| 摘要(英) |
Currently, the probability curriculum of Taiwan has only been officially implemented since the ninth grade. Compared with other countries, our curriculum is obviously very late. This phenomenon is the motivation for this study, and it is necessary to redesign the new probability curriculum of the eighth grade and practice it. On the methodology of mathematics education research, this study uses the French teaching theory Didactic Engineering (DE) to design the probability curriculum and materials to achieve the theory and practice. The study will realize the following ideologies. (1) Practice of DE: Four stages of curriculum development. (2) Tree diagram: Using Graph representation to deal with the probability problems. (3) Mathematics literacy: Cultivate probabilistic concepts and problem solving.
The curriculum of this study used the teaching materials designed by our team. The core feature of our method is the role of tree diagram as a consistent probability learning tool for developing concepts of subjective probability, frequentist probability and classical probability. Students reach the level of dealing with the complementary events, and developing a literacy to solve practical problems in life. Also, using DE as a set of methodology for this study, it provides the discipline of instructional design and classroom practice. Although it takes a lot of time to prepare for the materials, it can prevent the research failure and develop the students′ participation in the curriculum.
The study found that students who were not taught the probability curriculum, have already contained the spontaneous concept of range of probability values, subjective probability, frequentist probability, and classical probability. The researcher speculated that students might learn the concept of probability from daily experience. After our probability curriculum, it was found that the eighth-grade students had a growth in the post-study test, indicating that students need a systematic teaching of probability, and a few students can even extend to the concept of independence and multiplication, and few students vaguely revealed the concept of conditional probability.
On the other hand, in the students’ writings, this study identifies students’ myths of probability and tree diagram. (1) The concept of ideal value. (2) The sort of sample space. (3) Classification of tree diagram. (4) Probability value of asymmetric events (5) Adding principle and multiplication principle. However, six months later of the probability curriculum, the postponement test was conducted. Compared to the probationary post-test, the students′ grades showed a slight improvement indicating that the probability curriculum of the study was quite successful.
In summary, this study suggests that the probability subject can be moved ahead to the eighth-grade, with daily experience as the main content of probability curriculum, and tree diagram as the technical tool for solving the problem. As for the ninth-grade probability curriculum, it may include the concepts of exclusion-or events, independence, and multiplication principle. This study also shows that DE really provides a methodology for mathematics education, especially for the innovation of experimental courses. This study also summarized several difficulties in using DE. It will provide as a reference for educational colleagues who are going to engage in teaching design in the future. |
| 參考文獻 |
李岳霞（2015）。教孩子堅持不放棄！玩桌遊5大益處。親子天下雜誌電子報，69。取自 http://www.parenting.com.tw/article/506 7838-教孩子堅持不放棄！玩桌遊5大益處/?page=1
林福來（2012）。統計教育研究─人才培育與資訊整合總計畫。行政院國家科學委員會專題研究計畫成果報告（編號：98-2511-S-003-004-M）。臺北市：國立臺灣師範大學。
林福來、單維彰、李源順、鄭章華（2013）。十二年國民基本教育數學領域綱要內容之前導研究報告（計畫編號：NAER-102-06-A-1-02-03-1-12）。新北市：國家教育研究院。
侯采伶（2016）。用桌遊來翻轉學習－以國中數學質數為例。臺灣教育評論月刊，5（5），132-137。
徐右任（2001）。和原住民學童「玩」數學：一個探究數學態度與數學遊戲的質性研究。臺東師院教育研究所碩士論文，未出版，台東市。
教育部（2008）。國民中小學九年一貫課程綱要數學學習領域。取自 http://teach.eje.edu.tw/data/files/class_rules/math.pdf
教育部（2018）。十二年國民基本教育國民中小學暨普通型高級中等學校數學領域課程綱要。取自https://www.naer.edu.tw/ezfiles/0/1000/attach/49/pta_18524_6629744_60029.pdf
許哲毓（2019）。初探教學工法。（投稿中）
許哲毓、單維彰（2018）。數學「不確定性」教材與評量之分析規準。臺灣教育評論月刊，7（10），170-177。取自https://shann.idv.tw/article/zheyu2018.pdf
許哲毓、單維彰、劉柏伸（2016）。樹狀圖在機率教學的應用-臺灣與英國教科書之比較。論文發表於國立臺灣大學舉辦之「第四屆師資培育國際學術研討會」，臺北市。
陳宜良、單維彰、洪萬生、袁媛（2005）。中小學數學科課程綱要評估與發展研究。教育部，臺北市。
陳欣民、劉祥通（2002）。從兒童機率迷思概念之文獻分析談機率單元的教學與課程。科學教育研究與發展季刊，26，40-51。
陳德懷（2011）。數位科技與臺灣未來二十年教學的趨勢。前瞻科技與管理，1（1），1-13。
單維彰、許哲毓（2019）。建構下一代國中階段數學課綱：機率新課程。科技部專題研究成果報告（編號：NSC-107-2511-H-008-001），未出版。
單維彰、許哲毓、陳斐卿（2018）。以學前診測與自由擬題探討九年級學生的自發性機率概念。臺灣數學教育期刊，5（2），39-64。取自http://shann.idv.tw/article/tjme2018.pdf
單維彰、陳斐卿、許哲毓（2017）。以裸測與擬題探討九年級學生的自發性機率概念。科技部專題研究成果報告（編號：NSC-104-2511-S-008-002-MY2），未出版。
詹明峰、張鐵懷（2018）。遊戲學習分析架構。數位學習科技期刊，10（3），1-20。
臺灣PISA國家研究中心（2015）。PISA數學樣本試題。取自 http://pisa.nutn.edu.tw/download/sample_papers/2009/2011_1223_mathematics.pdf。
劉秋木（1996）。國小數學科教學研究。臺北：五南。
Artigue, M. & Perrin-Glorian, M.-J. (1991). Didactic Engineering, Research and Development Tool: some Theoretical Problems linked to this Duality. For the Learning of Mathematics, 11(1), 13-18.
Artigue, M. (1994). Didactic engineering as a framework for the conception of teaching products. In R. Biehler, R.W. Scholz, R. Sträßer & B. Winkelmann (Eds.), Didactics of Mathematics as a Scientific Discipline (pp. 27-39). Dordrecht: Kluwer Academic Publishers.
Artigue, M. (1999). The Teaching and Learning of Mathematics at the University Level. Crucial Questions for Contemporary Research in Education. Notices of the AMS, 46(3), 1377-1385.
Artigue, M. (2000). Didactic engineering and the complexity of learning processes in classroom situations. Communication to MADIF2. Gothembourg.
Artigue, M. (2009). Didactical design in mathematics education. In C. Winslow (Ed.), Nordic Research in Mathematics Education. Proceedingsfrom NORMA08 (p.7 - 16). Rotterdam: Sense Publishers.
Artigue, M. (2014). Didactic engineering in mathematics education. In S. Lerman (Ed.), Encyclopedia of mathematics education (pp. 159–162). New York: Springer. Available from http://www.springerreference.com/docs/navigation.do?m=Encyclopedia+of+Mathematics+Education+(Humanities%2C+Social+Sciences+and+Law)-book188. Accessed on January 14, 2013.
Artigue, M. (2015). Perspective on design research: The case of didactical engineering. In A. A. Bikner, K. Knipping, & N. Presmeg (Eds.), Approaches to qualitative research in mathematics education (pp. 467–496). Dordrecht, Heidelberg, New York, London: Springer.
Barquero, B., & Bosch, M. (2015). Didactic engineering as a research methodology: From fundamental situations to study and research paths. In A. Watson & M. Otani (Eds.), Task design in mathematics education. Dordrecht, Heidelberg, New York, London: Springer.
Bognár, K., & Nemetz, T. (1977). On the teaching of probability at secondary level. Educational Studies in Mathematics, 8(4), 399-404. doi: 10.1007/BF00310944
Borovcnik, M., Bentz, H. J., & Kapadia, R. (1991). A probabilistic perspective. In R. Kapadia, & M. Borovcnik (Eds.), Chance encounters: Probability in education (pp. 27-71). Boston, MA: Kluwer Academic Publishers. doi: 10.1007/978-94-011-3532-0_2
Chomsky, N. (1965). Aspects of the Theory of Syntax. Cambridge: The MIT Press.
Cohen, J., & Hansel, M. (1956). Risk and gambling: The study of subjective probability. London, UK: Longmans, Green & Co.
Fischbein, E. (1975). The intuitive sources of probabilistic thinking in children. Dordrecht, The Netherlands: D. Reidel. doi: 10.1007/978-94-010-1858-6
Green, D. R. (1983). A survey of probability concepts in 3000 pupils aged 11-16 years. In D. R. Grey, P. Holmes, V. Barnett, & G. M. Constable (Eds.), Proceedings of the First International Conference on Teaching Statistics (pp. 766-783). Shefield, UK: Teaching Statistics Trust.
Herbst, P. & Kilpatrick, J. (1999). Pour lire Brousseau. For the Learning of Mathematics, 19(1), 3-10.
Konold, C. (1991). Understanding students′ beliefs about probability. In E. von Glasersfeld (Ed.), Radical constructivism in mathematics education (pp. 139-156). Dordrecht, The Netherlands: Kluwer Academic Publishers . doi: 10.1007/0-306-47201-5_7
Piaget, J., & Inhelder, B. (1975). The origin of the idea of chance in children (L. J. Leake, P. D. Burrell, & H. D. Fischbein, Trans.). London, UK: Routledge & Kegan Paul. (Original work published 1951)
Shaughnessy, J. M. (1992). Research in probability and statistics: Reflections and directions. In D.A. Grouws (Ed.), Handbook of research on mathematics teaching and learning : A project of the National Council of Teachers of Mathematics (pp. 465-494).New York: National Council of Teachers of Mathematics and MacMillan.
Warfield, V. (2006). Invitation to Didactique. Seattle: University of Washington. |
[Endnote RIS 格式]
[相關文章]
[文章引用]
[完整記錄]
[館藏目錄]
[檢視]
plurk
funp
live
udn
HD
myshare
netvibes
friend
youpush
delicious
baidu
Google bookmarks
del.icio.us
hemidemi
facebook
twitter
google
reddit