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

Copyright © 2013 SciRe s .

260