题名

數學乘除問題情境發展之研究-以BBS爲管道

并列篇名

A Study of Developing Mathematical Problems of Multiplication and Division Using the BBS

DOI

10.6173/CJSE.2004.1201.03

作者

馬秀蘭(Hsiu-Lan Ma)

关键词

乘除法 ; 發展問題情境擬題 ; 電子佈告欄系統BBS ; Multiplication and Division ; Developing Problem Situations Problem Posing ; Bulletin Board System BBS

期刊名称

科學教育學刊

卷期/出版年月

12卷1期(2004 / 03 / 01)

页次

53 - 81

内容语文

繁體中文

中文摘要

本文旨在透過BBS,去促進學生做數學之意願,以培養其發展問題的能力,並從問題情境中去暸解學童對乘除法概念認知的程度,以及掌握不同問題情境的能力。研究結果發現,上網的樂趣,能促使全體學生在一學期的時間裡持續上網去發展問題,因而問題能真正反應出他們實際生活經驗中的乘除法模式及認知的程度;其中「倍數法」與「比例因子」及「等分除」是多數乘法及除法之問題情境類型,而「較小整數」且「符合計算信念」是問題的其它結構變項。而且拜BBS效益之賜,低學校能力者也願意投入數學的活動中,因此再次證明藉網路的BBS去促進學生「做數學」的意願是可行的,BBS可被視爲一個支援、協助學校能力低之學生發展數學問題的管道。

英文摘要

The purpose of this research was to investigate the effect of using the BBS on student attention and motivation to solve multiplication and division problems. In addition it provides information about students' cognitive levels and their abilities to control various problem situations. The results show that student interest in using the web can be used to motivate students to develop mathematical problems during a semester. The developed problems can reflect the students' ideas of daily experiences and the cognitive levels required by multiplication and division. The students most frequently use the concepts of ”multiple” and ”rate factor” and ”partitive division”. The concepts of the ”smaller integer” and ”computational thoughts” are also included in developed problems. Because of the use of the web, lower ability students are motivated to stay involved. Therefore the BBS might be viewed as a venue to assist students with low school abilities to develop mathematical problems.

主题分类 社會科學 > 教育學
参考文献
  1. 馬秀蘭(2001)。透過電腦網路來發展數學加減法問題之研究。科學教育學刊,9(4),375-399。
    連結:
  2. Ashcraft, M. H.(1992).Cognitive arithmetic: A review of data and theory.Cognition,44,75-106.
  3. Ashcraft, M. H.,Christy, K. S.(1995).The frequency of arithmetic facts in elementary texts: Addition and multiplication in grades 1-6.Journal for Research in Mathematics Education,26(5),396-421.
  4. Ball, D.(1990).Prospective elementary and secondary teachers` understanding of division.Journal for Research in Mathematics Education,21,132-144.
  5. Baroody, A. J.(1993).Problem solving, reasoning, and communication (K-8): Helping children think mathematically.New York:MacMillan.
  6. Bell, A. W.,Fischbein, E.,Greer, G. B.(1984).Choice of operation in verbal arithmetic problems: the effects of number size, problem structure and context.Educational Studies in Mathematics,15,129-147.
  7. Bell, A. W.,Greer, G. B.,Grimison, L.,Mangan, C.(1989).Children`s performance on multiplicative word problems: Elements of a descriptive theory.Journal for Research in Mathematics Education,20,434-449.
  8. Booth, L. R.(1986).Child-method in secondary mathematics.Educational Studies in Mathematics,12,301-316.
  9. Brown, J. S.(1981).Unpublished Pro Thesis, University of London, Chelesea College.
  10. Brown, J. S.,Collins, A.,Duguid, P.(1989).Situated cognition and the culture of learning: A systems approach to educational testing.Educational Researcher,18(10),32-42.
  11. Campbell, J. I. D.,Oliphant, M.(1992).The nature and origins of mathematical skills.Amsterdam:Elsevier.
  12. Charles, R.,Lester, F.(1982).Teaching problem solving: What, why and how.Palo Alto, CA:Dale Seymour.
  13. Connolly, P.,T. Vilardi (Eds.)(1989).Writing to learning mathematics and science.New York:Teacher College Press.
  14. Davis, G.(1984).Learning mathematics: The cognitive science approach to mathematics education.Norwood, NJ:Ablex.
  15. Davis, G.,Hunting, R. P.,Pearn, C.(1993).What might a fraction mean to a child and how would a teacher know.Journal of Mathematical Behavior,12,63-76.
  16. Davydov, V. V.,J. Teller (Trans.)(1991).Soviet Studies in Mathematics Education Series.Reston, VA:National Council of Teachers of Mathematics.
  17. Davydov, V. V.,L. P. Steff (Ed.)(1991).A psychological analysis of multiplication.Psychological abilities of primary school children in learning mathematics,6,9-85.
  18. Dehaene, S.,Mehler, J.(1992).Crosslinguistic regularities in the frequency of number words.Cognition,43,1-29.
  19. Dickson, L.,Brown, M.,Gibson, O.(1984).Holt, Rinehart and Winston for The Schools Council.
  20. Ellerton, N. F.(1986).Children`s made up mathematics problems-a new perspective on talented mathematicians.Educational Studies in Mathematics,17,261-271.
  21. Ellsworth, J. H.(1991).Paper presented at the National Conference on the Adult Learner.
  22. English, L. D.(1998).Children`s problem posing within formal and informal contexts.Journal for Research in Mathematics Education,29(1),83-106.
  23. Eslick, K. M.(1993).Long Beach,California State University.
  24. Figueiredo, A. D.,Steele, R.(1992).Commission of the European Communities, Brussels, Belgium.
  25. 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,16,3-17.
  26. Fischbein, E.,Kedem, I.,A. Vermandel (Ed.)(1982).Proceedings of the Sixth International Conference for the Psychology of Mathematics Education.Antwerp, Belgium:
  27. Fuson, K. C.,G. Leinhardt,R. Putnam,A. Hattrup (Eds.)(1992).Analysis of arithmetic for mathematics teaching.Hillsdale, New Jersey:Lawrence Erlbaum Associates.
  28. Graeber, A. O.(1993).Research into practice: Misconceptions about multiplication and division.Arithmetic,40,408-411.
  29. Greer, B.,D. A. Grouws (Ed.)(1992).Handbook of research on mathematics teaching and learning.New York:Macmillan publishing company.
  30. Greer, G. B.,Mangan, C.,J. M. Moser (Ed.)(1984).Proceedings of the sixth annual meeting of North American Chapter of the international group for the psychology of mathematics educational.Madison, WI:Wisconsin Center for Education Research, University of Wisconsin.
  31. Greer, G. B.,McCann, M.,F. Furinghetti (Ed.)(1991).Proceedings of the Fifteen International Conference for Psychology of Mathematics.Assisi, Italy:
  32. Hamann, M. S.,Ashcraft, M. H.(1986).Textbook presentations of the basic addition facts.Cognition and Instruction,3,173-192.
  33. Hart, K. M.(1981).Children`s understanding of mathematics: 11-16.London:John Murray.
  34. Hiebert, J.(1988).A theory of developing competence with written mathematical symbols.Educational Studies in Mathematics,19,333-355.
  35. Hiebert, J.,Behr, M.,J. Hiebert,M. Behr (Eds.)(1988).Number concepts and operations in the middle grades.Reston, VA:National Council of Teachers of Mathematics.
  36. Hodgin, K. W.(1987).Paper presented at the annual meeting of the National Council of Teachers of Mathematics.Anaheim, CA:
  37. Johanson, T. L.(1996).Corvalis, Oregon,Oregon State University.
  38. Krutetskii, V. A.(1976).The psychology of mathematical abilities in school children.Chicago:The University Chicago Press.
  39. Leung, S. S.(1993).Unpublished doctoral dissertation, University of Pittsburgh.
  40. Leung, S. S.,Wu, R. X.(1999).Problem posing with middle grades mathematics: Two real classroom examples.Mathematics teaching in the middle school,5(2),112-117.
  41. Ma, H. L.(2000).Paper presented at Second International Conference on Science, Mathematics and Technology Education.Taiwan:National Taiwan Normal University.
  42. Martin, W. G.,Harel, G.(1989).Proof frames of preservice elementary teachers.Journal for Research in Mathematics Education,20,41-51.
  43. Montana State Office of Public Instruction(1991).About METNET: Montana educational telecommunications network.Montana:Laws of Montana, 52nd Legislature.
  44. Muzio, J. A.(1992).A comparison of mainframe and personal computer based bulletin board systems for computer-mediated communications in distance education courses.Canada:British-Columbia.
  45. National Council of Teachers of Mathematics(1989).Curriculum and evaluation standards for school mathematics.Virginia:National Council of Teachers of Mathematics.
  46. Reitman, W.(1989).Cognition and thought.New York:Wiley.
  47. Rey, R. E.,Yang, D. C.(1998).Relationship between computational performance and number sense among sixth-and eighth-grade students in Taiwan.Journal for Research in Mathematics Education,29(2),225-237.
  48. Rudnitsky, A.,Etheredge, S.,Freeman, J. M.,Gilbert, T.(1995).Learning to solve addition and subtraction word problems through a structure-plus-writing approach.Journal for Research in Mathematics Education,26(5),467-486.
  49. Schliemann, A. D.,Araujo, C.,Cassuné, M. A.,Macedo, S.,Nicéas, L.(1998).Use of multiplicative commutativity by school children and street sellers.Journal for Research in Mathematics Education,29(4),422-435.
  50. Schliemann, A. D.,Carraher, D. W.,P. Light,G. Butterworth (Eds.)(1992).Context and Cognition.Hemel Hempstead, UK:Harvester-Wheatscheaf.
  51. Schwartz, J.,J. Hiebert,M. Behr (Eds.)(1988).Number concepts and operations in the middle grades.Reston, VA:National Council of Teachers of Mathematics.
  52. Siegler, R. S.,Shipley, C.,T. Simon,G. Halford (Eds.)(1995).Developing cognitive competence: New approaches to process modeling.Hillsdale, New Jersey:Lawrence Erlbaum Associates.
  53. Silver, E. A.(1994).On mathematical problem posing.For the Learning of Mathematics,14(1),19-28.
  54. Silver, E. A.(1995).The nature and use of open problem in Mathematics Education: Mathematical and pedagogical perspectives.International Reviews on Mathematics Education,2,67-72.
  55. Silver, E. A.,Cai, J.(1996).An analysis of arithmetic problem posing by middle school students.Journal for Research in Mathematics Education,27(5),521-539.
  56. Silver, E. A.,N. Nohda,F. L. Lin (Eds.)(1993).Proceedings of the seventeenth annual meeting of the international group for the psychology of mathematics education.Tsukuba, Japan:
  57. Silver, E.,J. Hiebert (Ed.)(1986).Conceptual and procedural knowledge: The case of mathematics.Hillsdale, New Jersey:Lawrence Erlbaum Associates.
  58. Simon, M. A.(1993).Prospective elementary teachers` knowledge of division.Journal for Research in Mathematics Education,24(3),233-254.
  59. Spanos, G.(1991).ERIC Digest.U.S., District of Columbia.
  60. Stigler, J. W.,Fuson, K. C.,Ham, M.,Kim, M. S.(1986).A analysis of addition and subtraction word problems in American and Soviet elementary mathematics textbooks.Cognition and Instruction,3,153-171.
  61. Stovanova, E.,Ellerton, N. F.,R. B. Corwin, (Ed.)(1996).Talking mathematics: Supporting children`s voices.Portsmouth, NH:
  62. Suydam, M. N.(1984).ERIC/SMEAC, Mathematics Education Digest No. 1. U.S..Ohio:
  63. Tsubota, E.(1987).On children`s problem posing.Japan:
  64. Usiskin, Z.,Bell, M.(1983).Applying arithmetic: A handbook of applications of arithmetic. Part II: Operation.IL:Chicago University.
  65. Wallerstein, N.(1983).Language and culture in conflict: Problem-posing in the ESL classroom.Reading, MA:Addison-Wesley.
  66. Winograd, K.(1990).Colorado,The University of Northern Colorado, Greeley.
  67. Zazkis, R.,Campbell, S.(1996).Divisibility and Multiplicative Structure of natural Numbers: Preservice Teachers` Understanding.Journal for Research in Mathematics Education,27(5),540-563.
  68. Zoni, S. J.(1992).Florida,Nova University, Fort Lauderdale.
  69. 王文科(1886)。教育研究法。台北市:五南圖書出版公司。
  70. 古藤伶、邱石虎譯(1986)。兒童與創造思考。板橋教師研習會。
  71. 朱建正(1997)。國小數學課程的數學理論基礎。台北市:朱建正。
  72. 周幸儀、梁淑坤(1994)。國小四年級乘除法文字題的擬題與解題的初步調查。論文發表於中華民國第十屆科學教育學術研討會,台北市:
  73. 坪田耕三(1987)。生動的算術:讓小朋友自行擬題(1、2、3 年級)。日本:國土出版社。
  74. 林碧珍(1991)。國小兒童對於乘除法應用問題之認知結構。新竹師院學報,5,221-288。
  75. 馬秀蘭(1999)。學童數學態度及解題策略延後評量的分析-以BBS爲溝通管道。論文發表於數理教學及師資培育研討會,彰化市:
  76. 馬秀蘭(1999)。學童透過電子佈告欄系統進行數學解題之研究。論文發表於中華民國第十五屆科學教育學術研討會,彰化市:
  77. 馬秀蘭(2000)。數學問題情境發展之探討-以BBS爲管道。中華民國第十六屆科學教育學術研討會,台北市:
  78. 馬秀蘭(2000)。數學解題之研究-以BBS爲工具。八十九學年度師範學院教育學術研討會論文集·資訊教育類
  79. 國立編譯館(2001)。國民小學數學教學指引-第九冊。臺北市:國立編譯館。
  80. 梁淑坤(1997)。行政院國家科學委員會行政院國家科學委員會,未出版
  81. 梁淑坤(1995)。行政院國家科學委員會行政院國家科學委員會,未出版
  82. 梁淑坤(1997)。行政院國家科學委員會行政院國家科學委員會,未出版
  83. 陳春杏(1989)。國民小學數學科乘除法教材類型之分析與研究。國教學報,2,253-290。
  84. 陳美芳(1995)。博士論文(博士論文)。台北市,國立台灣師範大學。
  85. 游麗卿(1999)。除法概念形成歷程中的錯誤分析對教學的啓示。高雄市:復文圖書出版社。
  86. 黃正文(1996)。碩士論文(碩士論文)。台北市,國立臺灣師範大學。
  87. 甯自強(1993)。單位量的變換。教師之友,34(1),27-34。
  88. 楊惠如(2000)。碩士論文(碩士論文)。嘉義市,國立嘉義大學。
  89. 楊錦潭、林佳毅(1998)。亙動式Java程式語言遠距課程設計。中華民國第十四屆科學教育學術研討會,高雄市:
  90. 劉秋木(1996)。國小數學教科教學研究。台北市:五南圖書出版公司。
  91. 蔣治邦、謝堅、陳竹村、吳淑娟、林昭珍(2000)。國小數學教材分析-整數的乘除運算。教育部臺灣省國民學校教師研習會,臺北縣:
  92. 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。臺中市:國立臺中師範學院。
被引用次数
  1. 馬秀蘭(2007)。發展問題知識—以數學能力低學童對乘除法算式為例。高雄師大學報,23(3),99-123。
  2. 馬秀蘭(2007)。學生思考過程之探究—以實務推理為例。科學教育學刊,15(4),387-410。
  3. 馬秀蘭(2008)。以van Hiele理論探討圖形樣式思考層次之研究。教育研究集刊,54(1),49-85。
  4. 謝佩宜、周倩(2006)。網路數學討論區使用者之批判思考表現、參與歷程觀感、動機與程度之相關研究。科學教育學刊,14(1),83-100。