S. LAAH-ON ET AL.

Summariza tion through

connec ti ng st udents’

mathematical ideas emerged

in the classr oom

Whole c lass discussion

and comparison

Students’ self learning

Posing open-ended problem

Figure 1.

Open approach as a teaching approach (Inprasitha, 2010).

the classroom (Inprasitha, 2010).

Illustration of classroom activities using the open approach

(Table 1) could be described as 1) Posing open-ended problem

—the open-ended problems or problem situations are posed in

the classroom and the students are often asked about a meaning

of the problems and challenged to solve the problems; 2) Stu-

dents’ self learning—this phase consists of a combination of

two parts: individual work and discussion by the whole class; 3)

Whole class discussion and comparison—the students’ activi-

ties are crucial to further development of a lesson in which the

teacher should try to identify those students who do not under-

stand the problems and provide more suggestions to stimulate

the students in a whole class to think according to the problems;

and 4) Summarization through connecting students’ mathe-

matical ideas emerging in the classroom—the teacher should

include all students’ prepositions and concentrate on one point

view, lead to a conclusion by integrating and arranging them

according to particular point of view, and also facilitate a

smooth transition to the next lesson (Inprasitha, 2010).

Moreover, the teachers mostly start the classes with a prob-

lem situation which is designed by using open-ended problems

and is closed to the students experience or what the students

have learned, and the learning organization in this classroom is

considered as a interaction process between a teacher and stu-

dents, and among students themselves where the teacher or-

chestrate the students’ mathematical ideas resulted from pro-

moting the students to think and solve the problems in their

own way. Therefore this process can be described by social and

cultural aspects (Inprasitha, Pattanajak, & Prakaikam, 2007).

These mean that the approach in this classroom necessarily

nurtures the students to learn mathematics in meaningful ways

according with the students own experiences.

As a result, what is needed for the teachers or mathematical

cultivator is a broad understanding of mathematics as a cultural

phenomena (Bishop, 1988). Therefore, the teachers should be

conscious about what kind of experiences the students could

learn best in mathematical culture. According to these points,

deep insight of the problem solving mathematics classroom is

very important for the teachers. Lesson study, consequently, is

necessary for the teachers to do their practices along with a

cycle of the lesson study (Figure 2). Collaboratively observing

the research lesson (Do) and collaboratively reflecting on

teaching practice (See) would support the teachers to compre-

hend their classroom where they could analyze the activities

occurring in the classroom and promote the students’ learning

according with the activities.

Research Methodology

Theoretical Frameworks

The theoretical frameworks used to conduct this research

Collaboratively de sign

research l esson

Plan

Collaboratively observe

the research lesson

(Do)

Collaborati vely reflect on

teaching p ractice

(See)

Figure 2.

Lesson study in Thailand (Inprasitha, 2010).

were composed of 2 theoretical frameworks; 1) Open Approach

as a Teaching Approach (Inprasitha, 2010) used to analyze

phases of the classroom that emphasize on problem solving,

and 2) Key Universal Activities (Bishop, 1988) used to ana-

lyzed activities occurred in each phase of the classroom

whether these activities composed of the key universal activi-

ties which are the foundations for students’ mathematical learn-

ing.

Objective of the Study

This research was aimed to investigate key universal activi-

ties, in which are the foundations for students’ mathematical

learning based on Bishop (1988), in the problem solving

mathematics classroom, in which the open approach is used as

the teaching approach based on Inprasitha (2011), that would

yield more realization for the teachers of how to promote the

students’ learning in meaningful ways.

Target Group of the Study

The target group in this research included six of grade 1 stu-

dents, who were studying at Ban Bueng-neum-bueng-krai-noon

School, Khonkaen province, and attending 5 learning activities

of the Length Comparison learning unit in the second semester

of the 2010 school year. The school has been participating in

the Project for Professional Development of Mathematics

Teachers through Lesson Study and Open Approach since 2007

school year, the teachers have been organizing learning activi-

ties by using the open approach as a teaching approach which is

supervised by the Center for Research in Mathematics Educa-

tion (CRME), Khon Kaen University.

Data Collection and Analysis

In this research, the lesson study team, including the teacher,

observing teachers, the author as a researcher, and a researcher

assistant, cooperatively designed the learning activities by using

a Japanese textbook “Study with Your Friends Mathematics for

Elementary School 1st grade” which emphasizing on “students’

how to learn” that supports students’ self learning (Inprasitha,

2010). Several methods were used to collect and analyze the

data in the classroom; video and audio recording, and field note

taking were used as methods for collecting data, the collected

data were then analyzed by using descriptive statistic and pre-

sented by using analytic description.

Results and Discussions

In the problem solving mathematics classroom of the learn-

ing unit of comparing length, there were all of 6 key universal

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