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研究生:許清陽
研究生(外文):Ching-Yang Hshu
論文名稱:國小學童數感理論模式建構與電腦化數感診斷測驗系統之研究
論文名稱(外文):The Study of Elementary Students’ Number Sense Theoretical Model Construction and Computerized Number Sense Diagnostic Test System
指導教授:吳裕益吳裕益引用關係
學位類別:博士
校院名稱:國立高雄師範大學
系所名稱:教育學系
學門:教育學門
學類:綜合教育學類
論文種類:學術論文
論文出版年:2006
畢業學年度:94
語文別:中文
論文頁數:286
中文關鍵詞:數感診斷測驗電腦化數感診斷測驗結構方程模式
外文關鍵詞:number sensediagnostic testcomputerized number sense diagnostic teststructural equation model
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  本研究之主要目的在建構數感之理論模式,並開發「電腦化數感診斷測驗系統」,以瞭解國小六年級學童的數感表現概況,且進一步分析受試者數感的錯誤類型與迷思概念。
  本研究之實施首先抽取南部縣市六年級學童539人進行電腦線上測驗,以建立數感診斷測驗之信效度;接著再抽取台灣本島22縣市六年級學童3462人進行電腦線上測驗,用以建構數感之理論模式,及瞭解六年級學童數感的表現概況,並進一步分析學童在數感診斷測驗中常犯的錯誤類型與迷思概念。
  本研究經資料蒐集與統計分析結果,其結論如下:
一、「國小學童數感理論模式」之適配度考驗採用Bagozzi 和 Yi (1988)所建議的三個標準:基本的適合標準(preliminary fit criteria)、整體模式適合度(overall model fit)及模式內在結構適合度(fit of internal structure of model)三方面來評鑑,評鑑結果發現,除了易受樣本數影響的指標外,其餘指標均符合評鑑標準,顯示研究者所提之「國小學童數感理論模式」十分恰當。。
二、不同背景之學童在數感能力的差異分析上,學校規模和父親的教育程度有顯著差異,而性別則無顯著差異。在數感與數學學業成就之相關檢定方面,64所學校中只有6所學校未達.05顯著水準,大部份學校學童的數感與數學學業成就有顯著相關
三、電腦化數感診斷測驗系統能提供測驗的PR值並具有診斷錯誤類型與迷思概念的功能。受試者在電腦線上測驗後能馬上知道自己的PR值,以瞭解自己在團體中的相對位置,藉此知道自己數感能力的優劣。除此之外,電腦化數感診斷測驗系統還提供受試者答錯題目所犯的錯誤類型和迷思概念,以便受試者能根據所回答的錯誤原因,進行自我診斷學習,教師也可根據診斷的結果,進行補救教學。
  根據研究結果,本研究分別對學校教師及未來之研究提出建議。
The main purpose of this study is to construct the theoretical model of number sense and to develop “Computerized Number Sense Diagnostic Test System” in order to understand the general situation of sixth graders in number sense performance as well as to further analyze the error types and misconception of the subjects.
This study firstly selected 539 sixth graders from southern counties and cities for computerized online test to construct the reliability and the validity of number sense diagnostic test. Then, 3,462 sixth graders from 22 counties and cities from Taiwan island were selected for computerized online test to construct number sense theoretical model and to understand the general conditions of sixth graders in number sense performance. The data was then used to further analyze the frequent error type and misconception of the students in number sense diagnostic test.
Data collection and statistical analyses of this study are concluded as the following:
1.The test of goodness of fit for “Elementary Students Number Sense Theoretical Model” adopts the three standards suggested by Bagozzi and Yi (1988): preliminary fit criteria, overall model fit, and fit of internal structure of model. The three models were used in assessment and results revealed that besides those indexes which are easily affected by samples, all other indexes conformed to the assessment standards. This shows that “Elementary Students Number Sense Theoretical Model” is perfectly appropriate.
2.In the analysis of number sense differences among the students from various backgrounds, school scales and father’s education level show significant differences while gender shows no significant difference. In the correlation test between number sense and mathematics achievement, there were only 6 out of 64 schools failed to reach 0.05 significance level. Most of the students show significant relation between number sense and mathematics achievement.
3.Computerized number sense diagnostic test system can provide PR value for the test and it also possesses the function in diagnosing error type and misconception. The subjects get to know their own PR value immediately after the online computer test. With this, the students learn about their relative position in the group and aware of their own strengths and weaknesses of number sense. Besides, computerized number sense diagnostic test system also provides the subjects with their error types and misconception so that the subjects can do self-review for improvement. Moreover, teachers can carry out remedial teaching base on the diagnostic results.
Base on the findings, this study proposes suggestions to school teachers and further studies respectively.
第一章 緒論
第一節 研究動機----------------------------------------1
第二節 研究目的----------------------------------------4
第三節 待答問題----------------------------------------5
第四節 名詞釋義----------------------------------------5
第五節 研究範圍與限制-----------------------------------6
第二章 文獻探討
第一節 數感的理論探討-----------------------------------7
第二節 數感及其相關概念---------------------------------24
第三節 數感的重要性------------------------------------40
第四節 診斷測驗----------------------------------------43
第五節 電腦化測驗的優缺點-------------------------------52
第三章 研究方法與實施
第一節 研究流程及架構-----------------------------------55
第二節 研究對象----------------------------------------58
第三節 研究工具----------------------------------------60
第四節 實施程序----------------------------------------90
第五節 資料處理與分析-----------------------------------92
第四章 研究結果與討論
第一節 國小學童數感理論模式適合度評鑑---------------------93
第二節 國小六年級不同背景之學童在數感能力上的差異分析-------108
第三節 電腦化數感診斷測驗之回饋系統-----------------------116
第五章 結論與建議
第一節 結論--------------------------------------------140
第二節 建議--------------------------------------------143
參考文獻
一、中文部份-------------------------------------------145
二、西文部份-------------------------------------------148
附 錄
附錄一 國小六年級學童數感診斷測驗作答選項原因分析問卷-------160
附錄二 國小六年級學童數感電腦化診斷測驗初編擬之試題---------174
附錄三 國小六年級學童電腦化數感診斷測驗專家內容效度問卷------210
附錄四 國小六年級學童數感電腦化診斷測驗正試試題-------------221
附錄五 驗證性因素分析觀察變項描述統計與相關矩陣-------------242
附錄六 數感診斷測驗各題原因選項配分------------------------244
附錄七 數感診斷測驗各題原因選項錯誤類型與迷思概念分析--------255
附錄八 「電腦化數感診斷測驗系統」之評鑑--------------------279
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