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題名：我國學童小數概念發展之調查研究
書刊名：科學教育學刊
作者：劉曼麗 引用關係
作者(外文)：Liu, Man-li
出版日期：2006
卷期：14:6
頁次：頁663-693
主題關鍵詞：小數；國小學童；Decimals；Elementary school students
原始連結：連回原系統網址new window
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  • 被引用次數被引用次數:期刊(1) 博士論文(0) 專書(0) 專書論文(0)
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  • 共同引用共同引用:23
  • 點閱點閱:53
本研究的主要目的在探討我國國小學童小數概念的發展情形，也包括學童的錯誤想法和迷思概念。筆試樣本是透過全國分層隨機取樣而來，包括北一、南一、北二、南二、山地及偏遠等六區四、五、六年級學童，共計 2850人。評量工具為自編的筆試試題。筆試試題分成四五年級卷與六年級卷，本文以此二份試卷的共同試題，包括小數圖像表徵、小數記數系統、小數與分數互換、單複名數轉換、估測、小數比大小、小數稠密性、小數加減等八個部分對三個年級學童的答題表現進行比較和分析。資料收集以筆試為主，而資料分析則以量化為主和質性為輔。研究結果發現，我國四至六年級學童的小數概念是隨著年級增加而成長，但學習成效普遍較不理想，僅有五、六年級的高程度學童表現不錯。此外，各年級學童在估測與小數加減部分的表現最好，在小數與分數互換、單複名數轉換與小數稠密性三部分的表現則最差。綜合歸納學童的錯誤想法和迷思概念，可歸結於學童是否能掌握小數符號的意義和小數符號的結構，而這關鍵處即在於學童是否能理解小數的十等分割意涵和小數的十進制記數系統。最後，根據本研究的發現，提出一些建議作為小數教材和教學的參考。
This study investigated the development of Taiwanese elementary school students’ concepts of decimals. The subjects of the study included 2,850 grade 4, 5 and 6 students which were randomly sampled and stratified from 6 different parts of Taiwan. Two sets of written tests developed by the researcher were given in which one set of the test was administered for the grade 4 and 5 students and another for grade 6 students. The following eight different kinds of decimals concepts were aimed to assess the students: iconic representations of decimal, notation system of decimal, conversion between decimals and fractions, conversion between different units used in measurement, estimation, comparison of decimal, density of decimal and addition/subtraction of decimal. The answers from three different graders were analyzed. Quantitative analysis showed that the students’ concepts of decimals improved as their age increased but they did not perform well on the test except for the high-level groups of grade 5 and 6 students. All students performed best on estimation and addition/subtraction of decimal, but poorly on conversion between decimals and fractions, conversion between different units used in measurement and density of decimal. Furthermore, based on the qualitative analysis of the mistakes that the students made in the test, the researcher concluded two major reasons that appears to account for the mistakes the students made. The students failed to understand the meaning for decimal notation and notation system of decimal, and the key is to partition by 10 and the base-10 place-value system. Based on the findings, suggestions for teaching decimals to elementary school students were proposed.
期刊論文
1.戴政吉(19990700)。四年級學生的小數迷思概念--由學生習作所犯之錯誤談起。國教天地，134，106-112。  延伸查詢new window
2.Carpenter, Thomas P.、Corbitt, M. K.、Kepner, H. S.、Lindquist, M. M.、Reys, R. E.(1981)。Decimals: Results and Implications from National Assessment。Arithmetic Teacher，28(8)，34-37。  new window
3.Sackur-Grisvard, C.、Le'onard, F.(1985)。Intermediate cognitive organization in the process of learning a mathematical concept: The order of positive decimal number。Cognition and Instruction，2(2)，157-174。  new window
4.Resnick, L. B.、Leonard, F.、Magone, M.、Peled, I.、Omanson, S.、Nesher, P.(1989)。Conceptual bases of arithmetic errors: The case of decimal fractions。Journal for Research in Mathematics Education，20(1)，8-27。  new window
5.Moskal, B. M.、Magone, M. E.(2000)。Making sense of what students know: Examining the referents, relationships and modes students displayed in response to a decimal task。Educational Studies in Mathematics，43(3)，313-335。  new window
6.Markovits, Z.、Sowder, J. T.(1991)。Students' understanding or the relationship between fractions and decimals。Focus on Learning Problems in Mathematics，13(1)，3-11。  new window
7.Irwin, K. C.(2001)。Using everyday knowledge of decimal to enhance understanding。Journal for Research in Mathematics Education，32(4)，399-420。  new window
8.Fischbein, E.、Deri, M.、Nello, M. S.、Marino, M. S.(1985)。The role of implicit models in solving verbal problems in multiplication and division。Journal for Research in Mathematics Education，16(1)，3-17。  new window
9.劉曼麗(20050300)。小數診斷教學研究。科學教育學刊，13(1)，29-52。new window  延伸查詢new window
10.劉曼麗、侯淑芬(20050400)。小數的教學活動。科學教育，277，25-32。  延伸查詢new window
11.楊德清(20010600)。國小六年級學生數字稠密性之認知的探討。科學教育研究與發展季刊，23，41-56。  延伸查詢new window
12.劉曼麗(1998)。國小數學新課程對「小數」概念的處理方式。屏師科學教育月刊，7，1-9。  延伸查詢new window
13.Hiebert, J.、Wearne, D.(1988)。Instruction and Cognitive change in Mathematics。Educational Psychologist，23(2)，105-117。  new window
14.Hiebert, J.、Wearne, D.(1985)。A model of students' decimal computation procedures。Cognition and Instruction，2(3/4)，175-205。  new window
15.Greer, B.(1987)。Nonconservation of multiplication and division involving decimals。Journal for Research in Mathematics Education，18(1)，37-45。  new window
16.Bell, A.、Swan, M.、Taylor, G.(1981)。Choice of operation in verbal problems with decimal numbers。Educational Studies in Mathematics，12(4)，399-420。  new window
17.劉曼麗(20010300)。國小學童的小數知識研究。屏東師院學報，14(下)，823-858。new window  延伸查詢new window
18.羅啟宏(1992)。臺灣省鄉鎮發展類型之研究。臺灣經濟月刊，190，41-68。  延伸查詢new window
19.Kouba, Vicky L.、Brown, C. A.、Carpenter, T. P.、Lindquist, M. M.、Silver, E. A.、Swafford, J. O.(1988)。Results of the Fourth NAEP Assessment of Mathematics: Number, Operations, Word Problems。The Arithmetic Teacher，35(8)，14-19。  new window
會議論文
1.Hiebert, J.、Wearne, D.(1983)。Students' conceptions of decimal numbers。The annual meeting of the American Educational Research Association。Montreal。  new window
學位論文
1.D'Entremont, Y. M.(1991)。The reconstruction of decimal knowledge in young adult(博士論文)。University of Alberta，Edmonton, Alberta。  new window
2.Thipkong, S.(1988)。Preservice elementary teachers' misconception in interpreting units and solving multiplication and division decimal word problems(博士論文)。University of Georgia。  new window
3.陳文利(2001)。國小四年級學童小數迷思概念之研究(碩士論文)。屏東師範學院，屏東市。  延伸查詢new window
4.杜建台(1996)。國小中高年級學童「小數概念」理解之研究(碩士論文)。國立台中師範學院。  延伸查詢new window
5.吳昭容(1996)。先前知識對國小學童小數概念學習之影響(博士論文)。國立臺灣大學。new window  延伸查詢new window
6.郭孟儒(2002)。國小五年級學童小數迷思概念及其成因之研究(碩士論文)。屏東師範學院，屏東市。  延伸查詢new window
7.陳永峰(1998)。國小六年級學童小數知識之研究(碩士論文)。國立屏東師範學院。  延伸查詢new window
8.林原宏(1994)。國小高年級學生解決乘除文字題之研究--以列式策略與試題分析為探討基礎(碩士論文)。國立台中師範學院。  延伸查詢new window
9.艾如昀(1994)。國小學生處理小數的歷程與困難(碩士論文)。國立中正大學。  延伸查詢new window
圖書
1.Hart, K. M.、Kerslake, D.、Brown, M. L.、Ruddock, G.、Kuchemann, D. E.、McCartney, M.(1989)。Children's understanding of mathematics: 11-16。London, England：John Murray。  new window
2.教育部(2003)。國民中小學九年一貫課程綱要。台北市：教育部。  延伸查詢new window
3.Frobisher, L.、Monaghan, J.、Orton, A.、Orton, J.、Roper, T.、Threlfall, J.(2002)。Learning to teach number: A handbook for students and teachers in the primary school。Cheltenham：Nelson Thornes。  new window
4.劉曼麗、江愛華、侯淑芬、梁惠珍(2003)。小數概念知多少？？？。高雄市：高雄復文圖書出版社。  延伸查詢new window
5.趙文敏(1985)。數學史：算術、代數與數論。台北市：協進出版社。  延伸查詢new window
6.教育部國民小學課程標準編輯審查小組(1993)。國民小學課程標準。臺北市：教育部。  延伸查詢new window
7.教育部(2001)。國民中小學九年一貫課程暫行綱要。台北：教育部。  延伸查詢new window
8.簡茂發、劉湘川(1993)。八十一學年度國民教育階段學生基本學習成就評量國小組試題編製及抽測結果報告。國立台中師範學院。  延伸查詢new window
其他
1.周筱亭(1990)。電子計算器對於國民小學小數運算學習之影響，台北縣。  延伸查詢new window
圖書論文
1.Steinle, V.、Stacey, K.(1998)。The incidence of misconceptions of decimal notation among students in Grades 5 to 10。Teaching mathematics in new times。Brisbane：hematics Education Research Group of Australia。  new window
2.Hiebert, J.(1992)。Mathematical, cognitive, and instructional analyses of decimal fractions。Analysis of arithmetic for mathematics teaching。Hillsdale, NJ：Lawrence Erlbaum Associates。  new window
3.Hiebert, J.、Wearne, D.(1986)。Procedures over concepts: The acquisition of decimal number knowledge。Conceptual and procedural knowledge: The case of mathematics。Hillsdale, NJ：Lawrence Erlbaum Associates。  new window
4.劉曼麗(1999)。小數認識與運算。國民小學數學實踐課程總結性評量分析。台北縣：教育部台灣省國民學校教師研習會。  延伸查詢new window
 
 
 
 
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