臺灣博碩士論文加值系統

學生經過教學過程後習得的概念結構是個令人關心的課題，但目前國內針對九年一貫代數部分的研究甚少。本研究以九年一貫課程綱要中的分年細目作為概念指標，探討學生的代數概念結構及差異。以臺中縣、嘉義縣、臺南縣及高雄縣共9所國民小學，一到三年級合計28個班級，共783名學生為研究樣本，於學生學習完代數課程後，對學生學習後的施測成果進行資料分析，以獲得學生概念結構圖。研究者依據模糊集群分析理論將學生分群，並採用多元計分試題關聯結構理論(polytomous item relational structure, PIRS)，繪製出各群學生的概念結構圖。本研究將施測所得資料，依據上述步驟分析後，逐一觀察比較概念結構圖，研究發現如下：
一、各年級受測學生中若要針對代數概念進行補強，恰好皆是分為兩組進行教學最適當。
二、不同分群學生所呈現出的概念結構圖互有差異，根據概念結構圖可以分析出各概念間的上下位關係。
各群學生的概念結構圖不盡相同，應有不同的補救教學策略，才能讓學生在教學過程中適才適性地學習。本研究提出的方法，供教師利用施測的資料，快速、準確地掌握各群學生的概念結構，藉此作為規劃補救教學活動與改進課程教學設計時的參考。

Teachers concern about the issue of the knowledge structure of students after a course. The purpose of this study is to explore the differences in the algebraic concept structure of students by using achievement tests. The samples include 783 first, second, and third graders from elementary schools in Taichung, Chiayi, and Kaohsiung county. Firstly, researcher classifies students into groups based on the analysis of fuzzy clustering. Secondly, PIRS is adopted to draw the concept structure of students respective to each group. From the result of this study, the findings are summarized as following:
1.All students of every grade are classified into proper two groups by fuzzy clustering analysis for the remedial instruction of algebraic concept.
2.The concept structure graphs of each group are varied. Researcher could analyze the precondition relationship among concepts according to the concept structure graphs.
The methodology of this research may provide some references for teachers so that the concept structure of students could be seized precisely. Teachers could design their teaching materials according to the characteristics of these concept structures. Finally some suggestions and recommendations are discussed for future research.

第一章 緒論
第一節 研究動機
第二節 研究目的
第三節 名詞解釋
第二章 文獻探討
第一節 九年一貫課程中的代數
第二節 資料分群方法
第三節 模糊集群分析
第四節 知識結構分析方法
第五節 多元計分的試題關聯結構模式
第三章 研究方法
第一節 研究架構
第二節 研究對象
第三節 研究工具
第四節 資料分析
第四章 研究結果與討論
第一節 一年級分群概念結構圖分析
第二節 二年級分群概念結構圖分析
第三節 三年級分群概念結構圖分析
第五章 結論與建議
第一節 結論
第二節 研究限制
第三節 後續研究建議
參考文獻
附錄一 國小一年級學生代數概念測驗
附錄二 國小二年級學生代數概念測驗
附錄三 國小三年級學生代數概念測驗

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