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Advances in Social Sciences Research Journal – Vol.7, No.8
Publication Date: August 25, 2020
DOI:10.14738/assrj.77.8847.
Uchida, A. (2020). A Review of the Studies on the Development of Concepts of Decimals and Fractions in Japanese Elementary School
Children. Advances in Social Sciences Research Journal, 7(8) 302-314.
A Review of the Studies on the Development of Concepts of Decimals
and Fractions in Japanese Elementary School Children
Akitoshi Uchida
Nagano Municipal Kohoku
Junior High School, Japan
ABSTRACT
This paper reviews the studies published in Japan on the development
of the concept of decimals and fractions in Japanese children. The Google
Scholar search using the keywords “concept of decimals” and “concept
of fractions” hit 59 articles published during 1982–2020 in Japan.
According to the Course of Study, the guideline for elementary school
education in Japan set by the Ministry of Education, Culture, Sports,
Science and Technology of Japan, decimals and fractions should be
taught in arithmetic classes of elementary schools. However, only 17
studies explored the concepts of decimals and fractions and the
development of those concepts of primary school children. Moreover,
none of them were conducted utilizing a scientific research method with
empirical data of Japanese elementary school children. It concluded that
the research on the education of ratio, including decimals and fractions,
in Japan was still in “the stone age” without utilizing genuine scientific
methods. (150 words)
Keywords: studies published in Japan, elementary school children,
arithmetic education, concept of decimals and fractions
INTRODUCTION
Uchida and Mori (2018) reported that there were 20% or more “fake math-dislikes” among
Japanese junior high school students. Those students replied, “I dislike mathematics” in the
questionnaire survey, while they performed positively toward “mathematics” assessed with a
paper-based Implicit Association Test (Mori, Uchida, & Imada, 2008). Uchida and Mori (2018) also
found that the number of “fake math-dislikes” increased with the year grades. There were more
“fake math-dislikes” in the second and third graders than the first graders in Japanese junior high
schools.
Since there were some proportion of students who showed the characteristics of the “fake math- dislikes” at the very beginning of the first year of junior high school, we should examine when
students would turn into “fake math-dislikes” during elementary school days. As a math teacher at
a junior high school, the present author has long experienced that many students lack appropriate
knowledge and skills of decimal numbers and fractions that they should have learned in elementary
school education. How do they learn the knowledge and skills of decimal numbers and fractions
during elementary school?
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Uchida, A. (2020). A Review of the Studies on the Development of Concepts of Decimals and Fractions in Japanese Elementary School Children. Advances
in Social Sciences Research Journal, 7(8) 302-314.
URL: http://dx.doi.org/10.14738/assrj.78.8847 303
Table 1: Objectives in Arithmetic Described in Course of Study for Elementary Schools (MEXT,
2017a)
Grade Objectives
Grade
1
(1) Through activities using concrete objects and so on, to help pupils enrich their number sense. To
help them understand the meaning and the representations of numbers, and to help them understand
addition and subtraction, and explore ways of the calculations, and use the calculations.
(2) Through activities using concrete objects and so on, to help pupils enrich their experiences that
will form the foundation for understanding quantities and measurements, and enrich their sense of
quantities.
(3) Through activities using concrete objects and so on, to help pupils enrich their experiences that
will form the foundation for understanding geometrical figures, and enrich their sense of geometrical
figures.
(4) Through activities using concrete objects and so on, to help pupils represent numbers and
quantities as well as their relations by using words, numbers, algebraic expressions, figures and
diagrams and interpret such representations.
Grade
2
(1) Through activities using concrete objects and so on, to help pupils enrich their number sense. To
help them deepen their understanding of the meaning and the representations of numbers, as well as
their understanding of addition and subtraction, and use the calculations. Furthermore, to help them
understand the meaning of multiplication, explore ways of the calculation, and use the calculation.
(2) Through activities using concrete objects and so on, to help pupils understand the units and
measurements of length and volume and so on, and enrich their sense of quantities.
(3) Through activities using concrete objects and so on, to help pupils understand geometrical figures
such as triangles and quadrilaterals, and enrich their sense of geometrical figures.
(4) Through activities using concrete objects and so on, to help pupils represent numbers and
quantities as well as their relations by using words, numbers, algebraic expressions, figures, diagrams,
tables, and graphs, and interpret such representations.
Grade
3
(1) To help pupils use additionand subtraction appropriately, to help them deepen their understanding
of multiplication and use the calculation appropriately. To help them understand the meaning of
division, explore ways of the calculation, and use the calculation. Furthermore, to help them
understand the meaning and the representations of decimal numbers and fractions.
(2) To help pupils understand the units and measurements of length, weight and time.
(3) To help pupils understand geometrical figures such as isosceles triangles and equilateral triangles
by paying attention to the elements that compose the geometrical figures.
(4) To help pupils represent numbers and quantities as well as their relations by using words, numbers,
algebraic expressions, figures, diagrams, tables, and graphs, and interpret such representations.
Grade
4
(1) To help pupils deepen their understanding of division and use the calculation appropriately. To
help them deepen their understanding of the meaning and the representations of decimal
numbers and fractions, understand the meaning of addition and subtraction of decimal
numbers and fractions, explore ways of addition and subtraction, and use them. Moreover, to
help them understand round numbers and use them according to their purposes.
(2) To help pupils understand the units and measurements of area, determine the area of geometrical
figures, and understand the unit and measurements of angle.
(3) To help pupils understand plane figures, such as parallelograms and rhombuses, and solid figures,
such as rectangular parallelepiped, by paying attention to the elements that compose the geometric
figures and the relationships of those elements.
(4) To help pupils represent numbers and quantities as well as their relations by using words, numbers,
algebraic expressions, figures, diagrams, tables, and graphs, and investigate such representations.
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Advances in Social Sciences Research Journal (ASSRJ) Vol.7, Issue 8, August-2020
Grade
5
(1) To help pupils deepen their understanding of properties of integers. To help them deepen their
understanding of the meaning of multiplication and division of decimal numbers as well as the
meaning of addition and subtraction of fractions, explore ways of the calculation, and use the
calculations.
(2) To help pupils determine the area of geometrical figures such as triangles and parallelograms and
the volume of solid figures such as rectangular parallelepiped. To help them understand the average of
measured value and the ratio of two quantities of different types.
(3) To help pupils deepen their understanding of plane figures, and to help them understand solid
figures such as prisms.
(4) To help pupils investigate relationships between numbers/quantities. To help them investigate the
features of data by using percentages and pie graphs.
Grade
6
(1) To help pupils deepen their understanding of the meaning of multiplication and division of
fractions, explore ways of the calculations, and use the calculations.
(2) To help pupils determine the area of circles and the volume of solid figures such as prisms. To help
them understand speed and determine it.
(3) To help pupils understand reduced figures, enlarged figures and symmetric figures, and deepen
their understanding of geometrical figures.
(4) To help pupils understand ratio and direct proportion, and use the idea of a function when exploring
the relationships of numbers/quantities, and represent the relationships in algebraic expressions. To
help them explore the distribution of data and investigate it statistically.
Note: The objectives related to decimals and fractions are in bold fonts.
The Ministry of Education, Culture, Sports, Science and Technology (MEXT) of Japan prepared and
publicly announced a new version of the Course of Study for Elementary Schools in 2017, starting in
the academic year 2020–2021 (Ministry of Education, Culture, Sports, Science and Technology of
Japan: MEXT, 2017a). The Course of Study 2020 guides each elementary school to make its
curriculum for 2020 onward. Therefore, we can determine how the decimal numbers and fractions
are taught in elementary schools through the Course of Study 2020. For example, Table 1 shows the
objectives of arithmetic education for each grade.
The Course of Study 2020 sets the various goals of learning decimal numbers during grades 3–5 and
fractions during grades 3–6 in elementary schools. It is noteworthy that there are no descriptions
of decimal numbers and fractions in the Course of Study for Junior High Schools (MEXT, 2017b). In
other words, learning of the concepts of decimals and fractions is completed in elementary
education. With this fact in mind, we examine further details of the descriptions of the Course of
Study for Elementary Schools for teaching the concepts of decimals and fractions (see Table 2). As
Table 2 shows, the description “To get to know simple fractions such as 1/2 and 1/3,” appears as
learning contents of grade 2, despite that the decimals and fractions first appear in the goals of grade
3. Except for this minor incongruence, the details of various aspects of decimals and fractions are
ordered coherently in the Course of Study’s learning contents.
Table 2: Contents of Learning Decimals and Fractions Described in Course of Study for Elementary
Schools (MEXT, 2017a)
Grade Decimal Numbers Fractions
Grade 1 (None) (None)
Grade 2 (None) To get to know simple fractions such as 1/2 and
1/3.