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Reforming of the Learning Processes in School Mathematics with Emphasizing on Mathematical Processes
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   Reforming of the Learning Processes in School Mathematics
with Emphasizing on Mathematical Processes
Dr. Maitree Inprasitha and others

The purpose of this research was threefold: 1) to investigate learning processes in school mathematics of elementary and junior highschool students using open-ended problems, 2) to construct a model for developing studentsí learning processes by implementing open-ended problems and metacognitive strategy, and 3) to disseminate the developed model to mathematics teachers in the Khon Kaen provincial areas.
This research used a qualitative methodology with 12 pairs of 4-6 grade students and another 12 pairs of 1-3 grade junior high school students. In the first phase, each pair of students solved each of three open-ended problems in a single day outside their classrooms. During the problem-solving session, research assistants conducted field notes related to studentsí important problem-solving behaviors. The research assistants then held interviews with each student in each pair respectively after problem-solving session. Audio - and video - tape recording was conducted through all sessions mentioned earlier.
The primary data to be used for protocol analysis was transcriptions of each pair of problem solving session. This data was used complementarily with data from field notes and from interview sessions, and other teaching and learning styles of participating schools. The research results from this phase have been used to construct a teaching model called ďMetacognitive Instruction ModelĒ. This model shows various factors influencing studentsí problem-solving and communication in problematic situations in classrooms. In the outer loop of the model, social and cultural factors are considered in context to be constraint to mathematical problem-solving activities. In the middle loop of the model, teaching, studentsí learning strategy, facilitation, and teachersí teaching strategy influence each other factor in a circulating manner and set a more closely related context for mathematical problem-solving activities. Particularly, in the middle loop, studentsí and teachersí strategies have their own sub-loop comprising of beliefs and previous experiences interacting with other factors in the just mentioned loop. In the inner loop, negotiation, studentsí activity, sharing, and teachersí activity are four factors interacting with each other and create the most apparent context for problem-solving and communication in the problematic situations in mathematical problem-solving activity in the classroom.
The metacognitive instruction model has two roles in this research: a hypothetical framework for characterizing teachersí and studentsí roles, and for analysis of studentsí learning processes in the classroom in the following phases: 1) The model has been used in the teaching experiment in the classroom. 2) The overall research results and the model have been disseminated to 200 mathematics teachers in the elementary and secondary schools in Khon Kaen province through workshop seminars.
The research results have revealed that: 1) using open-ended problems and protocol analysis methods for analyzing studentsí mathematical learning processes, particularly in mathematical processes, made it possible for researchers to indicate what kind of problem-solving behaviors illustrating metacognitive mathematical problemĖsolving behaviors. In other words, researchers can investigate whether each pair of students could become aware of their thinking process during mathematical problem-solving activity. In addition, the research results suggests that all open-ended problems used in this research create an appropriate situation for enhancing metacognitive mathematical problem-solving behavior. However, studentsí metacognitive problem-solving behaviors vary from problem to problem. The most apparent open-ended problems for students to demonstrate their metacognitive behaviors are wormís movement problem, telephone line, and magnetic problems in the elementary and secondary schools respectively. On the other hand, students both in elementary and secondary school demonstrated less Metacognitive behaviors in the geometrical problem; 2) In constructing metacogntive instruction model, the following factors have been taken into consideration: social and cultural factors, teachersí and studentsí beliefs and previous experiences in mathematics classrooms; 3) The research team has successfully disseminated the research results and the developed model to approximately 200 mathematics teachers from elementary and secondary schools in Khon Kaen province. From the questionnaire survey, the participant teachers suggest that open-ended approach is a promising teaching innovation consistent with the notion of reforming the learning process in current movement. They also suggest further in-service training programs in the following issues: learning process and technique in using open-ended approach in the classroom, and how to construct open-ended problems in other content areas.