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題名：國小學童數學直覺法則之認知評量分析與性別差異探討
書刊名：教育研究與發展期刊
作者：林原宏 引用關係／郭竹晏
作者(外文)：Lin, Yuan-horng／Kuo, Chu-yen
出版日期：2010
卷期：6:4
頁次：頁105-136
主題關鍵詞：直覺法則；混合Rasch模式；認知診斷；潛在類別；Cognition diagnosis；Intuitive rules；Latent class；Mixed Rasch model
原始連結：連回原系統網址new window
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直覺理論指出學童在數學問題常使用「More A─More B」、「Same A─Same B」、「無限細分」、「有限細分」等四種直覺法則（intuitive rule），這些法則會影響學童的數學解題表現。然而，學童使用這四個直覺法則的相關性和分群的問題，以及不同性別在表現上的差異性，文獻上卻甚少探討。基於此，本研究以國小五年級學童為對象，探討這四種直覺法則之相關性，利用多元計分混合Rasch模式（polytomous mixed Rasch model）進行直覺法則使用之分群，並進行性別表現差異探討。多元計分混合Rasch模式結果指出，全體學童和不同性別學童都可分成三個潛在類別，每個類別呈現的直覺法則使用各具特徵。不同性別之直覺法則使用相關性有所不同，但在各類別的人數分佈上並無差異。本研究結果有助於直覺法則的進階瞭解，以及提供教師採取同質性分組及補救教學之參考。
Intuitive theory had generated four intuitive rules about mathematics problems. Hence, intuitive rules played an important role in the mathematics education and mathematical concept construction. Research into this issue improved understanding of mathematical concept construction. However, most of the research focused on performance of intuitive rules and little was known about the dependence and relationship of these intuitive rules with comparisons between genders. The purpose of this study was to investigate latent class of rule usage and relationship on intuitive rules for pupils. The sample included fifth graders and polytomous mixed Rasch model was used to classify pupils. According to the results of data analysis, relationship among four intuitive rules varied. There were three latent classes and each latent class displayed its characteristics on intuitive rule usage. Relationship of intuitive rule usage between genders varied, but there was no significant difference in distribution of latent class for genders. Finally, results of this study improved understanding of intuitive rules and provide references for teachers on instruction.
期刊論文
1.吳毓瑩、林原宏(19960100)。潛在類別分析取向的除法概念結構。測驗年刊，43，345-358。new window  延伸查詢new window
2.莊嘉坤(19950600)。國小學生科學態度潛在類別的分析研究。屏東師院學報，8，111-136。new window  延伸查詢new window
3.Rost, J.(1990)。Rasch Models in Latent Classes: An Integration of Two Approaches to Item Analysis。Applied Psychological Measurement，14(3)，271-282。  new window
4.Masters, G. N.、Wright, B. D.(1984)。The essential process in a family of measurement models。Psychometrika，49(4)，529-544。  new window
5.Tall, D. O.(1981)。Intuition of infinity。Mathematics in School，10(3)，30-33。  new window
6.Austin, E. J., Deary, I. J.,、Egan, V.(2006)。Individual differences in response scale use: mixed Rasch modeling of responses to NEO-FFI items。Personality and Individual Differences，40，1235-1245。  new window
7.呂玉琴、陳瑞發(2004)。直觀規律對國小代課教師數學解題的影響。科學教育研究與發展季刊，34，66-87。  延伸查詢new window
8.Akaike, H.(1978)。A Bayesian analysis of the minimum AIC procedure。Annals of the Institute of Statistical Mathematics，30，9-14。  new window
9.Gunstone, R. F.、White, R. T.(1981)。Understanding of gravity。Science Education，65(3)，291-299。  new window
10.Stavy, R.、Tirosh, D.(1996)。Intuitive rules in science and mathematics: the case of 'more of A-more of B'。International Journal of Science Education，18(6)，653-667。  new window
11.Rost, J.(1991)。A Logistic Mixture Distribution Model for Polytomous Item Responses。British Journal of Mathematical and Statistical Psychology，44(1)，75-92。  new window
12.蔡秉恆、黃天佑(2005)。直覺法則對兒童數學概念影響之研究。南大學報：數理與科學類，39(1)，91-110。  延伸查詢new window
13.Akaike, H.(1978)。A Bayesian analysis of the minimum AIC procedure。Annals of the Instituteof Statistical Mathematics，30, Part A，9-14。  new window
14.Fischbein, E., Tirosh, D.,、Melamed, U.(1981)。Is it possible to measure the intuitive acceptance of a mathematical statement。Educational Studies in Mathematics，12，491-512。  new window
15.Fischbein, E., Tirosh, P.,、Hess, P.(1979)。The intuition of infinity。Educational Studies in Mathematics，12，491-512。  new window
16.Zazkis, R.(1999)。Intuitive rules in number theory: Example of “the more of A, the more of B' rule implementation。Educational Studies in Mathematics，40，197-209。  new window
17.蔡秉恆、黃天佑(2005)。直覺法則對兒童數學概念影響之研究。南大學報，39(1)，91-110。  延伸查詢new window
18.Fischbein, E.、Tirosh, D.、Melamed, U.(1981)。Is it possible to measure the intuitive acceptance of a mathematical statement。Educational Studies in Mathematics，12，491-512。  new window
19.Fischbein, E.、Tirosh, P.、Hess, P.(1979)。The intuition of infinity。Educational Studies in Mathematics，12，491-512。  new window
20.Nunez, R.(1991)。A 3-Dimension conceptual space of transformations for the study of the intuition of infinity in plane geometry。Proceedings of the Fifteen Conference for the Psychology of Mathematics Education，3，362-368。  new window
21.Zazkis, R.(1999)。Intuitive rules in number theory: Example of 'the more of A, the more of B' rule implementation。Educational Studies in Mathematics，40，197-209。  new window
會議論文
1.Akaike, H.(1973)。Information Theory and an Extension of the Maximum Likelihood Principle。The Second International Symposium on Information Theory。Budapest：Akademiai Kiado。267-281。  new window
2.Tirosh, D.、Stavy, R.(1999)。The intuitive rules theory and inservice teacher education。1999 International Conference on Mathematics Teacher Education。Taipei, Taiwan：Department of Mathematics, National Taiwan Normal University。205-225。  new window
3.Nunez, R.(1991)。A 3-Dimension conceptual space of transformations for the study of the intuition of infinity in plane geometry。Assisi, Italy。3，362-368。  new window
4.Schmidt, K. M.(2002)。Using the mixed Rasch model to discover latent classes of cognitive self-efficacy。New Orleans, LA。  new window
5.Schmidt, K. M.(2002)。Using the mixed Rasch model to discover latent classes of cognitive self-efficacy。New Orleans, LA。  new window
學位論文
1.楊美惠(2002)。直觀規律對k-6年級學童面積概念之探究(碩士論文)。國立台北師範學院，臺北市。  延伸查詢new window
2.張玉枝(2002)。探討國二學生詮釋地球科學課本附圖的相關因素(碩士論文)。國立臺灣師範大學。  延伸查詢new window
3.謝展文(2000)。直覺法則對於數學及科學學習的影響--以國小四、五、六年級學生為對象(碩士論文)。國立臺灣師範大學。  延伸查詢new window
4.Stavy, R.、Ronen, H.、Tirosh, D.、Tsamir, P.(1996)。The Role of Intuitive Rules in Science and Mathematics Education(碩士論文)。Tel-Aviv University，Israle。  new window
5.紀宗秀(2005)。從直觀法則分析學童的迷思概念及概念改變之研究(碩士論文)。國立花蓮師範學院。  延伸查詢new window
6.何健誼(2002)。直觀法則對K－6年級學童在體積概念學習上的影響(碩士論文)。國立台北師範學院。  延伸查詢new window
7.鄭蕙如(2006)。國中生數學內容知識與數學認知能力之混合Rasch模式分析研究(博士論文)。國立臺灣師範大學。new window  延伸查詢new window
圖書
1.Torff, B.、Sternberg, R. J.(2001)。Understanding and teaching the intuitive mind: Student and teacher learning。Mahwah, NJ：Lawrence Erlbaum Associates。  new window
2.Fischbein, E.(1987)。Intuition in science and mathematics: An educational approach。Dordrecht：Dordrecht Reidel Publishing Company。  new window
3.Stavy, R.、Tirosh, D.(2000)。How Students (Mis-)understand Science and Mathematics: Intuitive Rules。NY：Teachers College Press。  new window
4.Bozdogan, H.(1992)。Choosing the number of component clusters in the mixture model usinga new Informational complexity criterion of the inverse-fisher information matrix。Information and classification: Concepts, methods and applications。New York, NY。  new window
5.Rost, J.,、Langeheine, R.(1997)。A guide through latent structure models for categorical data。Applications of Latent Trait and Latent Class Modelsin the Social Sciences。New York, NY。  new window
6.Koeller, O.(1994)。Identification of guessing behavior on the basis of the mixed Rasch model。(ERIC NO ED369814)。  new window
7.Bozdogan, H.(1992)。Choosing the number of component clusters in the mixture model using a new Informational complexity criterion of the inverse-fisher information matrix。Information and classification: Concepts, methods and applications。New York, NY。  new window
8.Rost, J.、Langeheine, R.(1997)。A guide through latent structure models for categorical data。Applications of Latent Trait and Latent Class Models in the Social Sciences。New York, NY。  new window
圖書論文
1.Rost, J.、Carstensen, C.、von Davier, M.(1998)。Applying the mixed Rasch model to personality questionnaires。Applications of latent trait and latent class models in the social sciences。Waxmann。  new window
 
 
 
 
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