2021/4/11
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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 8: How to extend the number more than 10?
Isoda, Masami. Prof., Faculty of Human Sciences Director of CRICED, The University of Tsukuba, Japan
With collaborations of
Nguyen Chi Thanh, Erlina Ronda and Aida Yap Revitalizing Teacher Education
Adopting a 21stCentury Curriculum
Using what you already knew on the past 7 lessons!
Review
Participants of this program are able to imagine the ways of learning from the process of learning process.
Participants need to consider whatʼs new.
Acquisition Reflection Appreciations
Curriculum Standards: SEABES-CCRLS( by SEAMEO-RECSAM (Mangao, Ahmad, Isoda; 2017) 3 HOTS is Math. T.
Review Those terminology distinguish tasks and explain task sequence for the preparation of future learning.
Number
•
Existence and necessity
•
Order Larger or Smaller Greater or Less
•
Operations
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
By using what children learned!
Task sequence for preparation of future
ReviewNumerals In English as a language
Cardinal Number (set number):
One, two, three, ….nine, ten, eleven, twelve, …, nineteen, twenty, twenty-one(20+1), …, thirty, thirty-one, … notexact base ten system?
Ordinal Number:
First, Second, Third, Forth, …, ninth, tenth, eleventh,
…, nineteenth, twentieth, twenty first, … Show the position in order.
---
Multiple:
Once (one time), twice(two times), thrice(three times), …
Half, double (twofold), triple (threefold), …
In Japanese
Cardinal Number (set number):
Ichi(one), ni, san,…, jyu(ten), jyu (ten)-ichi (one) (eleven), jyu-ni (ten+two)… ni-jyu (two ten) exact base ten system
Historically Hitotsu, Futatsu, Mittsu, …, To (ten) Ordinal Number：C.N.＋番(ban) Ichi-ban, ni-ban, san-ban, … Multiple: C.N.＋倍(bai) Ichi-bai, ni-bai, san-bai, … How about in your language?
Number showsmagnitude (size) but not show the quantity.
Quantity (amount/measure) is represented by numberwith denomination.
ʻ3 applesʼ are denominated number:
an apple is the unit for counting (measurement). 3 is a number.
Review
10 is Ten ʻ10ʼ (one word) or 1+0 (two words)?
Term. : Idea of set which is defined by conditions or elements.
Term. : Order of Number/Numeral
Base Ten Place Value System (Arabic Number) VS Base Ten System (Numeral) Case of English
BTPVS
Arabic1 2 3 … 10 11 … 14 … 19 20 21 … 30 … 99 100 101 … 110 111 … 114 121 En.O
n e T w o T h r e e
T e n
E l e v e n
F o u r t e e n
N i n e t e e n
T w e n t y
T w e n t y O n e
T h i r t y
N i n e t y N i n e
H u n d r e d
H u n d r e d O n e
H u n d r e d T e n
H u n d r e d E l e v e n
H u n d r e d F o u r t e e n
H u n d r e d T w e n t y O n e 4-
10 9- 10
20 20- 1
30 90
-9 100 100-
1 100- 10
100- 11
100- 4-10
100- 20-1
Base Ten Place Value System (Arabic Number) VS Base Ten System (Numeral) Case of Japanese
BTPVS
Arabic1 2 3 … 9 10 11 12 … 20 21 … 30 … 99 100 101 … 110 111 … 121 … Jpn.I
c h i N i S
a n
K y u J y u
J y u I c h I
J y u N i
N i- J y u
N i- J y u I c h i
S a n- J y u
K y u- J y u K y U
H y a k U
H y a k u I c h i
H y a k u J y u
H y a k u J y u I c h i
H y a k u N i- J y u I c h i 10 10
-1 2- 10
2- 10 1
3- 10
9- 10 9
100 100 1
100 10
100 10 1
100 2-10 1
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.
2021/4/11
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How do you teach 11?
• By Counting and Ordering?
What is necessity to shift the base ten place value system?
What are changes/new?
What should learn?
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 change the way of counting?
Could you explain it by learned terminology?
Why we need the terminology ʻsemi-concrete objectʼ and ʻblockʼ?
When do you teach count by two and five?
Why we need the line of number? How it set the task sequence?
How each task chose the number and set the task sequence?
For what?
For what?
References
16
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
17 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
