08/05/2021

Appreciations

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?

Lesson 15: How to introduce Multiplication and It's Table (Rows)
Reflection

Isoda, Masami. Prof., Faculty of Human Sciences
Director of CRICED, The University of Tsukuba, Japan
With collaborations ofWe are reading the JP textbook by using terminology to explain to distinguish every
content of learning and sequence of content for knowing the way to develop children
who learn and think by and for themselves through the preparation of future learning.

Revitalizing
Teacher Education

Acquisition

Teh Kim Hong
Adopting a 21stCentury Curriculum

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

Review

HOTS isMath. T.

Thoseterminology
distinguishtasks andexplain task
sequence
for thepreparationof futurelearning.

2
ReviewUsing what you already knew on the past 14 lessons!

L12: How to introduce
column addition andsubtraction

L13: How to extend
column addition andL13:
subtraction?

What is the number?
We usually teach:How do you teach?
Make sense?
Acquisition of proficiency?

• Existence and necessity

For what?
Number sense?

• Order/Larger or Smaller/
Greater or Less

• Operations
 Participants need toconsider what’s new.

Problem of English Notation

Multiplicative situations (Vergnaud)

Which one is operator in English?
Add a to b: b + a, b is addend and a is augend
Subtract a from b: b – a, b is minuend and a is subtrahend
Multiply a by b: a x b, a is multiplier and b is multiplicand‘a times b’: a x b looks ‘(a x) b’
Divide a by b: a ÷ b, a is dividend and b is divisor

 Isomorphism of measure Product of measure Unique measure space

Binominal operation
 Multiplier x Multiplicand
 Factor x Factor

Repeated Addition VS AttributeDefinition by measurement: to get thetotal quantity when the unit quantity
and the number (amount) of unit aregiven.
Area
Cartesian ProductDescartes
Combinatory
1637
Tree Diagram
BE:BC = BD:BA, then BE × BA = BC × BD.
Splitting
If BA is a unit, it can be seen as BE = BC × BD.
Operator
 Multiple from two side

Try to teach how to extendthe number Participants of this program are able to imagine the ways oflearning from the past process of learning.

What is multiplication?
How do you introduce it?

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

Open Access

Find the answers
1→(x2)→ 2
1→(2x)→ 2
1
1→(÷2)→2112

2

Give me the situation (story problem)
for the following compound expression
1) (3+2) x 2 ÷ 52) 2 x (3+2) ÷ 5

1→(x 2)→ 2
1→(2÷)→2111→ ( x)→1

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Problem of English Notation 2 (Continued)

Problem of English Notation 2• In Japanese
there are noproblem
betweenJapaneseexplanationand notation.

How do you explain?

Why there are four chapters? Why this order?

The representation/model for the base...

These Multiplication Chapters are a best
chapter for knowing how Japanese try todevelop students who learn mathematics forthemselves based on what they learned.

systemFor Knowing it, we should review what welearned until last 15 lessons!

of 21?

When we should...

didFor what?

2

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Introduction ofMultiplication

Addition (1)What’s new?
Why there areapples andbananas?
 Threedoughnuts foreach dish andfive dishes Five dishes
and threedoughnuts foreach dishKnowing situation for multiplication explained by sentences.

Why there are four chapters? Why this order?

Multiplication (1)How many meanings?

See the situation for multiplication
Multiplicative Situation A, B, C, …
Pictures & Diagrams
Tape Diagram & Times
By using dishes & boxes
A Set of Group and a number of set

Properties of Rows
MathRowsof expression
Multiplication areMultiplication
binary operations.
as an operation
Proceduralization

Why there are four chapters? Why this order?
Repeatedaddition

A Set of Group x a number of set
How many meanings?

Every two-pages for each row is the same manner! Why?

For Learning How to Extend the Rows

For Learning the ways to extend the multiplication rows3

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See the situation for multiplication
Multiplicative Situation A, B, C, …
Pictures & Diagrams
Tape Diagram & Times
By using dishes & boxes
A Set of Group and a number of set

Properties of Rows
MathRowsof expression
Multiplication areMultiplication
binary operations.
as an operation
Proceduralization

Repeatedaddition

A Set of Group x a number of set

Conjecturing,
Justifying
and Proving

See the situation for multiplication
Multiplicative Situation A, B, C, …
Pictures & Diagrams
Tape Diagram & Times
By using dishes & boxes
A Set of Group and a number of set

Properties of Rows
MathRowsof expression
Multiplication areMultiplication
binary operations.
as an operation
Proceduralization

What is the next Lesson? Can you imagine?
Repeatedaddition

A Set of Group x a number of set
How many meanings?

Conjecturing,
Justifying
and Proving

For Learning How to Extend the Rows

Distribution in action

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

References

2005 Edition

10 Editions

2010 Edition

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

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

4 Editions

23Isoda, M., Tall, D. (2019). Junior High School
Mathematics Textbook, Gakko Tosho

4 Editions

NEWEST EDITION

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 Edition244

08/05/2021

References
Masami Isoda, Raimundo Olfos edited (2020). Teaching Multiplication with Lesson Study: Japanese and Ibero-American Theories forInternational Mathematics Education. Cham, Switzerland: Springer. (Open Access)
Masami Isoda, Aki Murata (2020). Study with your friends: Mathematics for Elementary School (12 vols.). 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: Gakko Tosho.
Dominador Dizon Mangao, Nur Jahan Ahmad, Masami Isoda edited (2017).SEAMEO basic education standards (SEA-BES): Common
core regional learning standards (CCRLS) in mathematics and science . Penang, Malaysia: SEAMEO-RECSAM,
http://www.recsam.edu.my/sub_sea-bes/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 . NewJersey, 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 (2021). Mathematics Challenges for Classroom Practices at the Lower Secondary
Level. Penang, Malaysia: SEAMEO-RECSAM
Hosomizu, Y. translated by Gould, P. Isoda, M., Foo, C. (2010). Red dragonfly mathematics challenge. Department of Education, NewSouth Wealth. https://schoolsequella.det.nsw.edu.au/file/20a29ac1-c6f3-4ca3-84b1-2d8488a4cbcd/1/reddragonfly.zip/index.html
Hosomizu, Y. translated by Gould, P. Isoda, M., Foo, C. (2011). Companion: Mathematics Challenges. Department of Education, NewSouth Wealth. https://www.mansw.nsw.edu.au/shop/pre-k-8-books/dragonfly-companion

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