| Summary: | 碩士 === 國立新竹教育大學 === 數理教育研究所 === 104 === Mathematical reasoning is a method of communicating concepts of mathematical convepts between teachers and students. This method has gradually gained its importance in mathematical education. Based on the case study method, this research aims to analyze the development of fifth graders' mathematical reasoning patterns through drawing the group's discussion and classrooms' discussion in three lessons' reasoning process, which showed by a classroom led by a teacher who participated in Ministry of Science and Technology’s research project.
The results found that in the group discussions, most students proposed conjectures through observation, and after testing the conjectures directly they generalized and applied them in the first instruction, so the reasoning process seemed relatively simple. Followed by second and third conjecturing instructions, when students proposing conjectures, they had not only to protect the conjectures by warrants, but also argue with other conjectutes. New observations were made in case of any refutation, which contributed to relatively complex reasoning pattern. The classroom discussion is composed by teachers and students, such as when the other team made the wrong guess, the whole class would question and refute the wrong suspect, and teacher would scaffold students to think from different ways and to produce reasoning. Based on the discussion between teacher and students, the classroom discussion could produce simple and complex reasoning process, causing more various reasoning patterns. Therefore, this research suggested that using conjecturing instruction in the mathematics classrooms can not only enhance students' understanding of mathematical concepts, but also promote the development of students' ability to express through discussion, and increase their self-confidence, and can enhance the students' reasoning ability. The conjecturing tasks and the objectives of instructions will influence the types of reasoning patterns, so teachers need to know sufficient expertise to guide students into reasoning.
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