2021/4/11

By using what children learned!
Review
Task sequence for preparation of futureFree 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 7: What is Subtraction?

Larger orSmaller
Greater or Less
• Operations

Isoda, Masami. Prof., Faculty of Human Sciences
Director of CRICED, The University of Tsukuba, Japan
With collaborations ofReview

Review

Questioning to others (Attitude), Easier & Beautifulness (Value)
Composite and de-composite of numbers(content), Cardinal Number (content, idea), Compare (idea)

In 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

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

Task sequence for preparation of future learning:

What children already prepared?
 On content
 On Thinking and Process On Values and Attitudes

Revitalizing
Teacher Education

Using what you already knew!

What did we learn about Japanese principle
to develop mathematical thinking

Review

Review

Difference-Situation

Task sequence of Japanese
textbook is prepared for futurelearning.
The role of teachers:
Left
Difference↓ Using learned↓
VS before Studentsʼ sense making

Difference

Addition is a binominal operation.

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

Left-Situation

Left

If children write thesituation by 2+2=4 insteadof 4-2=2 at the
introduction of subtraction,
how do you assess?
Story Problems
Mathematical Modeling
Altogether Situation A, B, C, …
Concrete Object
Explanation with blocks
manipulative
Semi Concrete Object
Explanation by sentences

If children answer thesituation 7+5 =12 bycounting, what preparation
is missing in yourteaching?

Appreciations
Reflection

Addition activity for what?

Difference-Situation

Task sequence of Japanese
textbook is prepared for futurelearning.
The role of teachers:
Left
Difference↓ Using learned
VS before↓ Studentsʼ sense making
Difference
Left

HOTS isMath. T.

If children write thesituation by 2+2=4 insteadof 4-2=2 at theintroduction of subtraction,
how do you assess?
If children answer thesituation 7+5 =12 bycounting, what preparation
is missing in yourteaching?

3

SubtractionofHow Japanese develop students who think mathematics by andfor
DifferentSets
themselves
themselves. Develop students who will make sense by and for Interpret the childrenʼs understanding from their replies and consider
how their ideas are related with the past task sequence.
 In relation to the past (already learned) task sequence:
 Utilize their idea positively for making clear the todayʼs task.
 If necessary, going back to the past task which is necessary forunderstanding todayʼs task.
What students can do to approach the unknown task is only using what
learned before. As long as students use their learned knowledge, teachers
should listen and ask others to consider.

What is addition?

Review

On situations in our life: 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 sameanswer with counting on natural number.
• Counting is necessary for the confirmation of sum on naturalnumber.

Left-Situation

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

Review

Math sentence
addition

Counting VS Adding

How many times did children experience?

Task sequence what students already knew.

What did we learn about Japanese principle
to develop mathematical thinking

Math expression
Addition: operation

On the world of number (mathematics): not denominatednumber/not quantity• Number(Existence/ necessity, set/cardinal), Order, Operation• Addition is a binominal operation;
It cannot be answered by counting but answered by memorizedcalculation such as composite of numbers.

• Operation put the structure into Number Set!
Children find anotherbeautiful structure/pattern of numbers
by using equivalenceclass on addition

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.

Task sequence what students already knew.

1

2021/4/11

Task Sequence of Addition (1)Do you remember how 0 was introduced in L2?
Getting proficiency of meaning and skill

Permanence of Form

Review

What is addition?

On situations in our life: 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 sameanswer with counting on natural number.
• Counting is necessary for the confirmation of sum on naturanumber.

Binominal operation but thearranged pattern of subtraction
cards is not the same asaddition cards arrangement

Review

On the world of number (mathematics): not denominatednumber/not quantity• Number(Existence/ necessity, set/cardinal), Order, Operatio• Addition is a binominal operation;
It cannot be answered by counting but answered by memorizedcalculation such as composite of numbers.

• 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

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-RECSAM Left Situation  Subtraction
 Semi-concrete
is aobject
binominal De-Composite
operation.
of numbers
 De Translate them
Composite ofintonumbers
mathematicalsentence forsubtraction
 Concepturalzation

 The World ofsubtraction.
 Translation
fromsubtraction
expression
to the story
problem forleft situation

References Now every
task isexplained byterminology.
 Which task
can you skip?
 CANNOT !!
Becauseeach task hassome role on
the process ofmodeling.
 It is third time.
 Terminology
is necessary
to consider
the task
sequence

14

Letʼs explain task sequence by using learned terminology

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

2005 Edition

NEWEST EDITION

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

4 Editions

 Proceduralization  Permanence Acquiring Difference Acquiring
 World of Numberof Form forproficiency on
situation
proficiency
on Subtraction
subtraction
meaning of Conceptualizati
on skills and Beautiful patternwith 0subtraction
on of difference
meaningbut it is not theon
leftandassubtraction
same pattern as
difference

One
toone
additionsituations
correspondence Minuend andSubtrahend
 Now every task is explained by terminology.
 Second time of Each task has some role on the process for modeling, conceptualization andarrangement ofproceduralization.
cards
 Terminology is necessary to consider the task sequence

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

10 Editions

2010 Edition

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

4 Editions

 LeftSituationquestion Semi-Concrete Object
 De For
Composite ofExplanation
numbersby
 How tosentences
represent?
 For
Learning
the way oftranslation
 Left-Situation

Review

Additionis theinverse
operationof subtraction.
• Additionis theinverse
operationof subtraction.

Letʼs explain task sequence by using learned terminology

 Concrete Object

References

What is subtraction?
On situation in our life
• Left, difference• It can be answered bycounting but...
On the world of number

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
152