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研究生:陳晚蓁
研究生(外文):Wan-Chen Chen
論文名稱:國一新生數學銜接方案之研究∼以分數單元為例
論文名稱(外文):The Study of Mathematics Curriculum Connection for 7th-grade Students ―Example of Fractions Unit
指導教授:楊德清楊德清引用關係
指導教授(外文):Der-Ching Yang Phd.
學位類別:碩士
校院名稱:國立嘉義大學
系所名稱:數學教育研究所
學門:教育學門
學類:普通科目教育學類
論文種類:學術論文
論文出版年:2004
畢業學年度:92
語文別:中文
論文頁數:149
中文關鍵詞:分數國一新生分數概念分數運算
外文關鍵詞:fractionthe 7th-grade studentsfractional conceptfractional calculation
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目前從國小畢業的國一新生,國小課程是85年版的課程,但國一卻採用九年一貫新課程,為了彌補兩種課程之間的落差,各國民中學均利用新生入學的暑假期間,加強銜接相關的數學課程。因此,本研究希望透過教師行動研究,先探究在接受課程銜接之前,國一新生已有的分數迷思概念類型,接下來分析在銜接方案實施之後,一般學生在分數概念及分數運算上的改變情形,最後再針對銜接方案的實施歷程作一檢討反省,作為日後相關教學方案設計之參考。
結果發現:
(一)在迷思概念方面,學生對於異分母分數的加減以及分數的乘法等分數算則,有明顯的迷思概念產生;在圖示分數的技巧上,學生多以算則解題,缺乏分數的基本概念。(二)在教學成效方面,採用概念為主的實驗組學生比傳統教學的對照組學生,能夠較為熟練地以圖示的方式來表徵分數的運算;當面對分數的運算時,實驗組學生也能夠以不同於傳統算則的方式來解題;在連續量與離散量的分割上,表現也比對照組學生好。(三)教學反思,教師應加強等分概念,讓學生瞭解等分時每一等分必須相等;以對照法為基礎來談分數加減法的教學,可避免學生產生分子加分子、分母加分母的迷思,但教材的設計仍有再修正的必要;在學習成就測驗的壓力下,如何跳脫傳統式的教學,對教學者來說是一大挑戰。
The 7th-year students, who were recently graduated from elementary schools and were educated with the former curriculum published in 1996, are asked to join the classes which are designed to compensate the gap between two curricula during summer vacation. Via teacher’s action research, the research is designed to probe the myths concepts of the 7th-year students first, analyzing the improvements on fractional concepts and calculations of ordinary students after the connection programs deployed. Finally, reassessments of the connection programs are carried out, and the results will be the reference of relevant mathematic education in the future.
The results reveal that
A: The myth concepts on fractional addition/subtraction of different denominators and multiple of fractions are recognized; as to plotting diagrams, without the fundamental concepts on fractions the routine techniques are often utilized to plot the diagrams.
B: As to practical achievements, the students who are educated with emphasis concepts are more skilled in displaying fractional calculations via plotting diagrams. Alternative techniques are often deployed by the students educated with emphasis concepts. In division of continuum or discrete the students educated with designed plans perform better as well.
C: Teachers should emphasize the concepts of equal fractions with the deep understanding of the equality of each fraction. The teaching technique of fractional addition/subtraction based on comparison can avoid the myth concepts. However the modification of materials are necessary. Under the pressure of basic competence test, it is quite a challenge for teachers to release themselves from traditional techniques.
第一章 緒論
第一節 研究動機……………………………………………………1
第二節 研究目的與待答問題………………………………………3
第三節 名詞解釋……………………………………………………3
第四節 研究範圍與限制……………………………………………4
第二章 文獻探討
第一節 分數概念的探討……………………………………………5
第二節 分數教材分析……………………………………………..14
第三節 分數教學的相關研究探討………………………………..17
第四節 分數教學活動的設計理念……………………………..…22
第三章 研究方法
第一節 研究方法與研究架構…………………………………….34
第二節 研究對象與研究參與者…………………………………..36
第三節 研究工具…………………………………………………..38
第四節 研究流程………..………………..………………………..42
第五節 資料的收集、整理與分析………………………………..45
第四章 研究結果討論
第一節 試題測驗結果及比較..……………………………………47
第二節 訪談資料分析……………………………………………..64
第三節 教學活動方案的實踐……………………………………..92
第五章 結論與建議
結論……………………………………………………………….110
建議……………………………………………………………….115
參考文獻
中文部分…………………………………………………………..117
英文部分……………………………………...…………………..119
附錄
附件一 教學活動設計………………………………………….122
附件二 國中課程銜接教材……………………………………138
? 附件三 前後測試題……………………………………………143
一、中文部分
呂玉琴(1991)。分數概念文獻探討。台北師院學報,第四期,573-605。
呂玉琴(1996)。國小教師的分數知識。台北師院學報,第九期,427-460。
呂玉琴(1998)。國小教師分數教學之相關知識研究。台北師院學報,第十一期,393-438。
林福來與黃敏晃(1993)。分數啟蒙課程的分析、批判與辨證。科學教育學刊,1(1),1-27。
林福來、黃敏晃與呂玉琴(1996)。分數啟蒙的學習與教學之發展性研究。科學教育學刊,4(2),161-196。
林碧珍(1990)。從圖形表徵與符號表徵之間的轉換探討國小學生的分數概念。新竹師院學報,第四期,295-347。
林彥宏(2002)。國小五年級學童分數概念的診斷與補救教學。台南:台南師範學院教師在職進修數學碩士學位班碩士論文。
Booth. L. R.(1987)。分數的學習困難(Booth 專題演講,林麗惠整理)。科學教育月刊,100,7-15。
邱山桐(2003)。九年一貫國中課程銜接教材。台南:翰林。
洪素敏、楊德清(2002)。創意教學〜分數的補救教學,科學育研究與發展季刊,29,33-52。
教育部(2000)。國民中小學九年一貫課程暫行綱要數學學習領域。台北:教育部。
教育部(2003)。樂在數學─國民中小學數學教學參考手冊。台北:教育部。
國立台北師院數學教育系(2002)。國民中小學九年一貫課程補充說明草稿。台北:台北師院。
陳伯璋(1988)。行動研究法:教育研究新取向。台北:宏圖。
陳靜姿 (1997)。國小四年級兒童等值分數瞭解之初探。國立台中師範學院初等教育研究所碩士論文。
陳晚蓁、楊德清(2003)。九年一貫教改先鋒~國一新生數學迷思概念之分析。九年一貫教學與課程研習手冊。台北:教育部。
楊壬孝(1988)。國中小學生分數概念的發展。國科會研究計畫報告。
楊瑞智(2000)。探究師院生之分數基本概念及分數概念的課室教學。台北市立師範學院學報,第31期,357-382。
楊德清(2000)。國小6年級學生回答數字常識所使用之方法,科學教育學刊,8(4),379-394。
楊德清(2002)。從教學活動中幫助國小6年級學生發展數字常識之研究,科學教育學刊,10(3),233-260。(NSC 89-2511-S-415-001)
楊德清與洪素敏(2003)。比較分數大小~從具體、半具體至抽象符號表徵之教學行動研究,南師學報,37(2),75-103。(NSC 91-2511-S-415-001)
蔡清田(1999)。行動研究取向與教育實習典範理念與實踐。教育實習的典範理念與實踐學術研討會。教育部指導,國立台灣師大主辦,1999,4,30,台北。
蔡清田(2000)。教育行動研究。台北:五南。
甄曉蘭(1995)。合作行動研究:進行教育研究的另一種方式。國立嘉義師範學報,1995 (9),297-318。
劉世能(2001)。臺灣北部地區國小高年級學童分數概念之研究。台北:國立台北師範學院數理教育研究所碩士論文。
二、英文部分
Anderson, C. L. , Anderson, K. M. & Wenzel, E. J. (2000). Oil and water don’t mix, but they do teach fractions. Teaching Children Mathematics, 7(3), 174-178.
Bass, H. (2003). Computational fluency, algorithms, and mathematical proficiency: One mathematician''s perspective. Teaching Children Mathematics, 9(6), 322-329.
Behr, M. J., Lesh, R., Post, T. R. & Silver, E. A. (1983). Rational number concepts. In R. Lesh, & M. Landan (Eds.). Acquisition of mathematics concepts, research processes. New York: Academic Press.
Behr, M. J., Wachsmuth, I., Post, T. R., & Lesh, R.(1984). Order and equivalence of rational numbers: A clinical teaching experiment. Journal for Research in Mathematics Education, 15, 323-341.
Cramer K. A., Post T. R., & delMas R. C. (2002). Initial fraction learning by fourth- and fifth-grade students: A comparison of the effects of using commercial curricula with the effects of using the rational number project curriculum. Journal for Research in Mathematics Education, 33(2), 111-144.
Dickson, L., Brown, M. & Gibson, O. (1984). Children learning mathematics: A teachers’ guide to recent research. New York: Holt, Rinehart and Winston.
Figueras, O. (1989). Two different views of fractions: Fractionating and operating. En Actas de la 13eme conference internationale, psychology of mathematics education, G.R. didactique, CNRS - Paris V, Vol. I, págs(pp268-275). Paris: Francia.
Fennema, E. & Franke, M. L. (1992). Teachers'' knowledge and its impact. In D. A. Grouws(Ed.), NCTM Handbook of research on mathematics teaching and learning (pp. 147-164). New York: Macmillan.
Galloway, P. J. (1975). Achievement and attitude of pupils toward initial fractional number concepts at various ages from six through ten years and of decimals at ages eight, nine and ten. Unpublished manuscript, University of Michigan.
Hunting, R. P. (1984). Rachel’s schemes for constructing fraction knowledge. Educational Study in Mathematics, 17, 49-66.
Judy, R. (1995). A common-cents approach to fraction. Teaching Children Mathematics, 2(4), 234-236.
Jecks, P. (1981). Conceptual issues in the teaching and learning of fractions. Journal for Research in Mathematics Education, 12, 339-348.
Kerslake, D. (1986a). Children’s Perception of Fractions. The 10th International Conference for the Psychology of Mathmatics Education.
Kerslake, D. (1986b). Fractions: Children''s strategies and errors. UK: NFER.
Kouba, V., Zawojewski, J., & Strutchens, M.(1997). What do students know about numbers and operations? In P. A. Kenney & E. A. Silver(Eds.), Results from the six mathematics assessment of the National Assessment of Education Process(pp.87-140). Reston, VA:NVTM.
Lankford, L. K.(1972). Final report: Some computational strategies of seventh grade pupils, Charlottesville, VA:University of Virginia.(ERIC Document Reproduction Service No.Ed 069496).
Larry, W. E. & Joseph, N. P. (1987). A teaching sequence from initial fraction concepts through the addition of unlike fraction. In M. Suydam (Ed.), Development computational skills (pp. 129-147), 1978 Yearbook of NCTM. Reston, VA: NCTM.
Lesh, R. Behr, M. & Post, T. (1987). Rational number relations and proportion. In C. Janvier(Ed.), Problems in teaching and learning of mathematics. London: New Jersey.
Mack, N. K. (1993). Learning rational numbers with understanding: The case of informal knowledge. In T. Carpenter, T. E. Fennema, & T. Romberg(Eds.), Research on the teaching learning and assessing of rational number concepts(pp.327-362). Hillsdale NJ: Lawrence Erlbaum Associates.
National Council of Teacher of Mathematics (2000). Principals and standards for school mathematics. Reston, VA:NCTM.
Painter, R. R. (1989). A comparsion of the procedural error patterns, scores, and other variables, of select groups of university and eight-grade studentd in Mississippi on a test involving arithmetic operation on fractions. Unpublished doctoral dissertation, University of Southern Mississppi.
Postlewait, K. B., Adams, M. R. & Shih, J.C. (2003). Promoting meaningful mastery of addition and subtraction. Teaching Children Mathematics, 9(6), 354-357.
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Sinicrope, R., Mick, H. W., & Kolb, J. R. (2002). Interpretations of fraction division. In B. Litwiller, & G. Bright(Eds), Making sense of fraction, ratios, and proportions(pp. 153-161), 2002 Yearbook of NCTM. Reston, VA:NCTM.
Streefland, L. (1991). Fractions in realistic mathematics education. Dordrecht: Kluwer.
Tirosh, D. (2000). Enhencing prospective teachers’ knowledge of children conception: The case of division of fractions. Journal forRresearch in Mathematics Education, 31(1), 5-25.
Watanabe, T. (2002). Representations in Teaching and Learning Fractions. Teaching Children Mathematics, 8(8), 457-463.
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