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  • 學位論文

國中學生的解題策略與推理歷程研究-以一個非例行性問題為例

A Study of Problem Solving Strategies and Reasoning Processes of Junior High School Students - One Non-routine Problem as an Example

指導教授 : 袁媛

摘要


本研究旨在探討不同背景變項(年級、性別、成就程度)的國中學生在一個非例行性問題的論證表現類型、解題策略及使用先備知識的歷程。本研究選取八、九年級學生為對象,依據全年級數學成績排序結果,選取九年級高成就男生8位、九年級高成就女生8位、九年級低成就男生8位、九年級低成就女生8位、八年級高成就男生8位、八年級高成就女生8位、八年級低成就男生8位、八年級低成就女生8位,合計共64位,再依據學生在研究問題單的表現、晤談紀錄表、觀察記錄、分年細目檢核表等資料進行分析。 主要研究結果顯示如下: 一、國中學生在解題後所進行的立即論證表現不佳。其中,九年級比八年級學生有更多論證元素可以採用;男生的論證類型較均勻分配,女生的論證類型集中於明確論證與空白兩端,高成就女生的論證表現比高成就男生來得好;低成就學生絕大多數未進入論證情境且論證品質不佳。 二、在一個非例行性問題的解題策略中,九年級比八年級低成就學生容易出現不合邏輯的情形;男生比女生容易找到最快解法,但是缺乏嚴密性;高成就學生會透過畫輔助線找線索,低成就學生大多沒想過或認為畫輔助線沒有用處,其中當高成就學生找出多種解題策略時,會選擇最簡單的解法應用在類似的數學問題。 三、在解一個非例行性問題所使用的先備知識中,九年級比八年級運用更多先備知識進行解題;不同性別學生所運用的先備知識沒有太大差異,僅少數個案有所不同;高成就男生對先備知識的立即憶取性比高成就女生來得差,低成就學生大多先備知識不足、存有迷思概念、不懂公式的意義、憶取表現差,其中直觀類型的學生,容易將先備知識憑直覺進行不合邏輯之聯結與推測,以致於有誤用公式、誤用單位之情形,而先備知識可做立即修補的空白類型學生,有能力完成解題。

並列摘要


Abstract The research explores the argumentation types, solving strategies, and the process of applying prior knowledge among junior high school students with different background variables in grade, sex and achievement level when they respond to a non-routine problem. The study targeted at the eighth and ninth graders and, based on their mathematic grades, selected eight male ninth graders with high achievement, eight female ninth graders with high achievement, eight male ninth graders with low achievement, eight female ninth graders with low achievement, eight male eighth graders with high achievement, eight female eighth graders with high achievement, eight male eighth graders with low achievement, and eight female eighth graders with low achievement, which amounted to sixty-four subjects. After that, an analysis of information was conducted according to the subjects’ responses to the questionnaires , interview sheets, observation records, and specific item checklists of separate grades. The major results of the study are as follows. 1. Junior high school students do not perform well on the immediate argumentation after problem solving. The ninth graders possess more argumentation elements to be used than the eighth graders do. The argumentation types of the male students are more uniform distribution; those of the female students are either definite and perfectly logical or blank, neither argumentation nor illogical inference. The argumentation performance of the female students with high achievement are above that of the male students with high achievement; most of the students with low achievement are unable to immerse themselves in the argumentation or even so, their argumentation quality is not desirable. 2. In the solving strategies of a non-routine problem, the ninth graders with low achievement have more illogical thinking than those with low achievement. It is easier for the male subjects to find the most prompt solution than the female ones, but it lacks rigor. The students with high achievement look for the clues through auxiliary lines; those with low achievement never think of the assisting lines or think that the lines are of no use. When the students with high achievement figure out various solving strategies, they will pick the easiest ones to apply to similar mathematic questions. 3. As for prior knowledge used to solve a non-routine problem, the ninth graders utilize more prior knowledge to solve problems than the eighth graders. The prior knowledge which students with different sexes use shows slight variations; only few cases are different. The male students with high achievement perform worse than the female students with high achievement in the immediate recall and retrieval of the prior knowledge. Most of the students with low achievement have inadequate prior knowledge, possess false concept, do not comprehend the meaning of formulas and perform poorly in retrieving prior knowledge. Among them, instinct-oriented students easily use prior knowledge by instinct to associate and infer illogically, so they tend to misuse formulas and units. However, the blank-typed students, whose prior knowledge can be taught immediately, are capable of solving problems. In the end, based on the findings of the research, suggestions were offered to function as reference for teachers’ teaching and future research.

參考文獻


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被引用紀錄


張夢萍(2014)。學習共同體結合合作學習策略於高級職業學校數學解題之行動研究〔碩士論文,淡江大學〕。華藝線上圖書館。https://doi.org/10.6846%2fTKU.2014.00576
蔡嘉琳(2016)。探究國中數學幾何圖形之輔助線〔碩士論文,中原大學〕。華藝線上圖書館。https://doi.org/10.6840%2fcycu201600522

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