J. SAENGPUN, M. INPRASITHA

pline by drill and practice, without a proper understanding of

the relationship between sign/symbol and their meanings. The

children just memorized the formal mathematics sign/symbols

without the help of any mediating tool or psychological tool.

Although the discussion given above is important theoreti-

cally, it is more important to interpret the theory for enlighten

development of a child’s semiotic activity in a school context.

This research focuses investigation on how first grade students

construct signs and symbols in solving addition problems with

the help of psychological tools in a mathematics classroom

taught by open approach. In this study, the mathematics class-

room used for analyzed is the one of mathematics classroom

innovated by “Lesson Study and Open Approach” (Inprasitha,

2010) in Thailand. The open approach as a teaching approach

(Inprasitha, 2010) used in this research was incorporated in the

process of lesson study, the core professional development

process Japanese teachers use to continually improve the qual-

ity of the learning experiences they provide to their students

(Yoshida, 1999). In Thailand, Lesson Study and Open Ap-

proach is becoming an innovation for Thai teacher professional

development that help teacher recognize this aspects of stu-

dents’ mathematics learning. In this study, the researcher pre-

sents the analysis the psychological tools that help or has a

crucial role in development of first graders’ semiotic activity in

learning how to add two numbers from Vygotsky’s cultural-

historical perspective.

Methodology

The research was carried out in one first grade mathematics

classroom including 32 students aged 6 - 7 years old and an

internship student who was classroom teacher. The mathemat-

ics classroom was choose to be target group is the one of class-

room in Ban Nam Prae school, an elementary school in Chiang

Mai province, which participated in the “Project for mathemat-

ics teacher professional development innovated by lesson study

and open approach in northern educational service areas” since

2009 academic year. The project was conducted by Center for

research in mathematics education, Khon Kaen University and

the mathematics education program, faculty of education,

Chiang Mai University.

Data were collected during November-December in the sec-

ond semester of 2010 school year and consist of daily video-

taped recording of 17 consecutive lessons on addition in first

grade mathematics classroom made by two cameras. During in

each classroom teaching, one camera focused primary on inter-

action between teacher and student, especially in whole-class

discussion. The second camera focused on students’ group

working. Moreover, documentation consists of 17 lesson plans

on addition; students’ written works; daily field notes that

summarized classroom events and student ways of thinking;

and audio taped interview with the teacher. The data from the

video recording of each class was transcribed into protocol to

be used for video analysis and discourse analysis to analyze the

semiotic activity based on the cultural-historical perspective.

The analysis focused on the method by which student make

their own sign and symbols in solving addition problem with

the help of psychological tool.

Results

From the analysis, in each lesson of the mathematics class-

room taught by Open Approach as a teaching approach has 4

steps as 1) posing open-ended problem situation 2) students’

self learning 3) whole discussion and comparison and 4) sum-

mary the lesson through connecting students’ ideas emerged in

the classroom. Three lesson (2/17, 4/17, 10/17) of a series of

seventeen addition lessons were choose to evidence the origin

and development of semiotic activity with the help of psycho-

logical tool. In the beginning of the lesson, the teacher typically

started with the presentation of the problem situation by telling

a story along with the real world objects and picture in an at-

tempt to motivate the student to learn about addition according

to the meaning of addition as “altogether” and “increasing”.

The task for first lesson, teacher ask student to express the ad-

dition sentence and think about how to add the two number (the

number of all children in play ground) in various way as fol-

lowings Figure 1.

Through this lesson, then children used units block and

base-ten blocks that teacher provided as thinking tool for solv-

ing the addition problem by decomposing and composing

strategy. Then, they drew picture and wrote up the process il-

lustrated their action in thinking about adding how to solve 9 +

4 as Figure 2.

The student reflected his thinking imagining using the num-

ber blocks and drew them up as shown above. The student took

out one single unit block and used arrow to transfer it to lining

of 9 blocks and finally showed the product of 10 to be com-

bined with the rest 3 blocks making the final product of 13. The

drawing was a psychological tool for developing semiotic ac-

tivity showing the thinking process using the blocks, which

served as the signifiers (meaning of addition) and the signified

(using the block in order to make ten).

Moreover, in the lesson 4/17 on the activity-Adding 8 + 3 I

can do it the students used the idea discussed in the previous

lesson in solving addition problem 8 + 3 from which the teacher

Problem: Nine students are playing with the sandbox and four ones are

playing on a slide. How many students are there in all? Tasks: 1) Write

mathematic al sentence; 2) Show how to calculate t his.

Figure 1.

Problem situation in lesson 2/17.

Figure 2.

Student’s drawing showing using unit blocks as a tool for decomposing.

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