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題名：國小六年級學童解未知數文字題之另類概念分析
書刊名：臺東師院學報
作者：邱志賢／毛國楠 引用關係
作者(外文)：Chiu, Chih-hsien／Mao, Kuo-nan
出版日期：2002
卷期：13(上)
頁次：頁23-60
主題關鍵詞：未知數文字題；另類概念；學生生手；學生專家；Algebraic word-problem；Alternative concepts；Student-novice；Student-expert
原始連結：連回原系統網址new window
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　　　　　本研究的目的有二：(一)探討學生在解數學未知數文字題時，在解題歷程中產生的另類概念；(二)探討學生專家與學生生手在解數學未知數文題時，在解歷程中認知差異的情形。為了達成上述研究目的，研究者以基隆市12位國小六年級的學生為樣本，以非同步放聲思考法分析其在「應用題能力測驗」、「數學解題歷程評量表」的表現。另外，本研究也針對12位目前任教國小的教師，進行非正式的訪談。本研究主要發現為：(一)學生在解題歷程中，有「不習慣運用未知數的概念」、「列式時無法分辨算式或等式」等另類概念存在；(二)學生專家與學生生手在解題歷程的差異表現，有「學生專家能夠具有題目中的 重要基模」、「學生專家的解題策略較多元化」等現象存在。
　　　　　The major purpose of the study was to (1)explore the alternative concepts in the process of solving word-problem; and (2)explore the differences between expert-student and novice-student. The subjects was twelve sixth grade students and teachers in the primary school. Through non-synchronic thinking-aloud method, the subjects are analyzed by their performances on the Test of Word-Problems and Test of Process of Solving Problems. The findings were as follows: (a)students do not know something about algebraic word-problems well and do not differentiate differences between algorithm and equality; (b)expert-student can catch the key point when reading the questions and their strategies are multiple and diverse when solving the word-problems.
期刊論文
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3.Sweller, J.(1989)。Cognitive technology: Some procedures for facilitating learning and problem solving in mathematics and Science。Journal of Educational Psychology，81(4)，457-466。  new window
4.Garofalo, J.、Lester, F. K. Jr.(1985)。Metacognition, cognitive monitoring, and mathematical performance。Journal for Research in Mathematics Education，16(3)，163-176。  new window
5.Raine, A.、Hulme, C.、Chadderton, H.、Bailey, P.(1991)。Verbal short-term memory span in speech disordered children: Implications for articulatory coding in short-term memory。Child Development，62，415-423。  new window
6.Anand, P. G.、Ross, S. M.(1987)。Using computer-assisted instruction to personalize arithmetic materials for elementary school children。Journal of Educational Psychology，79(1)，72-78。  new window
7.任晟蓀(19860300)。臺東縣國民小學數學科新課程實施現況之研究。國教之聲，19(3)，1-22。  延伸查詢new window
8.蔡榮貴(19901100)。Process/Product Question: A Good Approach to Help Teachers in Taiwan for Diagnosing Children's Errors in Arithmetic。嘉義師院學報，4，113-123。  new window
9.Carpenter, T. P.、Moser, J. M.(1984)。The Acquisition of Addition and Subtraction Concepts in Grades One through Three。Journal for Research in Mathematics Education，15，179-202。  new window
10.Burton, L.(1984)。Mathematical thinking: The struggle for meaning。Journal for Research in Mathematical Education，15，321-329。  new window
11.Bright, G. W.、Behr, M. J.、Post, T. R.、Wachsmuth, I.(1988)。Identify fractions on numbers lines。Journal for Research in Mathematics Education，19，215-232。  new window
12.De Corte, E.、Verschaffel, L.、De Win, L.(1985)。Influence of rewording verbal problems on children's problem representations and solutions。Journal of Educational Psychology，77(4)，460-470。  new window
13.Davis, E. J.、Cooney, T. J.(1977)。Identifying errors in solving certain linear equations。MATYC Journal，11，170-176。  new window
14.Carpenter, T. P.、Fennema, E.、Peterson, P. L.、Chiang, C. P.、Loef, M.(1989)。Using knowledge of Children's Mathematics Thinking in Classroom Teaching: A n Experimental Study。American Educational Research Journal，26，499-531。  new window
15.Hauff, H. M.、Fogarty, G. J.(1996)。Analysing problem solving behavior of successful and unsuccessful statistics students。Instructional Science，24，379-409。  new window
16.Hudson, T.(1983)。Correspondences and Numerical Differences between Disjoint Sets。Child Development，54，84-90。  new window
17.MacGregor, M.、Stacey, K.(1993)。Cognitive Models Underlying Students' Formulation of Simple Linear Equations。Journal for Research in Mathematics Education，24，217-232。  new window
18.Mayer, R. E.(1995)。Eastern eye-opener。The American School Board Journal，182，28-31。  new window
19.Moyer, J. C.、Sowder, L.、Treadgill-Sowder, J.、Moyer, M. B.(1984)。Story problem formats: Drawn versus verbal versus telegrahpics。Journal for Research in Mathematics Education，15，342-351。  new window
20.Steinberg, R. M.、Sleeman, D. H.、Ktorza, D.(1990)。Transfor-mations in High School Algebra。Journal for Research in Mathematics Education，22，112-121。  new window
21.黃敏晃(19870700)。如何解數學題：數學解題策略簡介。科學月刊，18(7)=211，515-522。  延伸查詢new window
22.Cobb, P.(1988)。The Tension between Theories of Learning and Instruction in Mathematics Education。Educational Psychologist，23(2)，87-103。  new window
23.Hegarty, M.、Mayer, R. E.、Monk, C. A.(1995)。Comprehension of arithmetic word problems: A comparison of successful and unsuccessful problem solvers。Journal of Educational Psychology，87(1)，18-32。  new window
24.Hiebert, J.、Carpenter, T. P.、Fennema, E.、Fuson, K.、Human, P.、Murray, H.、Olivier, A.、Wearne, D.(1996)。Problem solving as a Basis for Reform in Curriculum and Instruction: The Case of Mathematics。Educational Researcher，25(4)，12-21。  new window
25.Clements, D. H.、Battista, M. T.(1990)。Constructivist learning and teaching。Arithmetic Teacher，38(1)，34-35。  new window
26.許良榮(19931200)。談建構主義之理論觀點與教學的爭論。國教輔導，33(2)=298，7-12。  延伸查詢new window
會議論文
1.Hart, K.(1987)。Practical work and formalization, too great a gap。The Eleventh International Conference on Psychology of Mathematics Education。Montreal：Psychology of Mathematics Education。408-415。  new window
2.Kieran, C.(1984)。A comparison between novice and more- expert algebra students on tasks dealing with the equivalence of equations。Sixth Annual Meeting of Psychology of Mathematics Education in North America。Madison, Wilconsin。83-91。  new window
3.Perry, M.、Church, R.、Goldin-Meadow, S.(1988)。Learning a principle versus learning a procedure: Looking beyond what is taught。The annual meeting of the American Educational Research Association。New Orleans。  new window
4.Ross, S. H.(1986)。The development of children's place-value numeration concepts in grades two through five。The annual meeting of the American Educational Research Association。San Francisco, CA。  new window
研究報告
1.謝淡宜(1998)。國小數學資優生及普通生數學解題歷程之比較。  延伸查詢new window
學位論文
1.陳維民(1998)。兒童的未知數概念研究：一個國小六年級兒童的個案研究(碩士論文)。國立高雄師範大學，高雄。  延伸查詢new window
2.Lewis, A. B.(1989)。Enhancement of arithmetic word problem-solving skill through representation training(博士論文)。University of California，Santa Barbara。  new window
3.吳昭容(1990)。圖示對國小兒童解數學應用題之影響(博士論文)。國立臺灣大學。  延伸查詢new window
4.王佳文(1995)。國小六年級數學解未知數問題測驗之發展與學生在認知成份和錯誤組型之分析(碩士論文)。國立台南師範學院。  延伸查詢new window
5.周慧茹(1998)。建構教室中數學知識形成歷程之詮釋分析(碩士論文)。台北市立師範學院。  延伸查詢new window
6.梁新正(1996)。高雄地區高二學生數學解題之基模知識與歷程之分析研究(碩士論文)。國立高雄師範大學。  延伸查詢new window
7.游正旭(1999)。情境教學合作學習下同儕互動歷程之俗民誌研究(碩士論文)。淡江大學。  延伸查詢new window
8.蔡佳錚(1997)。國小學生工作記憶與數學解題歷程關係之研究(碩士論文)。國立台南師範學院。  延伸查詢new window
9.古明峰(1997)。加減法應用題語文知識對問題難度之影響暨動態評量在應用問題之學習與遷移歷程上研究(博士論文)。國立臺灣師範大學。new window  延伸查詢new window
10.李靜瑤(1994)。高雄市國二學生數學解題歷程之分析研究(碩士論文)。國立高雄師範大學。  延伸查詢new window
11.林碧珍(1989)。國小學生數學解題的表現及其相關因素之研究(碩士論文)。國立臺灣師範大學。  延伸查詢new window
12.徐文鈺(1992)。圖示策略訓練課程對國小五年級學生的數學應用題解題能力與錯誤類型之影響(碩士論文)。國立臺灣師範大學。  延伸查詢new window
13.郭美如(1999)。後設認知的教學成效及其相關變數之分析--以小六及國一數學資優生為對象(碩士論文)。國立臺灣師範大學，台北市。  延伸查詢new window
14.楊瑞智(1994)。國小五、六年級不同能力學童數學解題的思考過程(博士論文)。國立師範大學。new window  延伸查詢new window
15.劉貞宜(2000)。數學資優生的解題歷程分析--以建中三位不同能力的數學資優生為例(碩士論文)。國立臺灣師範大學，台北市。  延伸查詢new window
16.劉國芬(1997)。高雄地區高一學生高低數學成就之解題後設認知行為分析研究(碩士論文)。國立高雄師範大學。  延伸查詢new window
17.薛麗卿(1999)。數學寫作活動對國小學生解題能力及數學態度之影響(碩士論文)。國立臺灣師範大學，臺北市。  延伸查詢new window
18.張景媛(1994)。國中生數學學習歷程統整模式的驗證及應用：學生建構數學概念的分析及數學文字題教學策略的研究(博士論文)。國立臺灣師範大學，臺北市。new window  延伸查詢new window
19.謝毅興(1991)。國小兒童解數學應用問題的策略(碩士論文)。國立臺灣大學。  延伸查詢new window
20.紀惠英(1991)。國小六年級學生應用問題表徵類型輿同構性之研究(碩士論文)。國立臺灣師範大學。  延伸查詢new window
21.林奕宏(2000)。「多元智能與問題解決整合型教學模式」對國小學生數學學習表現之影響(碩士論文)。國立臺灣師範大學。  延伸查詢new window
圖書
1.Krutetskii, Vadim Andreevich、Teller, Joan、Kilpatrick, Jeremy、Wirzup, Izaak(1976)。The psychology of mathematical abilities in schoolchildren。Chicago, IL：University of Chicago Press。  new window
2.鄭毓信(1998)。數學教育哲學。臺北市：九章出版社。  延伸查詢new window
3.教育部(2000)。九年一貫課程數學學習領域研習手冊。  延伸查詢new window
4.教育部(2000)。國民中小學課程綱要--數學學習領域。  延伸查詢new window
5.Ginsburg, H.(1982)。arithematic: How they learn it and how you teach it。Austin, TX：Pro-Ed。  new window
6.Dossey, J. A.、Mullis, I. V. S.、Lindquist, M. M.、Chambers, D. L.(1988)。The Mathematics Report Card: Are We Measuring Up?。Princeton, NJ：Educational Testing Service。  new window
7.Piaget, J.(1952)。The origins of intelligence in children。New York, NY：International Universities Press。  new window
8.Mayer, Richard E.、林清山(1990)。教育心理學：認知取向。臺北市：遠流出版社。  延伸查詢new window
9.黃瑞琴(1991)。質的教育研究法。臺北：心理出版社。  延伸查詢new window
10.Mayer, R. E.(1987)。Educational Psychology: A cognitive approach。Little, Brown and Company。  new window
11.吳明清(1991)。教育研究：基本觀念與方法之分析。台北市：五南。  延伸查詢new window
12.Gagne, E. D.、Yekovich, C. W.、Yekovich, F. R.、丘修平(1998)。教學心理學：學習的認知基礎。臺北：遠流。  延伸查詢new window
單篇論文
1.Babbitt, B. C.(1990)。Errors and pattern in problem(No. ED 338500)。  new window
其他
1.周筱亭(2000)。從課程標準到課程綱要--以數學學習領域為例，http://www.iest.edu.tw/announce/9teach/chapper9.htm。  延伸查詢new window
圖書論文
1.Silver, E. A.(1987)。Foundations of cognitive theory and research for mathematics problem-solving instruction。Cognitive science and mathematics education。Hillsdale, NJ：Lawrence Erlbaum Associate, Inc.。  new window
2.Carpenter, T. P.、Corbitt, M. K.、Kepner, H. S.、Lindquist, M. M.、Reys, R. E.(1981)。National assessment。Mathematics education research: Implications for the 80's。Reston, VA：National Council of Teachers of Mathematics。  new window
3.Kantowski, M. G.(1981)。Problem solving。Mathematics education research: Implications for the 80's。Alexandria, VA：American Society for curriculum Development。  new window
4.Schoenfeld, A. H.(1987)。What's all the fuss about meatcognitions?。Cognitive science and mathematics education。Hillsdale, NJ：Lawrence Erlbaum Associate, Inc.。  new window
 
 
 
 
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