A. SURIYON ET AL.

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The data analysis results from Table 2 show the average time

used in each teaching step from the total number of study peri-

ods, 6. The study results also show that the time used differs in

each step, and there is an accounting provided of the time used

from most to least. The first order was the second step taking

approximately 29 minutes, 37 seconds. The third step taking 18

minutes, 49 seconds was ranked second. The fourth step took

10 minutes, 41 seconds, and the first took the least time, 5 min-

utes, 59 seconds. The total time used towards activity manage-

ment was 1 hour, 5 minutes, 5 seconds per study period.

3) Structure of students’ performing activities

Students participated in performing activities in 4 open ap-

proach-based teaching steps with different aims depending on

the intended purposes of learning for each study period, mathe-

matical contents, as well as the aim of monitoring students’

ideas. The structure of students performing activities is charac-

terized by 3 kinds of activities.

Individual activity is defined as an activity in which a teacher

requires each student to demonstrate ideas and methods of p rob-

lem solving by writing ideas from documents or writing ideas

on a piece of paper and then presenting these ideas (one person

per one piece of work). This activity emphasizes completing

exercises at the end of a study period for each learning unit

including activities in the learning unit 8 on addition (2) in the

study period 11/12 and review exercises.

Sub-group activity is an activity in which the teacher requests

a student who is a member of his or her group to show ideas

and ways of problem solving by writing ideas from documents

or writing ideas on a piece of paper and then presenting those

ideas (one group per 1-2 pieces of work). The number of mem-

bers of each group was between 3 and 5 people. Students de-

termined tasks for each member, and members of each group

studied together and presented their work in front of the class.

This kind of activity mainly emphasizes solving problems to-

gether. The first step consisted of presenting open-ended situa-

tion problems which could be taken from the activities in the

learning unit 8 on addition (2), in period 1/12, Children Playing

in Sandboxes and on Slides, in period 3/12, Buying Eggs to

Make Omelets, in period 6/12, Delighted Natalie including

activities in the learning unit 9 on subtraction (2), in period

11/13, and the learning unit 9 on addition or subtraction, in

period 5/5, Coming Train.

Whole class activity is an activity in which the teacher re-

quests a student who is a member of the class to show ideas and

ways of problem solving by writing ideas from documents or

writing ideas on a piece of paper and then presenting ideas (one

group per one piece of work or one group per 1-2 pieces of

work). Individual activities or group activities may be used for

whole class activities. Whole class activities in the research

were characterized by competition games included in activities

in the learning unit 8 on addition (2), in period 9/12, Let’s Ar-

range Cards, in period 10/12, Let’s Play Cards on Addition,

and in period 12/12, Wheel Ring of Addition.

4) Structure of student work presentation

The structure of the student work presentation in the mathe-

matic classroom using the open approach is described as fol-

lows.

a) The teacher was tasked to assign a group to give a presen-

tation with instructions provided for putting the presentations in

correct order based on incorrect ideas, uncomplicated ones, or

the ones that most students could perform. First, the teacher

presented the aforementioned ideas in order to illustrate the

required tasks. Next, the teacher chose complicated ideas and

the ideas that a small number of students could perform, which

were the concepts that reflected advances in achievement ac-

cording to purposes of each study period before entering the

next step.

b) After a person on behalf of his group finished giving a

presentation in front of the class, the audience asked questions

by raising their hands to show their intention to set problems or

ask questions.

c) When the person who gave a presentation got a question,

he then answered the question, or the teacher prompted mem-

bers in each group to help each other determine answers or

participate in showing opinions.

d) When there was no question, the person who gave a pres-

entation went back to his group. For group tasks posted on the

black board, the person who gave a presentation could not take

his group task back to his group because the specific task would

then be used for comparing ideas from each group and for

drawing conclusions to connect with ideas emerging in the next

step.

The Roles of Teacher in the Classroom

The data analysis findings on the teacher’s teaching behavior

in the open approach-based mathematics classroom illustrated

that in each teaching step, the teacher played an important role

in the development of students’ metacognitive strategies. Spe-

cifics for each of the teaching steps are detailed below.

Step 1 Posing open-ended problems: In this step, the teacher

was tasked as “a motivator” in order to allow students the op-

portunity to participate in problem solving and better under-

stand problems with an emphasis on students’ interpretations of

pictures or media used for presenting problem situations and

the teacher’s use of motivating questions such as the following

conversation in the learning unit 8, in period 1/12, Buying Eggs

to Make Omelets.

Teacher: “Well, look at this (posting the picture on the

blackboard). What is it?”

Students: Saying “Wow!” (all together, the whole class)

Student A: “It is a picture of people playing on swings”

Student B: “and playing in the sand”

(The student describes the picture as he sees it on the

board).

Moreover, the teacher encouraged students to take on more

participation as a demonstrator or as a person who took the

initiative or used role playing by calling on students in the class

to act out the proposed situation.

Step 2 Students’ self learning: In this step, the teacher was

tasked as “a supporter and a facilitator” with the intent to help

students more effectively and to realize her role of getting in-

volved in students’ problem solving. The aim of the second step

was that students learned to solve problems by themselves; that

is to say, the teacher could help students when they needed help

or asked clarification questions which could arise after they

encountered difficulties in problem solving. The teacher could

give advice to students so that they could solve problems and

overcome difficulties in problem solving by themselves. How-

ever, a teacher’s role did not include providing ways of solving

problems or giving answers to students. As for the teacher’s