T. NOPARIT, J. SAENGPUN

in two parts; the first is teachers’ lacking knowledge for teach-

ing fraction with understanding of proportional relationship and

the second is lacking linkage between fractions and proportion

in mathematics textbooks.

Japanese mathematics textbooks introduced how to think

about calculation of fraction with proportional number line in

order to develop the way students learn to calculate fraction by/

for themselves (Isoda, 2010). As Kishimoto (2010) defined a

proportional number line as use of two number lines to show

the multiplicative relationship between two quantities, and can

also be referred to as a line segment diagram, a multiple line

diagram, a double number line, or a functional scale. The pro-

portional line first came to be widely used in mathematics edu-

cation when the Japanese educational guidelines announced in

1958 assigned the “concept of ratios” as the implication behind

the multiplication and division of decimals and fraction (Ki-

shimoto, 2010). Typical Japanese mathematics textbook (e.g.

Gakkoh Tosho, 1995) first used tape diagram represent the

quantities at first grade and used tape diagram as a graphic

representation of multiplication in fifth grade on unit about

decimal multiplication, and the use of proportional number line

to calculate multiplication and division problem in sixth grade

since 1971. This approach is the consequence of the hundred

years of lesson study, Japanese teacher professional develop-

ment system.

Thailand has adopted lesson study to teacher education by

Center for Research in Mathematics Education, Khon Kaen

University since 2004. Inprasitha (2010) took open approach as

a teaching approach incorporating with lesson study process in

order to provide teacher who come to work collaboratively with

construct task and problem situation to teach student learning

and thinking by/for themselves. In Thailand, lesson study and

open approach is then becoming an innovation for Thai teacher

professional development that helps teacher recognize this as-

pect of students’ mathematics learning. The Open Approach as

“problem solving approach” used in Japan is one shared theory

for developing children who learn mathematics by/for them-

selves (Isoda, 2010). It includes teaching about learning how to

learn. The students often gain opportunities to learn mathemat-

ics with understanding and meaningful. Inprasitha (2010) has

conceived that the “Open Approach” is a teaching approach

used in cooperated with lesson study to design learning units

and lesson plans. The open approach is consisted of 4 steps as

follows: 1) posing open-ended problem situations, 2) students’

self-learning, 3) whole-class discussion and comparison, and 4)

summarization through connecting students’ mathematical

ideas emerged in the classroom.

One feature of lesson study in Thailand is usage of Japanese

elementary mathematics textbooks (e.g. Gakkoh Tosho, 1995)

to design unit and problem situation for teaching in real math-

ematics classroom. A group of student teacher from faculty of

education majoring in mathematics has participated in lesson

study and open approach project. They worked with in-service

teachers in lesson study process for one academic year and they

usually use the Japanese textbook as tool for their planning the

lesson. Although they have trained for teaching through open

approach, they often struggle with the concept of calculation on

fraction with proportional number line embedded in their text-

book. With their effort to beyond the struggle, in seminar class

for student teacher they took this topic to discuss with their peer

and supervisors to think critically on this subject matter and

how teaching should be. In this case, the authors concerned that

the teachers’ learning for teaching mathematics in their profes-

sional development is a crucial role to enhance and support stu-

dents’ learning (Ball et al., 2008; Ma, 1999).

This study aims to provide detailed insight into student

teacher’s learning by examining how they use proportional

number line to teach multiplication and division of fractions.

Specifically, we concerned what knowledge student teachers

gained from using Japanese mathematics textbooks plentiful

with proportional number line and also analyzed the student

learning process and outcomes from their teaching through each

step of open approach.

Context and Methodology

This study is a case study qualitative research. The study was

employed teaching experiment (Cobb and Steffe, 1983) for

conducting the research. Two case studies of mathematics stu-

dent from program in mathematics education, Chiang Mai Uni-

versity, who taught in sixth grade in Chum Chon Ban Bua Krok

Noi school and Ban Mae Sa school, the elementary schools in

Chiang Mai province, which participated in the “Project for

mathematics teacher professional development innovated by

lesson study and open approach in northern educational service

areas” since 2009 academic year. The project was conducted by

the center for research in mathematics education, Khon Kaen

University and the mathematics education program, faculty of

education, Chiang Mai University.

The teaching experiment was carried out in two sixth grade

mathematics classroom which is each class taught by each stu-

dent teacher. The first class includes 41 students aged 11 - 12

year and another class with 26 students the same age. Each

student teacher taught two chapters on “Multiplication and Di-

vision of Fraction” according to the sixth grade Japanese ele-

mentary mathematics textbook volume 2 (Gakkoh Tosho,

1995). The first chapter includes “Calculations of Fraction ×

Whole Number” and “Calculations of Fraction ÷ Whole Num-

ber”. Another chapter includes “Calculations of Fraction ×

Fraction” and “Calculations of Fraction ÷ Fraction”.

Data were collected during December 2012-January 2013 in

the second semester of 2012 school year and included daily

videotaped recording of whole unit consecutive lessons on

“Multiplication and Division of Fraction” in their mathematics

classroom teaching made by two cameras. During each class-

room teaching, one camera focused primary on interaction be-

tween teacher and student, especially in whole-class discussion.

The second camera focused on students’ group working.

Moreover, documentation consists of lesson plans; students’

written works; daily field notes that summarized classroom

events and student’s ways of thinking. The data from the class-

room video recordings of each class were transcribed into pro-

tocol and analyzed the way student teachers use proportional

number line in teaching calculation of fractions by video analy-

sis. After teaching the unit, the authors interviewed the student

teacher after they already taught the unit with the series ques-

tions in theme of “What you have learned for teaching calcula-

tion of fraction with proportional number line in context of

lesson study and open approach?” The interview was recorded,

and the transcripts were analyzed according with the video

record.

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