臺灣博碩士論文加值系統

　　本研究旨在以Ning所提出兒童分數詞的意義為基礎，對於國小四年級兒童的等值分數概念作一初探。
　　研究者採用國內學者鄭富森所發展的「無參數試題反應理論」為分析工具，期能精確地顯示受試者能力與答題表現之關係，以瞭解兒童的分數概念與解題策略，並進一步印證Ning所建構之理論模型。
　　研究者以國立台中師範學院輔導區國小四年級兒童為研究對象，採分層隨機抽樣，共得1064有效的筆測樣本。從筆測結果可以發現，若干試題特徵曲線出現一段水平，其表示在某特定能力範圍的受試者，可能無法跨越某個滯礙概念。研究者特別分析這些兒童的試卷並配合訪談之後，發現以下的情形：
　　一、能力值介－於1.26和－0.74之間的受試者，雖然具有數概念與分割活動，但是其數概念只是序列性合成運思，而分割活動未能將子分割單位數值化，其分數概念屬於「並置類型」。
　　二、能力值介於0.15和0.68之間的受試者，雖然具有累進性合成運思時的內嵌數概念，但無法正確的運用子分割活動，其分數概念屬於「內嵌並置類型」。
　　根據個案分析的結果，本研究假設該受試者是位於部份全體運思階段，其分數概念是「加法性分數」，其分數概念具有以下幾種性質：
　　一、幾分之幾可以當成一個分量
　　二、分裂量與分裂數成反比
　　三、分數可以是分數單位
　　四、把分數當成一個函數關係
　　五、分母就是代表將一個整體分割成幾份
　　六、參考單位點的迷失
　　七、將分子、分母中較大的數除以較小的數所得的商代表分數值

　　The purpose of the study is to investigate fourth graders'''' conceptions of equivalent fractions based on the children''''s meanings of fractional number words presented by Ning.
　　The item response theory of non-parameter developed by Jeng is used as an analytical tool to accurately show the relation between the ability and the performance of children, to understand children''''s conceptions of fractional numbers and their solution strategies, and to demonstrate the theoretical model built by Ning.
　　The fourth graders within the Taichung Normal College''''s assisted region are chosen as research subjects. Using the method of stratified random sampling, we obtain 1064 effective written samples. From the analysis of written tests, we can find some item characteristic curves show a flat segment indicating that children within a specific range of ability can not cross a certain obstacle-concept. After specifically analyzing these children''''s tests and interviewing them, we find the following situations:
　　(1)For those children with ability values between-1.26 and -0.74, they have the conceptions of numbers and the dividing activities, but their conceptions of numbers are just sequential integration operations and their dividing activities can not numberize the subdivided units. Their conceptions of numbers belong to juxtaposed patterns.
　　(2)For those children with ability values between 0.15 and 0.68, they have the conceptions of embedded numbers in progressive unitary operations, but they can not corretcly manipulate the subdividing activities. Their conceptions of numbers belong to embedded patterns.
　　According to the analysis of the interview with Yo (psendo name), this study assumes that Yo has the part-whole conceptions. Her conceptions of numbers belong to the type of additive fractions.