By Marsigit

Introduction

This research investigated teacher’s role and students’ activities to construct the comprehensive characteristics of numbers pattern in mathematics teaching at the 6th grade students of primary school. The aim of the study is to explore the role of teacher and the students’ activities in three different cycle of classroom action research. The activities are interpreted in the context of the students’ efforts to construct the comprehensive characteristics of numbers pattern. The analysis focuses on the way in which the teacher’s and students’ activities developed in their interactions. This study bounds territory in which events or processes occurred over a specified period. The framework of research is teaching action in mathematics teaching of Primary School Grade VI. Teacher is perceived to be co-worker in doing research and the researcher is not considered to an outside expert. Thus, the approach of the research is an evaluative-reflective-participatory-critical collaborative enquiry of teaching. In this research we have developed three cycles of classroom action research (CAR) of different teaching schemas which forms part of common practice in an educational setting. They aimed to extend children’s learning from cycle 1 to cycle 3 provide the students’ experience to develop their concepts.

The 1st cycle

In the first cycle, the teacher aimed the students to have some competencies to characterize some pattern of numbers producing by doing addition from any kind of two reversible numbers. The schema of teaching learning process in the 1st cycle was characterized as follows. Firstly, the teacher introduced the lesson, delivered information, posed the problems and explained what the students should do in the following activities. Secondly, having had ordering the students to produce additions from any kind of two reversible numbers, the teacher let the students to work in group-discussion; totally there were 8 group-discussions, each consisted of 4 students. Thirdly, the teacher encouraged the students to present their results of discussions and then strive to conclude the results. In this cycle the teacher developed worksheets and distributed them before the students work in their group-discussions.

The first step in the analysis was to provide a broad description of the sequence of events during the 1st cycle. In the 1st cycle it was recorded that there was considerable variation in terms of student’s activities. The recorded detail brief descriptions of the sessions were used to refer to analyze and to get feedback for preparing the 2nd cycle. In this session we found that there are some characteristics of students’ efforts to construct their knowledge. Some students indicated that they activities were routine execution of tasks; however, ideas are developed and they try to construct the concepts. Interaction in 1st cycle was characterized as an obvious discussion to share understanding among the children.

The students’ activity reflects their deep engagement and interest in the problem solving task There was no indication that the students has a conflict mode to reflects disagreement, however the dominantly role of a certain student begun to be an evident. It was indicated that with the developed schema of teaching learning processes the teacher did not explicitly force their students to pursue the aims of teaching. On the other hand, she encouraged students’ activities towards the achievement of goals by taking the benefits from asymmetrical relationship between teacher and their students and among the students themselves in group-discussion. Some aspects of students’ constructions of their knowledge were invisible and some of them were invisible.

The 2nd cycle

In the 2nd cycle, the teacher aimed the students to have some competencies to characterize some pattern of numbers producing by doing subtraction from any kind of two reversible numbers. The schema of teaching learning process in the 2nd cycle was characterized as follows. Firstly, the teacher introduced the lesson, delivered information, posed the problems and explained what the students should do in the following activities. Secondly, having had ordering the students to produce subtractions from any kind of two reversible numbers, the teacher let the students to work in group-discussion; totally there were 8 group-discussions, each consisted of 4 students. Thirdly, the teacher encouraged the students to present their results of discussions and then strive to conclude the results. In this cycle the teacher developed worksheets and distributed them before the students work in their group-discussions.

The analysis of session in the 2nd cycle examines the ways in which teacher’s approach and process of teaching tasks in their small-group activities. It aims at highlighting students’ activities and situated positions towards knowledge, learning to construct their knowledge. In this session, students are seen as dynamic and contextual in nature, being socially constructed in their interactions small-group discussions. The students’ activity reflects their deep engagement and interest in the problem solving task. There were no indications that the students did not focus on the task. Interaction in 2nd cycle was characterized as an obvious collaborative interaction. The students were not working individually in the group but developed their ideas together. The teacher encouraged students’ activities towards the achievement of goals by taking the benefits from asymmetrical relationship between teacher and their students and among the students themselves in group-discussion.

There were several examples of conversations in which some students did not want their talking to be heard by the teacher; on the other word, the teacher needed to give enough time for them to have a discussion in a certain group. There was no indication that the student has a conflict mode to reflect disagreement. In this entire session there was no indication of the students to refuse to engage in certain activity. Some aspects of students’ constructions of their knowledge were visible and some of them were invisible.

The 3rd cycle

In the 3rd cycle, the teacher aimed the students to have some competencies to characterize some pattern of numbers producing by doing multiplication from any kind of two reversible numbers. The schema of teaching learning process in the 3rd cycle was characterized as follows. Firstly, the teacher introduced the lesson, delivered information, posed the problems and explained what the students should do in the following activities. Secondly, having had ordering the students to produce multiplications from any kind of two reversible numbers, the teacher let the students to work in group-discussion; totally there were 8 group-discussions, each consisted of 4 students. Thirdly, the teacher encouraged the students to present their results of discussions and then strive to conclude the results. In this cycle the teacher developed worksheets and distributed them before the students work in their group-discussions.

In this session, collaborations in group-discussion reflected balancing in students’ social status and power. The constructive interaction among the students reflects various different understandings in a rational way by giving judgments and justifications. This led them to share their understanding of the concepts; it was indicated by their showing for helping and explaining for the purpose of assisting the other to understand the problems. In this session, there were indications that different group-discussion require different situational teacher intervention. The students’ activity reflects their deep engagement and interest in the problem solving task

There was no indication that the students have a conflict mode to reflect disagreement. The teacher encouraged students’ activities towards the achievement of goals by taking the benefits from asymmetrical relationship between teacher and their students and among the students themselves in group-discussion. The results of observations indicated that, among the students, there were various interests of different activities and different way to construct their activities. Some of the children have a separate discussion in the same group-discussion; while others initiated a variety of activities; others kept on the task and the left concentrated to prepare the answer orally the teacher’s question. Most aspects of students’ constructions of their knowledge were visible.

Results

In this study we have been concerned with describing and understanding interactions between teacher and their students and among the students themselves in group-discussions. The theoretical notions from which our analysis started were activity theory, constructive and the concept of guided participation. In particular, the students’ activities and the teacher’s role to encourage them are aspects that were highlighted in this study. Theoretical framework indicated that that the teacher used to emphasize her goal and then directs the students towards it. In group-discussions setting, the unfolding and development of activities is seen both implicitly and explicitly, also there were indications that there were opportunities for students to develop their understanding. When activities did not have a clear endpoint, both the teacher was able to influence the course of the activity, in line with her own interests.

The teacher’s role in the activity would be difficult to interpret in the absence of information about the principles group-discussions. The teacher’s perceptions of her role in supporting children’s learning and their intentions for the activity seemed to be changed from one cycle to the next one; and in the entire her activities this also seemed to be evident; one of indication was that the fact that in the initial interviews the teacher described her intentions in general terms and saw the building activity as a vehicle for general cognitive development was not so clear. Teacher’s introductions at any cycle may then be seen as related to the general aims which were adaptable to the development of the individual child. The teacher’s role became one of important factors for their children to develop their cognitive among their constraints in group-discussions. These important roles were not only evident in her having an awareness of the developmental goals, but also the knowledge of their students, her sensitivities to the student’s interests and motivation.

There were indications that in each cycle the students were not only simply behave as the performer of the activities but also as the active agent in constructing the activities themselves. Some students were not only remained in their role as the constructor in much of the sessions but also actively adopted other roles while the teacher taking on the role of assistant. The strike effect of activity in group-discussions was that conversational skill of them became the evident; some of them deliver their own initiations, and the other students seemed to take in such a defensive position on their arguments. By observing on the transitions from one activity to another, it became evident that an important aspect of the interaction was concerned with activities of negotiation. Students’ way to achieve the tasks seemed to be different; some did them through quiet persistence and others through explicit way.

References

Brannen, J., 1992, Mixing Methods: Qualitative and Quantitative Research, Aldershot: Averbury.

Miles, M.B. and Huberman, A.M, 1994, Qualitative Data Analysis: An Expanded Sourcebook, London: Sage Publications.

Shuard, H., 'Issues for curriculum development in primary mathematics' in Bourne, J., 1994, Thingking Through Prac¬tice, London: Routledge.

Tangyong, A.F., Gardner, R. (1994) 'The Active Learning Through Professional Support (ALPS)

project in Indonesia' in Beyond Jomtien, (1994) Implementing Primary Education for All, London :The MacMillan Press

Yin, R.K., 1993, Applications of Case Study Research: Applied Social Research Methods

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