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Free Program for SEAMEO School Network from the University of Tsukuba, Affiliate Member of SEAMEO Teaching Mathematics to Develop Mathematical Thinking as Higher Order Thinking
:
How do you teach? Why?
Lesson 11: How to extend Number more than 10 Isoda, Masami. Prof., Faculty of Human Sciences
Director of CRICED, The University of Tsukuba, JapanWith collaborations of
Nguyen Chi Thanh and Aida Yap
Revitalizing Teacher Education
Adopting a 21stCentury Curriculum
Acquisition Reflection Appreciations
Curriculum Standards: SEABES-CCRLS( by SEAMEO-RECSAM (Mangao, Ahmad, Isoda; 2017) 2 HOTS is Math. T.
Review Those terminology distinguish tasks and explain task sequence for the preparation of future learning.
Normally, teachers strangle to make sense in their teaching.
Is it possible to develop students’ HOTS on this mind set?
For developing children who learn mathematics by and for themselves and think by themselves, to use what they already learned/knew is necessary.
For this, Necessary for teachers are sense making of students who are able to make sense by themselves.
Then, task sequence for preparation of future is necessary to develop students who think by themselves.
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.
Using what you already knew on the past 10 lessons!
Review
Participants of this program are able to imagine the ways of learning from the past process of learning.
Participants need to consider what’s new.
What is the number?
We usually teach:
• Existence and necessity Cardinal (Set) Number
• Order/Larger or Smaller/
Greater or Less
• Operations
How do you teach?
Make sense?
Acquisition of proficiency?
For what?
Number sense?
In Japan:
Make sense (understand meaning)
Think about how to
calculate/operate/find the easier way to answer Acquisition of proficiency Try to teach how to extend the number
How do we teach the number more than ten?
How do we teach addition more than ten?
How do we teach subtraction more than ten?
Please fill in your question for today!
How do we teach the number more than hundred?
What is the representation/model for the base ten place value system
A B
Which number is really base ten place value system?
How children shift new way of counting?
Terminology!
Idea of Set and Unit, Number, Arabic digit, Numeral, Concrete object, Semi-concrete object, Denominated number, Base ten system, Base ten place value system
Count by 10:
10 is a unit for counting Grouping for 10
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?
How each task chose the number and set the task sequence.
Extend the number by using the idea of the base ten place value system: Permanence of Form, Analogical Reasoning based on what children already learned
Necessity of using 0 as for showing place value
Why children have to put 0 in here?
Why we need the line of number in here?
Why the number table begin from 0?
What’s new? Why here?
New way of representation of ordinal number for BTPVS New way to represent cardinal number for BTPVS
For what?
Necessity of re- grouping/re- arrangment under base ten place value system to show (cardinal) number See the situation as base 10.
For what?
Number can be seen under the various units by using attributeof concrete object on situations.
It is a preparation of multiplication.
Use the attribute for one things to see any number as a unit
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Number up to 10: Counting unit is one, compose & de-compose, and beautiful pattern by arrangement
Number more than 10: Counting unit is one & ten, and addition &
subtraction, and beautiful pattern by arrangement, line and table of numbers (start from 0)
Number more than 100: Counting unit is one, ten & hundreds, and addition & subtraction with column method, and pattern of numeral with arrangement,
Bar for 10 blocks
Square for 10 bars Cube for 10 squares
Number more than 100: Counting unit is one, ten & hundreds, and addition & subtraction with column method, and pattern of numeral with arrangement,
Number & Decimals: Relativity of base unit on recursive three digits numeral system: one, Thousand and addition & subtraction with column method, and pattern of numeral with arrangement,
Decimal Multiplied by 10
Divided by 10
References
15
2005 Edition 2010 Edition
Primary School Textbook 2001 Curriculum 2005 Japanese Edition 2005 English Edition
↓ 2010 Thai Ed.
2012 Mexico Ed.
2019 Chile Pro. Ed.
2011 Curriculum 2011 Japanese Edition 2011 English Edition
↓ 2019 Papua N.G. Edit.
2020 Indonesian Edi.
2020 Chile Ed.
2015 Japanese-Edition 2015 English-Edition 2020 Curriculum 2020 Japanese Edition 2020 English Edition 10 Editions4 Editions
Junior High S. Textbook 2012 Curriculum 2016 Japanese-Edition 2019 English-Edition 2020 Indonesian-Edition 202X Thai Ed.
4 Editions
16 Gakko Tosho: Study with your friends:
Mathematics for Elementary School Series
Isoda, M., Tall, D. (2019). Junior High School Mathematics Textbook, Gakko Tosho NEWEST EDITION
References
Masami Isoda, Raimundo Olfos edited (2020). Teaching Multiplication with Lesson Study: Japanese and 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 (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. 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-RECSAM
ISODA Masami, TEH Kim Hong, GAN Teck Hock (in printing). Mathematics Challenges for Classroom Practices at the Upper Primary Level. Penang, Malaysia: SEAMEO-RECSAM
GAN Teck Hock, ISODA Masami, TEH Kim Hong (20augi21). Mathematics Challenges for Classroom Practices at the Lower Secondary Level. Penang, Malaysia: SEAMEO-RECSAM
