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研究生:陳佳甫
研究生(外文):Chia-Fu Chen
論文名稱:國小高年級學生在數列組型問題之表現分析及概念階層結構探討
論文名稱(外文):A Study on the Performance of Sequence Pattern and the Hierarchical Structure of Concepts on the Fifth and Sixth Graders
指導教授:林原宏林原宏引用關係
指導教授(外文):Yuan-Horng Lin
學位類別:碩士
校院名稱:國立臺中教育大學
系所名稱:數學教育學系在職進修教學碩士學位班
學門:教育學門
學類:普通科目教育學類
論文種類:學術論文
論文出版年:2007
畢業學年度:95
語文別:中文
論文頁數:92
中文關鍵詞:概念階層結構數列次序理論廣義多元計分的次序理論數列組型
外文關鍵詞:hierarchical structureordering theorygeneralized polytomous ordering theorysequencepattern
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本研究旨在進行國小高年級學生數列組型問題之表現分析及概念階層結構分析。研究者自編「數列組型測驗」,研究了來自台中縣市五、六年級學生共1063名,並利用獨立樣本t 檢定、單因子變異數分析來比較不同背景學生(年級、性別、能力組別)在測驗上表現的差異情形。在概念分析上,將受試者各概念上的得分進行多變量統計分析,同時也以廣義多元計分的次序理論模式,進行概念階層結構分析。研究結果發現:
(一)數列組型測驗的表現,六年級表現優於五年級;且女生、男生表現無顯著差異;.高分組優於中分組,中分組優於低分組。
(二)不同年級在數列組型認知歷程中概念的表現上,在三個認知歷程中的所有概念,六年級的表現均優於五年級;而且六年級在分類歷程與映射檢查歷程中的概念階層結構和五年級不同。
(三)不同性別在數列組型認知歷程中概念的表現上,在三個認知歷程中的概念,男生只在「複合」、「差距」概念優於女生,其餘無差異;而且女生在所有認知歷程的概念階層結構均和男生相同。
(四)不同年級在數列組型認知歷程中概念的表現上,除了高分組和中分組在「固定」概念的表現無差異外,在三個認知歷程中的其它概念,兩兩之間均存差異;中分組和高分組在分類歷程的概念階層結構相同,但卻和低分組相異;不同能力組別在理解關係歷程的概念結構相同;低分組和中分組在映射檢查歷程的概念結構相同,但卻和高分組相異。
根據研究發現,研究者提出未來研究和教育實務之相關建議。
The study aims to analyze the performance of sequence pattern and the hierarchical structure of concepts on the fifth and sixth graders. The instrument is “The Sequence Pattern Test” designed by the researcher. There are one thousand and sixty three valid samples of the fifth and sixth graders from Taichung City and County. Data are analyzed by means of t-test and one-way ANOVA to compare and contrast the performance of the subjects among different backgrounds (grade, gender, and ability). With regard to conceptual analysis, subjects’ scores are dealt with MANOVA, whereas the hierarchical structures of concepts are examined by generalized polytomous ordering theory.
The findings are as the follows:
1. The performance of the Sequence Pattern Test: The sixth graders are superior to the fifth. There are no differences between boys and girls. The high-score group is superior to the middle-score group, whereas the middle-score group is better than the low-score group.
2. Conceptual performance of cognitive process on sequence pattern between different grades: With respects to all concepts that represent three cognitive processes, the sixth graders are superior to the fifth; the sixth graders possess different hierarchical structure of concepts from the fifth in terms of classification and mapping and checking.
3. Conceptual performance of cognitive process on sequence pattern between different genders: Among concepts of three cognitive processes, the boys are just superior to the girls in terms of “complex” and “interval”. Girls and boys have the same hierarchical structure of concepts among all cognitive processes.
4. As to conceptual performance of cognitive process on sequence pattern between different grades, the differences occur between groups of different ability in terms of other concepts that represent three cognitive processes except the high and middle score group on the concept of “fixed”. Though middle score group possesses the same hierarchical structure of concepts to that of the high score group, those results are different from the low score group. Groups of different ability present the same hierarchical structure of concepts on “relation reasoning.” With regard to “mapping” and “checking”, the results in low score group are equivalent to those in middle score group, but differ from high score group.
Finally, based on the results and findings, some recommendations and suggestions are provided for future research.
第一章 緒論 1
第一節 研究動機 1
第二節 研究目的 4
第三節 名詞解釋 4
第四節 研究範圍與限制 5
第二章 文獻探討 7
第一節 數列組型的意義 7
第二節 數列組型的相關研究 10
第三節 次序理論及其相關研究 31
第三章 研究方法和步驟 35
第一節 研究架構 35
第二節 研究樣本 36
第三節 研究工具 37
第四節 研究程序 46
第五節 資料處理 47
第六節 試題品質分析 48
第四章 研究結果與討論 51
第一節 數列組型測驗表現的分析 51
第二節 不同年級在數列組型概念表現之分析 53
第三節 不同性別在數列組型概念表現之分析 62
第四節 不同能力組別在數列組型概念表現之分析 69
第五章 結論與建議 79
第一節 結論 79
第二節 建議 81
參考文獻 83
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貳、西文部分 85
附錄 90
附錄一 施測說明 90
附錄二 數列組型測驗 91
附錄三 試題概念成分細格與試題概念成分矩陣 92
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