研究生: |
孫晉忻 Sun Chin Hsin |
---|---|
論文名稱: |
MathCAL-II:應用派特里網路理論所建置之數學解題輔助系統 MathCAL-II: A Petri-net Based System for Assisting Mathematical Problem Solving |
指導教授: |
林美娟
Lin, Mei-Chuen |
學位類別: |
碩士 Master |
系所名稱: |
資訊教育研究所 Graduate Institute of Information and Computer Education |
論文出版年: | 2005 |
畢業學年度: | 93 |
語文別: | 中文 |
論文頁數: | 116 |
中文關鍵詞: | 派特里網路 、電腦輔助學習 、電腦輔助解題系統 、數學解題 |
英文關鍵詞: | Petri net, Computer assist learning, Mathematical problem solving |
論文種類: | 學術論文 |
相關次數: | 點閱:221 下載:28 |
分享至: |
查詢本校圖書館目錄 查詢臺灣博碩士論文知識加值系統 勘誤回報 |
數學解題是當今數學教育重要的課題。解題訓練依據坡里亞定義,可區分為瞭解問題、擬定計畫、實施計畫、回顧解答四個步驟。然而以講述為主的傳統教學型態受限於人力及時間,常無法引導學生完成解題步驟並達到適性化教學目標,應用電腦科技做為輔助工具,應可彌補傳統教學的某些不足。民國84年林美娟教授及莊志洋教授提出將派特里網路應用至數學解題,並完成MathCAL數學解題練習系統。此構想利用派特里網路中權杖的傳遞,系統可將解題步驟以文字或圖形的方式呈現,並可分析使用者的解題步驟以提供必要的引導。本研究修正歷年MathCAL系統核心、診斷與矯正機制等部份細節,在發展過程中邀請數學教師和高中學生參與測試與建議,並且將教師的教學知識融入系統發展中,完成MathCAL-II。系統完成後針對高中生進行實驗研究,分析實驗結果發現,MathCAL-II可有效地輔助學生解題,並且達到顯著成效。實驗中的問卷調查結果亦顯示MathCAL-II所提供的功能皆符合使用者解題的需求,並且能夠加強學生對於數學概念的瞭解,對學生的學習態度與學習興趣皆有正向影響。
MathCAL-II is a piece of software for students to practice solving mathematical word problems in trigonometry. At the core of the system is a database that stores experts’ problem-solving paths. These solution paths are stored as Petri net graphs internally. MathCAL-II also dynamically records a learner’s solution path during a practicing session. Thus it can compare a learner’s partial solution path against all correct solution paths to identify a best match, which can then be used to provide guidance to a learner in case s/he requests help. In a series of experiments that we conducted in a local high school, 58 students who participated voluntarily were divided randomly into the treatment group and the control group. The treatment group used MathCAL-II to practice solving trigonometric word problems, whereas the control group used the traditional pencil-and-paper approach. Results revealed that the students in the treatment group made significantly more progress than those in the control group. A questionnaire survey also showed that MathCAL-II not only improved students’ understanding of mathematical concepts in trigonometry but had positive influence on students’ attitudes toward learning trigonometry.
一、中文部份
[1]王文中(民93):統計學與Excel資料分析之實習應用。博碩文化股份有限公司。
[2]王進成、戴進耘(民90):高職學年學分制資訊科新課程與電腦硬體裝修乙級技術士術科測驗之技能學習內涵關係分析研究。第十六屆全國技術及職業教育研討會,頁11-20。
[3]王進成(民91):應用鷹架學習理論及派翠西網路技術在網路化輔助學習模式之研究-以「電腦硬體裝修丙級學科技能檢定」為例。國立臺灣師範大學工業教育研究所碩士論文。
[4]朱耀明(民87):網路合作學習與傳統教學的整合。第七屆國際電腦輔助教學研討會大會論文,頁551-557。
[5]何榮桂、朱延平(民86):CAI課程軟體編製技術參考手冊。臺北市:教育部電子計算機中心。
[6]李宏彥(民90):適合國小學童之錯誤類型導引式數學學習系統:以國小三角形面積單元為例。國立臺北師範學院數理教育研究所數學組碩士論文。
[7]林伯成(民91):利用知識地圖診斷數學問題之研究。中原大學資訊工程研究所碩士論文。
[8]林秀鳳(民90):解題歷程導向之電腦輔助數學應用題解題系統。國立臺灣師範大學資訊教育研究所碩士論文。
[9]林美娟、莊志洋、孫鵬宗、許金葉、黃瀧輝、盧思靜、黃凱澤(民92):一個數學解題練習系統之設計理念,科學教育學刊,11(1),27-50。
[10]洪榮昭、劉明洲(民88):電腦輔助教學之設計與應用。臺北市:師大書苑。
[11]數學學門規劃資料,行政院國家科學委員會75年出版
[12]孫茂鑫(民86):以派翠西網路為基礎之數學解題系統-高中數學之「圓」單元。國立臺灣師範大學資訊教育研究所碩士論文。
[13]孫晉忻、林美娟、盧思靜(民92):物件導向設計應用於數學解題練習系統之實例研究。第十四屆物件導向技術與應用研討會(OOTSIG 2003)論文彙編。頁281-287。
[14]孫鵬宗(民87):一個網路化的數學解題系統-國中數學之「三角函數」。國立臺灣師範大學資訊教育研究所碩士論文。
[15]秦靜儀(民88):部份給分之電腦化適性測驗系統。國立臺灣師範大學資訊教育研究所碩士論文。
[16]教育部(民93):國民中學課程標準。教育部國教司。
[17]張昆平(民82):派翠西網路應用在教學軟體流向控制之研究。國立臺灣師範大學工業教育研究所碩士論文。
[18]張炳雄(民93):專家診斷系統應用於文書處理術科評量機制之研究,頁225-227。國立臺灣師範大學工業教育研究所碩士論文。
[19]許金葉(民88):以派翠西網路為基礎的數學解題診斷矯正模式。國立臺灣師範大學資訊教育研究所碩士論文。
[20]陳定邦(民93):鷹架教學概念在成人學習歷程上應用之研究。國立臺灣師範大學工業教育研究所碩士論文。
[21]陳鵬昌(民90):一個物件導向的數學概念學習與診斷工具。國立中央大學數學研究所碩士論文。
[22]黃正志(民86):問題解決式數學科教學軟體解題流程分析-運用派翠西網路。國立臺灣師範大學資訊教育研究所碩士論文。
[23]黃瀧輝(民89):MathCAL的教學資料庫設計。國立臺灣師範大學資訊教育研究所碩士論文。
[24]葉秀芳(民93):以派翠西網路矯正國小三角形面積計算錯誤類型之適性引導系統。國立臺北師範學院數理教育研究所數學組碩士論文。
[25]葉重新(民90):教育研究法。臺北市:心理出版社股份有限公司。
[26]楊錦潭(民85):媒體教學與數學教育。教學科技與媒體,27(6),頁3-9。
[27]盧思靜(民90):數理科解題練習系統設計。國立臺灣師範大學資訊教育研究所碩士論文。
[28]坡里亞(民80):怎樣解題。(閻育蘇譯)。臺北市:九章出版社。(原著出版年:1948年)
[29]戴建耘、黃國峰(民88):應用超連結作教學流向控制分析。技術與職業教育學報第2期,頁69-82。
[30]戴建耘、蔡志宏、袁熒助(民91):運用派翠西網路規劃各校活動線上填報機制之研究:以技職資訊傳播入口網為例。第十七屆全國技職教育研討會論文集,頁599-608。
[31]謝仙進(民92):「微軟Office專家認證」資訊課程內涵建構之研究。國立臺灣師範大學工業教育研究所碩士論文。
[32]離散數學-電腦輔助教學CAI,取自:http://www.cis.nctu.edu.tw/~is83039/discret/discrete.html
二、英文部份
[33]Abudiab, M. (2001). The impact of technology on teaching an ordinary differential equations course. Journal of Circuits, Systems, and Computers 16, 3, 7-18
[34]Botana, F., & Valcarce, J. L.. (2002). A dynamic-symbolic interface for geometric theorem discovery. Computers & Education, 38, 21-35.
[35]Campione, J. C., Brown, A. L., & Connell, M. L.(1989). Metacognition: on the importance of understanding what you are doing. In R. I. Charles & E.A. Silver(Eds.), The teaching and assessing of mathematical problem solving, 93-114. Hillsdale, NJ:Erlbaum.
[36]Cloer, T., Jr. (1981), Factors Affecting Comprehension of Math Word Problems - A Review of the Research. ERIC Document Reproduction Service, No. ED209655.
[37]Cockcroft, W. H. (1982). Mathematics Counts: Report of the Committee of Inquiry into the Teaching of Mathematics in Schools under the Chairmanship of Dr. W. H. Cockcroft. England: HMSO.
[38]Dehnert, J., Gajewskyk, M., Lembke, S., & Weber, H. (2001). The Petri Net Baukasten: 2nd Installment. Electronic Notes in Theoretical Computer Science 44 No. 4. http://www.elsevier.nl/locate/entcs/volume44.html
[39]Dynamic Geometry (DG)
http://sunflower.singnet.com.sg/~okheng/dg/gsp.html
[40]Gao, Xiao-Shan., Zhu, Changcai., & Chou, S. C. (1998). Geometry expert. Taiwan : Nine Chapters Publishers.
[41]Gao, Xiao-Shan., & Huang, Yong. (1998). Building Dynamic Mathematical Model with Geometry Expert I. Geometric Transformations, Functions and Plane Curves, Proceedings of ATCM98.
[42]Kadijevich, DJ., Haapasalo, L.(2001). Linking procedural and conceptual mathematical knowledge through CAL. Journal of Computer Assisted Learning, Jun2001, Vol. 17 Issue 2, p156.
[43]Kamii, C. & Ewing, J. K., (1995). Basing teaching on Piaget's constructivism. Childhood Education, 72(5) , 260-264.
[44]Klawe, M. M.(1998). When does the use of computer games and other interactive multimedia software help students learn mathematics? Available from http://taz.cs.ubc.ca/egems/home.html
[45]Laborde, J.M. & Bellemain, F. (1994). Cabri geometry II. Dallas: Texas Instruments.
[46]Lin, Janet M.-C., Juang, Jie-Yong, and Sun, Ponson (1999). An Internet-Based CAL Software for Solving Trigonometric Problems. Proc. of International Conference on Mathematics/Science Education and Technology, Association for the Advancement of Computing in Education, Charlottesville, VA. 275-280.
[47]Lin, Janet M.-C., Juang, Jie-Yong, and Sun, Ponson (2000a). Representation of Problem-Solving Procedures in MathCAL. Proc. of International Conference on Mathematics/Science Education and Technology, Association for the Advancement of Computing in Education, Charlottesville, VA. 265-270.
[48]Lin, Janet M.-C., Hsu, C.-Y., Huang, K.K., and Juang, Jie-Yong (2000b). MathCAL’s Diagnostic Sub-System. Proc. of 8th International Conference on Computers in Education, Taipei, Taiwan, 709-715.
[49]Lin, Janet M.-C., Huang, L.-H., Huang, K.K., and Juang, Jie-Yong (2001). MathCAL and Its Database Design. Proc. of World Conference on Educational Multimedia, Hypermedia & Telecommunications, Tampere, Finland. 1131-1136.
[50]Maredi, M., & Oosthuizen, H. J. (1995). A Problem-Solving CAI---Factor-Q, Computers & Education, 25, 235-250
[51]Math Soft Engineering & Education Publishers (2002). Study Works! 2002.
[52]Meece, J. L., Wigfield, A. & Eccles, J. S. (1990). Predictors of math anxiety and its influence on young adolescents’ course enrollment intentions and performance in mathematics. Journal of Educational Psychology, 82, 60-70.
[53]Murataa, T., (1989). Petri nets: Properties, analysis and applications, Procedings of the IEEE, 77, April, 541-579.
[54]National Council of Supervisors of Mathematics (1977). Position paper on Basic Mathematics Skills. Washington, D.C.: National Institute of Education.
[55]National Council of Supervisors of Mathematics (1989). Essential Mathematics for the Twenty-First Century: The Position Paper of The National Council of Supervisors of Mathematics, Arithmetic Teacher, 37(1), 44-46.
[56]National Council of Teachers of Mathematics (1989). Curriculum and Evaluation Standards for School Mathematics. Reston, VA: National Council of Teachers of Mathematics.
[57]Nine Chapters Publishers (2003). The Geometer’s Sketchpad 3. Taiwan: Nine Chapters Publishers. http://ccmp.chiuchang.com.tw/software/gsp.html
[58]Peterson, J. L. (1981). Petri Net Theory and the Modeling of Systems. Englewood Cliffs, N. J: Prentice-Hall.
[59]Polya, G. (1945). How to Solve It. Princeton,N.J.: Princeton University Press.
[60]Princeton Review (2003). Algebra Smart. http://www.princetonreview.com/
[61]Recio, T., & Gonzalez-Lopez, M.J..(1998). Dose Computer Algebra help at all learning about real numbers? Mathematics and Computers in Simulation 45, 185-195.
[62]Reising, W. (1985). Petri Nets: An Introduction. Springer-Verlag.
[63]Sanchez, J. C., Encinas, L. H., Fernandez, R. L., & Sanchez, M. R. (2002). Designing hypermedia tools for solving problems in mathematics. Computers & Education, 38, 303-317.
[64]Schoenfeld, A. H. (1985). Mathematical problem solving. New York: Academic Press.
[65]Steele, M. M. & Steele, J. W.(1999). DISCOVER: an intelligent tutoring system for teaching students with learning difficulties to solve word problems. Computers in Mathematics and Science Teaching, 18(4), 351-9.
[66]Steffe, L. P. & D'Ambrosio, B. S., (1995). Toward a working model of constructivist teaching: A reaction to Simon. Journal of Research in Mathematics Education, 26(2) , 146-159.
[67]Taylor, L. (1999). An integrated learning system and its effect on examination performance in mathematics. Computers & Education, 32, 95-107.
[68]Tobin, K., Briscoe, C. & Holman, J. R. (1990). Overcoming constraints to effective elementary science teaching. Science Education, 74(4), 409-420.
[69]Ubuz, B., & Ersoy, Y. (1997). The Effect of Problem-Solving Method with Handout Material on Achievement in Solving Max-Min Word Problems. Journal of Mathematical Behavior, 16(1), 75-85.
[70]Wenger, E. (1987). Artificial intelligence and tutoring systems: computational and cognitive approaches to the communication of knowledge. Morgan Kaufmann Publishers Inc., San Francisco, CA, 1987.
[71]Yourdon, E.(1989). Modern structured analysis. Englewood Cliffs, NJ:Prentice-Hall.