| Summary: | 碩士 === 國立彰化師範大學 === 科學教育研究所 === 98 === The purpose of this study is to explore the conjecturing thinking process of the students involved in a case study in a Conjecturing-centered teaching situation and further to analyze the mathematical problem solving process of students with different academical achievements. Action research method was used to conduct mathematical conjecturing activities for about six months. Teaching method was continuously improved during the two action research cycles to eventually form a mathematical teaching model centered around conjecturing.
The students of eighth grade year taught by the researcher were the subjects of this study. From them, two students from each group of low, middle and high academical achievements were selected for the case study. Data were collected from the learning sheets of mathematical conjecturing activities, the exercise sheets of students' mathematical problem solving, teachers' reflection log, class video recording, interview recording, etc. Qualitative research method was used to analyze the conjecturing thinking process of the students involved in the case study during these two action research cycles, and their mathematical problem solving process was observed.
The results of the study suggested that in a conjecturing activity-centered teaching situation:
1. Conjecturing thinking process is an individualized thinking model.
(1) Students of higher achievement are able to adjust their starting points of conjecturing thinking process according to the type of test questions and different conditions. Normally, their conjecturing thinking process will end with a generalized result.
(2) Students of average achievement are able to increase the diversity of their conjecturings through discussion with peers or within a group. Through explanation on the reason for conjecturing, students can examine their thinking and improve their conjecturing process.
(3) Students of lower achievement seldom come up with their own conjecturings. A
(4) conjecturing thinking starting with “believe it or refute it” can facilitate their conjecturing thinking process.
2. A conjecturing activity-based teaching method can inspire students to come up with more diversified problem solving strategies:
(1) Through conjecturing thinking, students of higher achievement are able to come up with more diversified problem solving strategies and verification methods.
(2) Students of average achievement are able to diversify their conjecturings through discussion within a group or by listening to the opinions from other students. Besides, they are capable of applying their conjecturing thinking process to the verification of answers.
(3) Students of lower achievement are able to guess answers to mathematical test questions in a bolder way to strengthen their motives for problem solving instead of rushing to come up with answers without conducting any analysis. Their conjecturing ability can be activated through conjecturing activities.
At last, four tangible suggestions were presented in this study to serve as reference for future teaching application and researches.
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