05/05/2021

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 13: How to extend column addition and subtraction
Reflection

Isoda, Masami. Prof., Faculty of Human Sciences
Director of CRICED, The University of Tsukuba, Japan
With collaborations ofAdopting a 21stCentury Curriculum

We 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

Aida Yap and Teh Kim HongThose
terminology
distinguishtasks andexplain task
sequence
for thepreparationof futurelearning.

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

Review

HOTS isMath. T.

Using what you already knew on the past 12 lessons!

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

L12: How to introduce
column addition andsubtraction

 Participants
need toconsider what’snew.

L13: How to extend
column addition andL13:
subtraction?

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

In Japan:
Make sense (understandmeaning)
How do we extend column addition and subtraction? Think about how to
calculate/operate/find theHow do we teach the number more than ten?
How do wePleaseteachthenumbermorethan hundred? easier way to answer
fill inyourquestion fortoday!
Acquisition of proficiency• Operations• Order/Larger or Smaller/
Greater or Less

How do we teach addition more than ten?
How do we teach subtraction more than ten?
How do we teach column addition and subtraction?

For Making 10,
decompose andthen compose

Make sense: conceptualizationby using already learned!

Try to teach how to extend
the number

What’s new for
more than 10?

Skill:
Proceduralization

Simple, Easier& Beautiful

Decompose 10
and thencompose

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Can your children use
learned for learning
column methods?
Can children draw the block
diagram for place value system
by and for themselves to explain
the base 10 place value system?
Altogether situation.
Tape Diagram for Part-Part
Whole: Addition

It was Composition of Number

LearnedDifferent setsituation.
Tape Diagram
for Part-Part
Whole: Addition

It wasComposition ofNumber

From largest place value
for mental estimation
From smallest place value
for column M.
Block representation(semi-concrete objects)
for BTPVS
Addition Algorithm

Set of 10: regrouping
Bar for 10 blocks
block for ones

Do youremember?

Translation!
‘1 bar and 2 bar’ is 3 bar.
‘1 set(group) of 10 and 2set(group) of 10’ is 3 bar.

Carrying/regrouping: How do you explain by using terminology?
Think about how to calculate: What does it mean here? For What?
Why 2+41 isend?

What children can learn
from these process.

Bar and single blocks
for base 10 place value
system are functioning
as container to explain
column addition
algorithm

Think about how tocalculate: What doesit mean here?
For What?
What will comenext?

When we use these rules?

What children can learn
from these process.

Learned square for 100
blocks, bar for 10
blocks, single for 1
became the container
for explanation ofaddition the answer
become more than 100.

Think about
how tocalculate!

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05/05/2021

How do you plan the task sequence for column subtraction by using terminology?

Conceptualization

Extend carrying/regrouping

Extend it for carrying/regrouping

Produce the algorithm using the baseProduce the base for meaning

How do you plan the task sequence for column subtraction
Blocks representation for base 10 place value system arebased on addition?
functioning as containar to explain column addition algorithm

Left situation
Whole-part part relationship
It was decomposition of number

Set of 10: regrouping
Bar for 10 blocks and block forones: Semi concrete object forbase 10 place value system.

Translation!
‘Remove 1 bar from 2 bar’means 20 – 10 and 2-1 ontens place.

Think about
how tocalculate!

Proceduralization

Homework!

Then, borrowing/regrouping

Homework!

Bar for 10 blocks andblock for ones: Semi
concrete object forbase 10 place valuesystem.
It functions as
container to explain
column subtraction
algorithm.

Can you explain
why the taskorder is from38-12 to 29-6?

Homework!
Could you explain why the order from 45-27 to 70-23 and then 35-8?

Addition and subtraction are inverse operations on the situation
when we represent it by tape diagram on part whole relationshipFor preparation for what?

Homework!

Could you explain (please fill in)?

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05/05/2021

New! But what’s new?

What’s new?

What’s new?

What is the challenge
for children?

What is the challenge
for children?

Can you imagine thetask sequence?

Can you imagine thetask sequence?

Could you explain the order of task?
How the blocks representations are functioning?

Can you imagine my next question?

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

References

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

2005 Edition

10 Editions

2010 Edition

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

4 Editions

25

Isoda, 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 Edition
26References
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_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. 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 (2021). Mathematics Challenges for Classroom
Practices at the Lower Secondary Level. Penang, Malaysia: SEAMEO-RECSAM

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