研究生: |
林秀鳳 Hsiu-Feng Lin |
---|---|
論文名稱: |
解題歷程導向之電腦輔助數學應用題解題系統 |
指導教授: |
張國恩
Chang, Kuo-En |
學位類別: |
碩士 Master |
系所名稱: |
資訊工程學系 Department of Computer Science and Information Engineering |
論文出版年: | 2001 |
畢業學年度: | 89 |
語文別: | 中文 |
論文頁數: | 94 |
中文關鍵詞: | 解題歷程 、數學應用題 、數學解題 、數學解題系統 |
英文關鍵詞: | mathematical problem-solving process, mathematical word problems, mathematical problem-solving, mathematical problem-solving system |
論文種類: | 學術論文 |
相關次數: | 點閱:217 下載:17 |
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 |
本研究的主要目的為發展以數學解題歷程為設計導向的電腦輔助解題系統,並以較複雜或多步驟包含加減乘除四則運算的數學應用題為研究範圍,應用於自行發展的電腦輔助解題系統中。
本研究是以北市吳興國小五年級四個班級的學生作為實驗對象,該四個班級是以本研究自行設計之國小五年級數學應用題解題測驗甲卷及五年級上學期國語及數學平均成績為條件共篩選出49位學生,分為實驗組及控制組。實驗組學生採用本研究中所設計之電腦化數學解題系統,而控制組則採用紙筆方式進行輔助學習。系統將以國小五年級下學期之數學應用問題作為實驗教材。
研究結果有以下的發現:(1)實驗組學生經過8次的電腦化數學解題訓練後,其解題能力表現顯著優於控制組。(2)就實驗組而言,經過8次的電腦化數學解題訓練後,其後測的解題能力表現亦顯著高於前測。(3)由「電腦輔助數學解題系統使用問卷」中可看出,受過電腦化數學解題系統進行輔助解題訓練的學生,對於電腦化數學解題系統在數學解題的教學或學習上的效果,大都抱持正面的態度。
The main goal of this study is to develop a computer-assisted mathematical problem-solving system, which includes more complex and multistep word problems requiring skills of some or all of the four mathematical operations: addition, subtraction, multiplication and division.
Forty-nine fifth-grade elementary school students participated in the experiments to assess the practicability and instructional effect of this system. The students were randomly assigned into two groups. Experiment groups learned through the training of the computer-assisted mathematical problem-solving system, whereas the control groups learned in the form of paper-and-pencil. Word problems taught in the second semester of fifth grade were used as materials in the experiments.
The results are as follows: (1) After eight training sessions, the mathematical problem-solving ability of those in the experiment groups is significantly better than that of the control groups. (2) For the students in the experiment groups, their mathematical problem-solving ability has significantly improved after eight training sessions. (3) Those who participate in the designed computer-assisted mathematical problem-solving training, in their responses to the questionnaires, show positive attitude towards the use of computer-assisted systems in mathematical problem-solving instruction and learning.
參 考 著 作
林清山、張景媛(1993),國中生後設認知、動機信念與數學解題策略之關係研究,教育心理學報,26,53-74頁。
吳昭容(1990),圖示對國小學童解數學應題之影響。國立台灣大學心理學研究所碩士論文。
何縕琪、林清山(1994),表徵策略教學對提升國小低解題正確率學生解題表現之效果研究。教育心理學報,27,259-279頁。
邱上真、王惠川、朱婉豔、沈明錦(1992),國小中年級數學科解題歷程導向之評量。特殊教育與復健學報,2,235-271頁。
孫達剛(1992),雄中﹑雄女學生數學解題之研究—Polya解四階段論取向。國立高雄師範大學教育研究所碩士論文。
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。國立台灣師範大學教育心理與輔導研究所碩士論文。
翁嘉英(1989),國小兒童解數學應用問題的認知歷程。國立台灣大學心理學研究所碩士論文。
張景媛(1994),數學文字題誤概念分析及學生建構數學概念的研究,教育心理學報,27,175-200頁。
張景媛(1994),國中生數學學習歷程統整模式之研究,教育心理學報,27,141-174頁。
張憶壽(1990),怎樣解題。台北市:長橋出版社。
黃幸美(1997),兒童的概念學習與迷思概念。教育研究雙月刊,55,55-59頁。
謝毅興(1991),國小兒童解數學應用問題的策略。國立台灣大學心理學研究所碩士論文。
Bachor, D. (1987). Towards a taxonomy of word problem. In J. C. Bergeron, N. Herscovics, & C. Kieran (Eds.), Proceedings of the 11th International Conference for the Psychology of Mathematics Education (vol. 2, pp.163-169). Montreal, Canada: Universite’de Montreal.
Blandenship, C., & Lilly, M. S. (1981). Mainstreaming students with learning and behavior problems:Techniques for classroom teachers. NY:Holt, Rinehart and Winston.
Campione, J. C. (1989). Assisted assessment:A taxonomy of approaches and an outline of strengths and weaknesses. Journal of Learning Disabilities, 22 (3), 151-165.
De Corte, E., Verschaffel, L., & De Win, L. (1985). The influence of rewording verbal problems on childrens’ representations and solutions. Journal of Educational Psychology, 77, 460-470.
Derry, J. S., & Hawkes, L. W. (1993). Local Cognitive Modeling of Problem Solving Behavior:An Application of Fuzzy Theory. In S. P. Lajoie & S. J. Derry (Eds.). Computers as cognitive tools. (pp. 107-140). Hillsdale, N. J.: Lawrence Erlbaum Associates.
Gibson, L. S. (1991). The effects of modeling multiplication on the conceptual understanding of the operation and its application to word problem-solving performance of third grade students. Unpublished doctoral dissertation, Temple University.
Hargest, J. T., Wood, C., Rose, W. H., & Coughlin, L. (1986). Preparing learning disabled adolescents for a state competency math test. Unpublished Manuscript. Bel Air, MD Harford Co MD Public Schools.
Kotovsky, K., Hayes, J. R., & Simon, H. A. (1985). Why are some problem hare? Evidence from the tower of Hanoi. Cognitive Psychology, 17, 248-294.
Krulik, S. K., & Rudnick, J. A. (1989). Problem solving: A handbook for senior high school teachers. Boston, MA: Allyn & Bacon.
Lee, K. S. (1982). Fourth-grades heuristic problem-solving behavior. Journal for Research in Mathematics Education, 13, 110-123.
Lester, K. F. (1983). Trends and issues in mathematical problem-solving. In R. Lesh & M. Landau (Eds.). Acquisition of mathematics concepts and processes. New York:Academic Press.
Lester, F. K., & Kroll, D. L. (1991). Assessing student growth in mathematical problem solving . In G. Kulm (Ed.), Assessing Higher Order thinking in Mathematics. NW: American Association for the Advancement of Science.
Lewis, A. B., & Mayer, R. E. (1987). Students’ miscomprehension of relational statements in arithmetic word problems. Journal of Educational Psychology, 79, 361-371.
Lewis, A. B. (1989). Training students to represent arithmetic word problems. Journal of Educational Psychology, 81, 521-531.
Mayer, R. E (1982). Memory for algebra story problems. Journal of Educational Psychology, 74, 199-216.
Mayer, R. E.(1985). Implications of cognitive psychology for instruction in mathematical problem solving. In E. A. silver (Ed.), Teaching and learning mathematical problem solving:Multiple research perspectives (pp.123-138). Hillsdale, NJ:Erlbaum.
Mayer, R. E. (1985). Educational Psychology:Cognitive Approach. NY:Freeman.
Mayer, R. E. (1987). Educational Psychology: A cognitive approach. Boston: Little, Brown and Company.
Mayer, R. E. (1991).Thinking , Problem Solving , Cognition. New York: Freeman.
Mayer, R. E. (1992). Cognition and instruction:Their historic meeting within educational psychology. Journal of Educational Psychology, 84, 405-412.
Mayer, R. E. (1992). Thinking , Problem Solving ,Cognition. New York. : W. H. Freeman and Company.
Muth, K. D. (1991). Effects of cuing on middle-school students’ performance on arithmetic word problems containing extraneous information. Journal of Educational Psychology, 83(1), 173-174.
Mestre, J. P. (1988). The role of language comprehension in mathematics and problem solving. In R. R. Cocking & J. P. Mestre (Eds), Linguistic and Cultural influences on learning mathematics (pp. 201-220). Hillsdale, NJ:Erlbaum.
Nesher, P., & Teubal, E. (1975). Verbal cues as an interfering factor in verbal problem solving. Educational studies in mathematics, 6, 41-51.
Pass, F. G. W., van Merrienboer, J. J. G., & Adam, J. J. (1994). Measurement of cognitive load in educational research. Perceptual and Motor Skill, 79, 419-430.
Reed, S. K. (1984). Estimating answers to algebra word problems. Journal of experimental psychology: Learning, Memory and cognition, 10, 778-790.
Reusser, K. (1996). From Cognitive Modeling to the Design of Pedagogical Tools. In S. Vosnadiou, E. De Corte, R. Glaser and H. Mandl (Eds.), International Perspectives on the Design of Technology Supported Learning Environments (p. 81-104). Hillsdale, NJ : Lawrence Erlbaum Associates.
Romberg, T. & Carpenter, T. (1986). Research on teaching and learning mathematics: Two disciplines of scientific inquiry. In M. Wittrock (Ed.), Handbook of reaearch in teaching, American Education Research Association.
Schoenfeld. A. H (1985). Mathematical Problem solving. NY: Academic Press.
Silver, E. A. (1987). Foundations of cognitive theory and research for mathematics problem-solving instruction. In A. H. Schoenfeld (Ed.), Cognitive science and mathematics education (pp.33-60). Hillsdale, NJ: Erlbaum.
Steele, M. M., & Steele, J. W. (1999). DISCOVER: An Intelligent Tutoring System for Teaching Students with Learning Difficulties to Solve Word Problems. Journal of Computers in Mathematics and Science Teaching, 18(4), 351-359.
Sweller, J., van Merrienboer, J. J. G., & Paas, F. G. W. C. (1998). Cognitive architecture and instructional design. Educational Psychology Review, 10, 251-296.
Thomas, C. P. (1980). The effect of instruction on first-grade children’s initial solution processes for basic addition and subtraction problem. A paper presented at the 1980 Annual Meeting of the American Educational Research Association.
Tougan, P. W. (1993). A study of the effect of using an ‘open approach’ to teaching mathematics upon the mathematical problem-solving behaviors of secondary school students. Unpublished doctoral dissertation, Southern Illinois University At Carbondate.
Vergnaud, G. (1987). Conclusion. In C. Janvier (Ed.), Problems of representation in the teaching and learning of mathematics 227-232. Hillsdale, NJ: Erlbaum.
Wilburne, J. M. (1997). The effect of teaching metacognition strategies to preservice elementary school teachers on their mathematical problem-solving achievement and attitude. Unpublished doctoral dissertation, Temple University.
Willis, G. B., & Fuson, K. C. (1988). Teaching children to use schematic drawing to solve addition and subtraction word problems. Journal of Educational Psychology, 80, 192 –201.
Wittrock, M. C. (1986). Students’ thought process. In M. Wittrock (Ed.) Handbook of research on teaching, AERA.
Yancy, A. V. (1981). Pupil generated diagrams as strategy for solving word problems for elementary mathematics (Journal Announcement:RIEJAN86), Specialist in Education Degree Thesis, University of Louisville (ERIC Document Reproduction Service No. ED260992 SE045962).