The Textbook Analysis on Multiplication:The Case of Japan, Singapore and Thailand

doi:10.4236/ce.2013.44038

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Creative Education

2013. Vol.4, No.4, 259-262

Published Online April 2013 in SciRes (http://www.scirp.org/journal/ce) DOI:10.4236/ce.2013.44038

The Textbook Analysis on Multiplication:

The Case of Japan, Singapore and Thailand

Suttharat Boonlerts1, Maitree Inprasitha2,3

1Department of Mathematics Education, Faculty of Education, Khon Kaen University, Khon Kaen, Thailand

2Center for Research in Mathematics Education, Khon Kaen University , Khon Kaen, Thailand

3Centre of Excellence in Mathematics, Commis s i o n of Higher Education in Thailand (CHE), Bangkok, Thailand

Email: [email protected]

Received January 29th, 2013; revised February 28th, 2013; accepted March 15th, 2013

Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any

medium, provided the original work is properly c ite d.

This paper analyzes the presentation of multiplication in elementary textbooks from Japan, Singapore and

Thailand. The methodology consisted of content analysis comparing the overall structure and sequence of

topics and how to introduce the meaning of multiplication. We identified both similarities and differences

among the three countries.

Keywords: Multiplication; Mathematics Textbook; Content Analysis; Comparative Study

Introduction

This paper presents an analysis of the presentation of multi-

plication in elementary textbooks from Japan, Singapore, and

Thailand. Textbooks from these Asian countries were targeted

because these counties represent different levels of perform-

ances in the TIMSS (1995, 1999, 2003, 2007); Singaporean and

Japanese students performed well, while Thai students per-

formed poorly. Thus, this study is aimed at investigating the

features of textbooks, which Fan & Zhu (2007) mentioned that

the teachers and students used with an underlying belief that

textbooks played an important role in the process of teaching

and learning.

Various researches have revealed that the teaching ap-

proaches adopted by classroom teachers and embodied in text-

books used in their classrooms are often highly alike (e.g.

Bierhoff, 1996; Brown, 1973; Fan & Kealey, 2000; Fujii, 2001;

Fan & Zhu, 2007).

“Multiplication” was widely discussed among the mathe-

matics education research groups as a difficult topic in the cur-

riculum (Anghileri, 1989; Bell et al., 1989; Graeber & Tanen-

haus, 1993; Behr et al., 1994; Confrey & Smith, 1995; Chung

& Lew, 2007; Mulligan & Mitchelmore, 1997; Irwin, 2004).

Gelman (1999) suggested that multiplicative concepts are not

among the naïve mathematical concepts learned by all. Piaget

(1985, 1987 cited in Irwin, 2004) asserted that multiplication is

more complex than addition, as it involves implicit quantifica-

tion. Students who operate multiplicatively know that there is a

certain quantity in each of the numbers multiplied, but do not

need to refer to the individual items or numbers in a group.

The study examined elementary textbooks from Grades 1 - 3,

and similarities and differences in the presentation of multipli-

cation in elementary mathematics textbooks in three countries

were documented. It addressed the following question: When

and how is multiplication introduced and developed?

Method

In this section, the study describes the selection of textbooks

chosen for examination and the conceptual frameworks used to

analyze the presentation of multiplication in these books.

Selection of Textbooks

Three elementary mathematics textbook series from Japan,

Singapore, and Thailand were chosen for this study. These

three countries come from East Asia and South East Asia.

Singapore is one of the Asian countries where the students

always score well. In 1995, 1999 and 2003, students from Sin-

gapore were ranked number one in the world and fell to third

place in 1997. Japanese students ranked 3rd in 1995, 5th in

1999, 3rd in 2003 and 5th in 2007. Thai students ranked 22nd

in 1995, 27th in 1999, and 29th in 2007 respectively. The over-

all score consistently was below average in every assessment

despite the changing composition of participating countries

with each study (TIMSS, 1995, 1999, 2003, 2007).

Thailand sets a national curriculum, and a single textbook se-

ries is used throughout the country. The Ministry of Education

distributes the mathematics textbooks used in Thailand, which

is developed by the Institute for the Promotion of Teaching

Science and Technology (IPST).

Japan also sets a national curriculum, but six commercial

textbook series are available for use in the schools (Alajmi,

2011). In Japan, private companies publish the textbooks,

which are based on the Course of Study and the Accompanying

Teaching Guide published by the Ministry of Education (Isoda,

2010). All textbooks must pass through the textbook authoriza-

tion process that is overseen by the Textbook Authorization

Council. At present, there six publishers offer mathematics

textbooks for elementary and a lower range of secondary

schools (Shimizu & Watanabe, 2010).

S. BOONLERTS, M. INPRASIT HA

Singapore is similar to many other Asian countries; the Min-

istry of Education (MOE) develops and issues a national

mathematics curriculum (syllabus), and all schools are required

to follow the syllabus in teaching, learning, and assessment.

Accordingly, textbooks must align with the syllabus. All school

textbooks in Singapore first must be reviewed and approved by

an evaluation committee appointed by the Ministry of Educa-

tion (Fan, 2010).

For Japan and Singapore, textbooks in this study were se-

lected from one publishing company and based on their wide

use by schools. These Japan textbooks were translated into the

Thai Language in 2009. This Thai version has been in use in

the 22 Schools participating in the Research project. The Sin-

gapore textbooks, which are published in English, have been

used in some Thai bilingual schools In total, the following 14

mathematics textbooks from the three countries were examined

in this study: in Japan, five Mathematics for Elementary School

for grades 1 - 3 published by Gakkoh Tosho were selected; in

Singapore, six “My Pals Are Here” (2nd ed.), published by

Marshall Cavendish Education (2010) were selected for first to

third Grades, in Thailand, three mathematics textbooks are

provided for first to third Grades and published by IPST.

Conceptual Frameworks

Two conceptual frameworks were used to analyze the pres-

entation of multiplication in mathematics textbooks through

content analysis reported Son & Senk (2010). These analyses

focused on aspects of the textbooks Overall structure (number

of units or lessons and sequence of topics)

The analysis of the textbooks’ content focused on the prob-

lem situations in multiplication in each textbook. Using Greer’s

the classes of situations involving multiplication and division of

integers: equal groups, multiplication comparison, Cartesian

product, and rectangular area (Table 1). This study analyzed

problems in the entire textbook.

Results

The study examines the overall structure and sequence of

topics in the textbooks and the general format of each lesson.

The Overall Structure and Sequence of Topics

In each country, all the textbooks in grades 1 - 3 present

number and operation (addition subtraction, multiplication,

division of whole number), geometry (shape, volume, length,

mass) and table and graph. Only the Singapore series contains

different content in the textbook such as fractions, area and

perimeter, perpendicular and parallel lines.

The Thai textbooks present a chapter on multiplication in

each grade (2nd and 3rd grades) and have one chapter that be

related, is review, word problem and making problem of addi-

tion, subtraction, multiplication and division. Singapore and

Japanese textbooks consist of several chapters in each grade.

For example, Japanese textbooks for second grade consists of

(1): expression as a multiplication sentence, multiplication (2):

The 2×, 5×, 3× 4× multiplication table, multiplication (3): the

6×,7×,8×,9×, 1× multiplication table, and multiplication (4):

multiplication game, multiplication table. Similarly, Singapore

textbooks consist of several chapters for multiplication in each

grade.

The Japanese and Thai textbooks begin teaching multiplica-

tion in the second grade whereas Singapore textbooks introduce

multiplication in the first grade.

In the Japanese second grade textbooks, the sequences of

topics in multiplication are: learning unit 1; the meaning of

multiplication, multiplication sentence, unit 2: the multiplica-

tion tables of 2, 5, 3, 4, unit 3: multiplication tables of 6, 7, 8, 9,

1, and unit 4: multiplication table, multiplication game. In sum-

mary, the learning units of multiplication are organized as the

meaning of multiplication, multiplicands, multipliers, and mul-

tiplication table. The laws of calculation (commutative, asso-

ciative, and distributive), algorithm and the rules of multiplica-

tion are introduced in the elementary mathematics textbooks.

In the Singapore textbooks, the meaning of multiplication is

introduced through the use of equal-sized groups and arrays.

The chapter is divided into small topic, such as in first grade,

making multiplication stories and solving word problems. In

second grade, the meaning of multiplication is defined by re-

lating to whole number system through many representations,

including equal-sized groups, array, and equal “jumps” on

number line for multiplication. Students learn the basic multi-

plication facts and computation. Singapore textbooks follow the

following sequences: the topic of multiplication tables of 2, 3, 4,

5 and 10 in second grade and multiplication tables of 6, 7, 8 and

9 in third grade. They use the properties of addition and multi-

plication (commutative, associative and distributive properties,

without being named) to multiply in the whole numbers system

and apply increasingly sophisticated strategies with these prop-

erties to solve multiplication and division problems involving

the basic facts. By comparing the variety of solution strategies,

students set multiplication and division as inverse operations.

Thai textbooks begin teaching multiplication in the second

grade. There are 46 pages in the chapter on multiplication, with

the introduction of the meaning of multiplication making up

approximately 8.7% and the procedural rules of multiplication

takes up 50%. In the third grade the emphasis is on procedural

rules and obtaining results (Table 2). Thai textbooks have a

sequence of topic of multiplication tables of 2, 3, 4, 5, 6, 7, 8

and 9 in the second grade. In second grade and third grades

they emphasize procedural calculation.

Meaning Given to Multiplication

The content analysis of the multiplication content found that

Japanese, Singapore and Thai textbooks have similar and dif-

ferent issues in the sequence of introducing multiplication,

meaning of multiplication. It can be summarized as follows

(Table 3).

Singapore and Thai mathematics textbooks are similar in in-

troducing the meaning of multiplication through equal group

with repeated addition, while Japanese mathematics textbooks

start with presenting the description of multiplication through

equal group, then presenting repeated addition later.

Discussion

The results of the content analysis indicate that Japanese

textbooks devoted more pages to multiplication than Thai and

Singapore textbooks. However, the percentage of pages is not

enough to justify the importance of multiplication topic in the

textbook. Other aspects of the textbook were analyzed. While

Singapore textbooks begin teaching multiplication in the first

grade, Thai and Japanese textbooks begin in the second grade.

Japanese and Singapore mathematics textbooks emphasized the

260

S. BOONLERTS, M. INPRASIT HA

Table 1.

The classes of situations involving multiplication of integers (Greer, 1992).

Type of

situation Description Example

The mathematization of cases of natural Replication n people have 5n fingers

Repetition of a sequence of actions Taking three s teps four times

Equal grou ps

Human practices such as giving the same number of

objects to a number of people. The equal-groups

situation is in terms of a rate.

If there are 4 cookies per child, how many do 3

children have?

Multiplication comparison n times as many as

John has 3 times as many apples as Mary. Mary has 4

apples. How many apples does John have?

Cartesian product If 4 boys and 3 girls are dancing, how many different

partnerships are possible?

Rectangular area

The rectangle with integer side s , say 4 cm by 3 cm. On the

rectangular array, such a diagram bears an obvious simi-

larity to the physical arrangement of m  n objects in a

rectangular array with m rows and n columns.

Table 2.

The number of ch apters and pages on mul tiplication in each book series by grade.

Countries

Number of chapters and pages on multiplication in each

book ser i es by grade Japan Singapore Thailand

Grade 1 2 3 1 2 3 1 2 3

Number of chapters in the bo ok 13 17 15 19 17 18 14 12 12

Number of pages in text book 124 184 208 269 310 310 284 250 254

Number of pages in text book - 4 3 1 4 3 - 2 2

Number of pages in multiplicatio n - 57 47 9 63 34 - 51 46

Percent of pages with multiplication - 30.9 22.6 3.3 20.3 11 - 20.4 18.3

Table 3.

The analysis of types of multiplication

Countries Types of situatio ns

Japan Equal grou p , rectangular array, and multiplica ti ve

comparison

Singapore An equal gro up and recta ng ul ar array

Thailand Equal group

topics on the meaning of multiplication, the multiplier and mul-

tiplicand distinction, and the multiplication tables. By contrast,

Thai textbooks emphasized operations and manipulation of

numbers.

Through situation analysis, it was found that there are three

kinds of situations, equal group, rectangular array, and multi-

plicative comparison, in Singapore textbooks, two kinds of

situations, equal group and rectangular array in Japanese text-

books, and only one kind of situation, equal group, in Thai

textbooks. Kouba and Franklin (1993) point out “It is crucial

that children in grades K-4 have experience with a wide range

of multiplication and division situations. The rank of situations

should be expanding.” Greer (1992) found that the most impor-

tant class situations involving multiplication and division of

integers include: equal groups; multiplication comparison; Car-

tesian product; rectangular area.

Conclusion

Japan and Singapore have always ranked high in mathemat-

ics achievement in international assessments such as TIMSS

and PISA (Singapore participated in PISA for the first time in

2009) for more than a decade, while Thailand, like many other

non-affluent countries has been ranked below average. Com-

paring what teachers teach and what students learn in those

countries will provide useful information to improve mathe-

matics instruction in Thailand and other countries facing similar

problems.

Acknowledgements

This research is (partially) supported by the Centre of Excel-

lence in Mathematics, the Higher Education Research Promo-

tion and National Research University Project of Thailand,

Office of the Higher Education Commission, through the Clus-

ter of Research to Enhance the Quality of Basic Education, the

Office of the Higher Education, Graduate School Khon Kaen

University, Center for Research in Mathematics Education, Khon

Kaen University, Thailand for supporting by grant fund under

S. BOONLERTS, M. INPRASIT HA

the program Strategic Scholarships for Frontier Research Net-

work for the Ph.D. Program Thai Doctoral degree Commission

for this research

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