08/11/2021

Questions for teachers.

SEAMEO School Network Program provided by CRICED-University of Tsukuba

1) If you teach the following
as a procedure ofmultiplication (at 6th grade),1 3 1×3× =2 5 2×5
why you do not teach thefollowing as a procedure ofaddition (at 4th grade)?
13
1+3+ 5 = 2+52

Mathematics Education to Develop Students Agency:
The Case of Fractions
Teaching Mathematics to Develop Mathematical Thinking as Higher Order Thinking:
How do you teach? Why? IILesson 3: Addition with different denominator2) How can you
proceduralize the meaning?

Lectured by: Masami Isoda, Prof/PhD., University of Tsukuba, Japan
With support of: Maitree Inprasitha, Assoc. Prof/Phd., Narumon Changsri, Assis. Prof./PhD,, and3) What meaning isnecessary to beproceduralized?

Nisakorn Boonsena, PhD., Auijit Pattanajak , Assoc. Prof., Khon Kaen University, Thailand
With participation of: Ms. Laura Lopez Zarate, Colombia
Mr. Diego Solis, Costa Rica

Page 20.a

3rd grade, Gakko tosho textbook (2011): How different? Could you explain task sequence by using learned terminology?

In Japan, before
students learn theaddition with differentdenominators, theylearn the addition withthe same denominator.

Grade 2: Dividing F./Part-W. for half and 1 quarter,
2 quarters and 3 quarters.

Page 20.b

Grade 3: from Operational F. for measuring by using
remaining part to Dividing F. through using
Quantity fraction.
Then, produce the unit for measurement (Unit F.).
Integration of Operational F. and Dividing F.

Addition of the same denominator at 3rd grade:
Could you explain the task by using learned terminology?

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When you teach
Dividing F., do youteach the whole?
Should it be thesame?
When you teachshading the diagram
for learning Dividing
F., what is the objectof counting?
When you teachdrawing the diagramfor F., do you ask thewhole to be thesame?
By using Dividing Fraction without quantity, we shouldnote we can not compare and add! Dividing Fraction canbe compared and added only in the case the whole is kept.
Page 21.bPage 22.aLet’s produce theprocedure based on themeaning which isrepresented bydiagrams!

It is Unit F. on Operational F.

Which diagrams areappropriate to explain
the meaning ofaddition?

In mathematics,
general idea is strong!

Why the whole shouldbe the same?
Page 22.b

Page 23.a

In mathematics,
general idea is strong!
For generalization, weshould developstudents who say “Forexample”!
Counter example isused for dialectic.
Page 23.b

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References
Isoda, M. (1996). Problem Solving Approach with Dialectic. (written in Japanese:多様な考えを生み練り合う問題解決授業 : 意味とやり方のずれによる葛藤と納得の授業づくり. 東京：明治図書出版) in English: Isoda, M. (2007). Developing Mathematical Thinking inClassroom, APEC Project report on

http://www.criced.tsukuba.ac.jp/math/apec/apec2007/progress_report/specialists_session/Masami_Isoda.pdf

Masami Isoda et al. (2010). Mathematics Education Theories for Lesson Study: Problem Solving Approach and the Curriculum
through Extension and Integration, Journal of Japan Society of Mathematical Education, 92(11). 1-158.
Shin Hitotsumatsu et al. (2005). Study with your friends: Mathematics for Elementary School (12 vols). Tokyo: Gakkotosyo.
Masami Isoda et al. (2010). Study with your friends: Mathematics for Elementary School (12 vols). Tokyo: Gakkotosyo.
Masami Isoda, Tenoch Esaú Cedillo Ávalos, et al. (2012). Matemáticas para la educación normal (11vols). Estado de México : Pearson
Educación de México.
Tenoch Cedillo, Masami Isoda, et al. (2013) Matemáticas para la educación normal : guía para el aprendizaje y enseñanza de laaritmética, Estado de México : Pearson Educación de México.

Page 24.b

The textbook used in this course must be
cited as shown below:
Masami Isoda (2013). Fraction for Teachers: Knowing What before
Planning How to Teach. Tokyo: CRICED, University of Tsukuba.

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