2021/4/26

Review:Teaching Mathematics to Develop Mathematical Thinking as Higher Order Thinking

How do you teach? Why?

Lesson 11: How to extend Number more than 10

For developing children who learn mathematics by and for themselves
and think by themselves, to use what they already learned/knew isnecessary.

For this, Necessary for teachers are sense making of students who areable to make sense by themselves.

Reflection

Isoda, Masami. Prof., Faculty of Human Sciences
Director of CRICED, The University of Tsukuba, JapanAppreciations

Normally, teachers strangle to make sense in their teaching.
Is it possible to develop students’ HOTS on this mind set?

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

Then, task sequence for preparation of future is necessary to develop
students who think by themselves.

With collaborations ofAdopting a 21stCentury Curriculum

Revitalizing
Teacher Education

We are reading the JP textbook by using terminology to explain todistinguish every content of learning and sequence of content forknowing the way to develop children who learn and think by and forthemselves.

Acquisition

Nguyen Chi Thanh and Aida YapCurriculum Standards: SEABES-CCRLS( by SEAMEO-RECSAM (Mangao, Ahmad, Isoda; 2017)

HOTS isMath. T.

Thoseterminology
distinguishtasks andexplain task
sequence
for thepreparationof futurelearning.

2Review

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

What is the number?
We usually teach:

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

How children shift
new way of counting?

• Existence and necessity

For what?
Number sense?

Idea of Set and Unit,

Cardinal (Set) Number

In Japan:Make sense (understandmeaning)
Think about how to
calculate/operate/find theHow do we teach the number more than ten?
How do wePleaseteachnumbermorethan hundred?easier way to answer
fill thein yourquestion 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?

Terminology!

Using what you already knew on the past 10 lessons!

Which number is really base ten place value system?

 Participants
need toconsider what’snew.

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

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

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

Grouping for 10

Number, Arabic digit,
Numeral, Concrete object,
B
A
Semi-concreteobject,
Denominated number,Base ten system, Baseten place value system
Count by 10:
10 is a unit
for counting

Try to teach how to extend
the number

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

Why the number table begin from 0?
What’s new? Why here?
Why children
have to put 0in here?

Why we need
the line ofnumber in here?

For
what?

For
what?

Necessity of regrouping/rearrangment
under base tenplace valuesystem to show
(cardinal)
numberNumber can beseen under thevarious units byusing attribute ofconcrete object onsituations.

See the situationas base 10.

It is a preparation ofmultiplication.

Use the attributefor one things to
see any number asa unit

Necessity of using 0 as for showing place value12021/4/26

Number up to 10: Counting unit is one, compose & de-compose,and beautiful pattern by arrangement

Number more than 100: Counting unit is one, ten & hundreds, andaddition & subtraction with column method, and pattern ofnumeral with arrangement,

Bar for 10 blocks
Decimal
Number more than 10: Counting unit is one & ten, and addition &subtraction, and beautiful pattern by arrangement, line and tableof numbers (start from 0)

References

Multiplied by 10
Divided by 10

Number & Decimals: Relativity of base unit on recursive threedigits numeral system: one, Thousand and addition & subtraction
with column method, and pattern of numeral with arrangement,

Cube for 10 squares

Square for 10 bars

Number more than 100: Counting unit is one, ten & hundreds, andaddition & subtraction with column method, and pattern ofnumeral with arrangement,

15

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

2005 Edition10 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 EditionsIsoda, 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
16References
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 educationstandards (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

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