臺灣博碩士論文加值系統

本研究應用潛在類別分析（latent class analysis, LCA）與混合Rasch模式（mixed Rasch model, MRM）分析國小學童於比例理解與機率理解的測驗資料， 根據分析所得各潛在類別之反應組型，與文獻中規則解題所得之規則組型進行比較，藉以了解各類別受試者所採之解題規則。
研究分別以25題果汁濃度測驗及10題機率理解測驗，樣本為來自臺灣中部地區國小四至六年級學童，分析的結果顯示，各類別間的異質性高，而類別內的受試者同質性高。比例理解測驗經分析後可將受試者分為6個類別，而機率理解測驗分析後可將受試者分為3個類別，各類別可與文獻中相關規則相互對應，其類別反應組型與規則組型相符度極高；不同年齡受試者與採用規則呈顯著差異，而性別與採用規則則無明顯差異。
本研究之結果與發現，可提供國小中、高年級學童比例理解及機率理解解題規則的訊息，對於規則使用判斷及補救教學具有參考價值，研究者亦對未來相關研究提出研究限制及相關建議，可提供後續相關研究之參考。

The purpose of this study is to apply latent class analysis (LCA) and mixed Rasch model (MRM) to analyze the rule usage of proportional reasoning and probability reasoning for pupils. Latent classes are acquired according to response pattern so that the classification of rule usage is clearly displayed. As to the test of proportional reasoning, there are 25 items. In addition, probability reasoning test consists of 10 items. The sample includes fourth, fifth and sixth graders who are from elementary school in central district in Taiwan. The results show that there is various characteristics among groups, and there is similar characteristics for students within same group.
There are six classes for proportional reasoning and there are three classes for probability reasoning test. Each response pattern of class could be explained by rule pattern. There is obvious difference of rule usage among grade, but there is no difference between gender.
The findings of this research should be helpful for problem solving rule and could be used as references for remedial instruction. Finally, some recommendations and suggestions for future research are provided.

中文摘要………………………………………………………………i
英文摘要………………………………………………………………ii

第一章　緒論…………………………………………………………1
第一節　研究動機…………………………………………………………… 1
第二節　研究目的…………………………………………………………… 6
第三節　名詞解釋…………………………………………………………… 6

第二章　文獻探討……………………………………………………8
第一節　機率概念的相關研究……………………………………………… 8
第二節　機率理解測驗與解題規則…………………………………………22
第三節　比例概念的相關研究………………………………………………25
第四節　柳橙汁濃度測驗與解題規則………………………………………33
第五節　規則評量方法………………………………………………………36
第六節　分析模式的探討及適配度的選擇…………………………………43
第七節　規則解釋力與規則區別力…………………………………………54

第三章　研究方法……………………………………………………57
第一節　研究架構……………………………………………………………57
第二節　研究對象……………………………………………………………60
第三節　應用軟體資料分析步驟……………………………………………62

第四章　結果分析與討論……………………………………………63
第一節　OJT及機率理解測驗試題規則解釋力及規則區別力……………63
第二節　OJT比例理解測驗分析結果………………………………………65
第三節　機率理解測驗分析結果……………………………………………76

第五章　結論與建議…………………………………………………85
第一節　OJT比例理解概念解題規則分析結論……………………………85
第二節　機率理解概念解題規則分析結論…………………………………86
第三節　研究限制……………………………………………………………87
第四節　研究結論……………………………………………………………88
第五節　研究建議……………………………………………………………89

參考文獻………………………………………………………………91
中文部分………………………………………………………………………91
英文部分………………………………………………………………………96

附錄
附件一　OJT施測試卷………………………………………………………107
附件二　機率理解測驗試卷…………………………………………………109

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