subtractionaddition method

NEWEST EDITION

 Proceduralization
 Beautifulness ofadditions

 Proceduralization
 Beautifulness ofSubtraction

Isoda, M., Tall, D. (2019). Junior High School
Mathematics Textbook, Gakko Tosho
Junior High S. Textbook
2012 Curriculum2016 Japanese-Edition
2019 English-Edition2020 Indonesian-Edition
202X Thai Ed.

4 Editions

Story
Problems

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

4 Editions

 Think abouthow to Made 10
 De-compositeof Augend
 De-compositeof Addend2012 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 Edition182

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References
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 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-RECSAM3