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Lesson #1
SEAMEO School Network Program provided by CRICED-University of Tsukuba

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? II

Lesson 2: Dividing and Operational Fraction, and Quantity Fraction
Lectured by: Masami Isoda, Prof/PhD., University of Tsukuba, Japan
With support of: Teh Kim Hong, Ms., SEAMEO-RECSAM, Malaysia
Raimundo Olfos, Prof/PhD., Pontificia Universidad Catolica de Valparaiso, Chile
With participation of: Ms. Laura Lopez Zarate, Colombia
Ms. Mei Nakada, JapanMr. Diego Solis, Costa Rica

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Lesson #1

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Lesson #1

Page 9.bPage 12.aTerminology to explain
the nature/objective ofeach task and task
sequence.
Terminology to design
Learning trajectory byusing what students
already learned.
Quantity Fraction
Operational Fraction
Quotative Division

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Dividing Fraction
Partitive Division (Learnedat Grade 2 as half andquarter).

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Here the definition is not
the part-whole relationship.
Unit Fraction.

Quotative division
Remaining part

Quotative Division canextend more than whole byusing unit
fraction/remaining part asa scale.

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Page 15.aPage 15.bPage 16.aPage 16.b

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Euclidean Algorithm is the way tofind a unit measurement for given
two numbers as greatest common
divisor through measuring byremaining part.

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References

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The textbook used in this course must be
cited as shown below:Behr, M., Lesh, R., Post, T. and Silver, E.: 1983, Rational number concepts. in R. Lesh and M. Landau (eds.), Acquisition of Mathematics Concepts and Processes,
Academic Press, New York, pp. 91–125.
Charalabous, C. Y., Pitta-Pantaze, D. (2007). Drawing a theoretical model to study student’s understanding of fractions. Educational Studies in Mathematics. 64,239-316.
Gould. P.(2010). Fraction notation and textbooks in Australia. 4th APEC-Tsukuba Conference. Sited on
http://www.criced.tsukuba.ac.jp/math/apec/apec2009/index_en.php
Lewis, C. (2011). Lesson Study with Japanese Curriculum Materials: A Randomized Controlled Trial. Sited on
http://www.criced.tsukuba.ac.jp/math/apec/apec2011/index_en.php
Masami Isoda et al. (2010). Mathematics Education Theories for Lesson Study: Problem Solving Approach and the Curriculum through Extension andIntegration, Journal of Japan Society of Mathematical Education, 92(11). 1-158.

Masami Isoda (2013). Fraction for Teachers: Knowing What before
Planning How to Teach. Tokyo: CRICED, University of Tsukuba.

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 la aritmética, Estado de México :Pearson Educación de México.
Masami Isoda, Raimundo Olfos. Edited. (2021). Teaching Multiplication with Lesson Study. Cham: Springer.

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