跳到主要內容

臺灣博碩士論文加值系統

(3.235.185.78) 您好!臺灣時間:2021/07/27 18:19
字體大小: 字級放大   字級縮小   預設字形  
回查詢結果 :::

詳目顯示

: 
twitterline
研究生:陳瓊瑜
研究生(外文):Suen C. Chen
論文名稱:國小三年級數學學習困難學生乘法應用問題解題歷程之研究
論文名稱(外文):The study of the problem solving process of multiplication word problems at the third grade students with mathematical learning difficulties
指導教授:徐享良徐享良引用關係
指導教授(外文):Won-Zone Su
學位類別:碩士
校院名稱:國立彰化師範大學
系所名稱:特殊教育學系在職進修專班
學門:教育學門
學類:特殊教育學類
論文種類:學術論文
論文出版年:2002
畢業學年度:90
語文別:中文
論文頁數:228
中文關鍵詞:解題歷程數學學習困難學生放聲思考晤談
外文關鍵詞:the problem solving processthinking aloudinterview
相關次數:
  • 被引用被引用:112
  • 點閱點閱:2267
  • 評分評分:
  • 下載下載:598
  • 收藏至我的研究室書目清單書目收藏:19
本研究旨在比較國小三年級高數學能力學生與低數學能力學生在乘法應用問題之解題歷程的差異,進而依此差異來探索低數學能力學生在解乘法應用問題時其認知運作歷程可能遭遇的障礙。研究之對象包括低數學能力學生與高數學能力學生各五人,共計十人;研究材料為中難度與高難度之乘法應用問題各五題,共計十題;研究方法為放聲思考與晤談兩種。本研究依放聲思考之口語資料與晤談資料分析兩組受試的解題歷程,及解題歷程的差異。研究結果如下:
1.高能力組受試在解題歷程的五個要素,大致能表現出良好的運作狀況。比較容易出現錯誤的是在問題整合與解題執行等兩個階段,另外,高能力組受試對計算錯誤的覺察狀況也不甚理想。
2.低能力組受試在解題歷程的五個要素都可能出現錯誤,其中以問題整合與解題執行兩個要素的運作特別容易出現障礙。另外,低能力組受試也缺乏對整體之解題狀況的覺察。
3.比較兩組受試的解題歷程發現,高能力組受試的解題速度顯著的快於低能力組受試,且高數學能力受試在整個解題歷程的各個要素大致都能有良好的運作,其比較容易出現錯誤的是計算的疏忽以及單位間換算的統整。相反的,低數學能力受試在整個解題歷程的各個要素都可能出現錯誤,尤其是在問題整合、解題執行、與問題轉譯等方面。
4.低數學能力受試在解乘法應用問題時,其認知運作歷程可能遭遇的障礙在於,其對特定概念的理解有困難(如題目中的關係語句),加上乘法概念的知識不足,以至於難以運用這些概念知識來促進其對問題的轉譯與題意的整合。另一方面,也因為計算技能不夠熟練,解題監控的狀況不夠積極,導致解題的效率不佳,解題錯誤的情形容易出現。
This study aims at comparing and contrasting the difference of multiplication application problems solving process of the third graders of elementary students between those of high mathematical ability and those of low. Based on the result, or the differences, I will further study the possible difficulties these students of low mathematical ability might face while they are solving the multiplication application problems. Five for each ability group, ten in total, took part in this study. We will work on ten problems of multiplication application, include five for the middle difficult and five for the highly difficult problems. I will apply the research methods of thinking aloud and meeting. According to the oral records of thinking aloud and the meeting records, I analyze the problem solving process, and the difference of the process between the two groups as following:
1. The most students of the group of high mathematical ability can apply the five problem solving elements well. They often make mistakes at the stages of problem integration and problem solving execution. Also, they are less aware of their mistakes made in calculation.
2. It’s very possible for the students of low mathematical ability to make mistakes anytime, but the most difficult for them are the two elements: problem integration and problem solving execution. They are not aware of their mistakes made while they are working on the problems.
3. To summarize, obviously the students of high mathematical ability and solve the problems faster than the low. The group of high mathematical ability can apply the five problem solving elements well while the low can make mistakes at any elements. The group of high mathematical ability often makes mistakes while doing calculation and the integration of unit conversion. The group of low mathematical ability often makes mistakes at problem integration, problem solving execution, problem translation, etc.
4. The possible cognitive difficulty of solving multiplication application problems the group of low mathematical ability might face is the students’ comprehensive problem of specific concepts, such as the relative clauses occur in the question. Also, they don’t have enough multiplication knowledge for them to apply upon problem translation and integration of meaning. Besides, due to their lack of calculation skill proficiency and their passive attitude at problem solving monitoring, they are lack of efficiency on problem solving, and it’s easy for them to make mistakes during the process.
國小三年級數學學習困難學生乘法應用問題解題歷程之研究
目 錄
第一章 緒論……………………………………………………….1
第一節 問題背景…………………………………………….1
第二節 研究目的與研究問題……………………………….4
第三節 名詞解釋…………………………………………….5
第二章 文獻探討………………………………………………….8
第一節 數學學障兒童的學習特質………………………….8
第二節 數學解題歷程……………………………………… 15
第三節 乘法的相關研究…………………………………… 24
第三章 研究方法………………………………………………….35
第一節 研究流程…………………………………………….35
第二節 研究對象…………………………………………….36
第三節 研究工具…………………………………………….38
第四節 研究步驟…………………………………………….43
第四章 結果與討論……………………………………………… 49
第一節 高數學能力受式的解題歷程……………………….49
第二節 低數學能力受式的解題歷程……………………….72
第三節 高低數學能力學生之解題歷程的差異…………….97
第五章 結論與建議……………………………………………….110
第一節 結論………………………………………………….110
第二節 建議………………………………………………….114
第三節 研究限制…………………………………………….116
參考文獻……………………………………………………………117
附錄一、乘法應用問題……………………………………………126
附錄二、晤談指引…………………………………………………127
附錄三、乘法應用問題之難度資料………………………………128
附錄四、放聲思考與觀察原始資料………………………………129
附錄五、晤談原始資料……………………………………………152
表 目 錄
表2-1 認知─後設認知的數學解題模式…………………………..18
表2-2 Mayer(1992)數學解題分析模式………………………….20
表2-3 第四冊南一書局出版乘法單元目標…………………………24
表2-4 第五冊康軒版乘法單元目標……………………………… 25
表2-5 乘法問題解題策略……………………………………………32
表2-6 乘法相關研究…………………………………………………34
表3-1 受試基本資料………………………………………………..37
表3-2 受試在學期間所使用之教科書各類型乘法問題之
出現次數表………………………………………………….40
表3-3 解題歷程的要素說明表……………………………………..42
表4-1 高能力組受試在第一題之解題歷程的分析摘要表………..55
表4-2 高能力組受試在第二題之解題歷程的分析摘要表…………56
表4-3 高能力組受試在第三題之解題歷程的分析摘要表…………57
表4-4 高能力組受試在第四題之解題歷程的分析摘要表…………58
表4-5 高能力組受試在第五題之解題歷程的分析摘要表………..59
表4-6 高能力組受試在第六題之解題歷程的分析摘要表………..64
表4-7 高能力組受試在第七題之解題歷程的分析摘要表…………65
表4-8 高能力組受試在第八題之解題歷程的分析摘要表………..66
表4-9 高能力組受試在第九題之解題歷程的分析摘要表………..67
表4-10 高能力組受試在第十題之解題歷程的分析摘要表………..68
表4-11 高能力組受試在中、高難度題目之解題歷程的摘要表…..70
表4-12 低能力組受試在第一題之解題歷程的分析摘要表………..79
表4-13 低能力組受試在第二題之解題歷程的分析摘要表………80
表4-14 低能力組受試在第三題之解題歷程的分析摘要表………81
表4-15 低能力組受試在第四題之解題歷程的分析摘要表………82
表4-16 低能力組受試在第五題之解題歷程的分析摘要表……..83
表4-17 低能力組受試在第六題之解題歷程的分析摘要表……..88
表4-18 低能力組受試在第七題之解題歷程的分析摘要表……..89
表4-19 低能力組受試在第八題之解題歷程的分析摘要表………90
表4-20 低能力組受試在第九題之解題歷程的分析摘要表……..91
表4-21 低能力組受試在第十題之解題歷程的分析摘要表……..92
表4-22 低能力組受試在中、高難度題目之解題歷程的摘要表…94
表4-23 不同能力學生在不同難度題目之作答時間的T考驗
摘要表……………………………………………………..97
表4-24 兩組受試在不同難度題目之平均答對題數與解題
錯誤原因之摘要表………………………………………..100
表4-25 兩組受試在中難度題目之解題歷程比較…………………102
表4-26 兩組受試在高難度題目之解題歷程比較…………………104
圖 目 錄
圖3-1 研究流程圖………………………………………………..36
圖3-2 放聲思考實施流程圖………………………………………46
參考書目
一、 中文部分
古明峰(民87):加減法應用問題語文知識對問題難度之影響暨動態評量在應用問題之學習與遷移歷程上研究。新竹師院學報,11,391-420。
朱經明、蔡玉瑟(民89):動態評量在診斷國小五年級數學障礙學生錯誤類型之應用成效。特殊教育研究學刊,18,173-189。
吳仁俊(民85):兒童的乘法概念研究─一個三年級的個案。國立高雄師範大學數學系未出版之碩士論文。
李光榮(民86):國小兒童正整數乘法概念之研究─一個四年級兒童之個案研究。國立嘉義師範學院國民教育研究所未出版之碩士論文。
李俊仁(民81):一位數乘法答題策略發展之研究。國立中正大學心理研究所未出版之碩士論文。
李盛祖、林世華(民88):國小數學乘法系列診斷測驗題庫的建立與應用。師大學報:教育類,44(1&2),55-74。
林原宏(民83):國小高年級學生解決乘除文字題之研究─以列式策略與試題分析為探討基礎。國立台中師範學院初等教育研究所未出版之碩士論文。
林淑玲(民88):國小學習障礙學生對比較類加減應用題解題表徵之研究。國立台灣師範大學特殊教育學系未出版之碩士論文。
林碧珍(民80):國小兒童對於乘除法應用問題之認知結構。國立新竹師範學院學報,5,221-288。
周台傑、蔡宗玫(民86):國小數學學習障礙學生應用問題解題之研究。特殊教育學報,12,233-292。
邱上真(民90):跨領域多層次的數學學障研究:從學習障礙的官方定義談起。載於2001數學學習障礙研討會手冊。台北:台灣師範大學。
邱佳寧(民90):國小數學學習障礙學生解題策略之研究。國立彰化師範大學特殊教育學系系未出版之碩士論文。
邱裕淵(民89):國小六年級學生在乘法文字題的解題表現。國立嘉義師範學院國民教育研究所未出版之碩士論文。
洪碧霞、吳裕益(民85):國小數學診斷測驗。台北市:教育部訓育委員會。
柯華葳(民88):閱讀理解困難篩選測驗。行政院國家科學委員會特殊教育工作小組。
許天威、蕭金土(民88):綜合性非語文智力測驗。台北市:心理出版社。
許美華(民90):國小二年級乘法解題策略之變化─以三位學童為例。花蓮師院學報,12,173-199。
陳美芳(民84):「學生因素」與「題目因素」對國小高年級兒童乘除法應用問題解題影響之研究。國立台灣師範大學心理與輔導研究所未出版之博士論文。
張莉莉(民88):加減問題之解題活動類型: 一個國小二年級兒童的個案研究。臺南師院學生學刊,20, 114-132。
教育部(民89):國民中小學九年一貫課程暫行綱要。台北:教育部。
黃秀霜(民88):中文年級認字量表。行政院國家科學委員會特殊教育工作小組。
鄭昭明(1993):認知心理學。台北市:桂冠。
楊明家(民86):六年級不同解題能力學生在數學解題歷程後設認知行為之比較研究。國立嘉義師範學院國民教育研究所未出版之碩士論文。
秦麗花(民84):國小數學學習障礙兒童數學解題錯誤類型分析。特殊教育季刊,55,33-38。
二、 英文文獻
Anderson, J. R. (2000). Cognitive psychology and its implications(5th ed.). New York: Worth Publishers and W. H. Freeman.
Anderson, J. R. (1982). Acquisition of cognitive skills. Psychological review, 89, 369-406.
Anghileri, J.(1989). An investigation of young children’s understanding of multiplication. Educational Studies in Mathematics, 20,367-385.
Badian, N. A. (1983). Dyscalculia and nonverbal disorders of learning. In H. R. Mykelbust (Ed.), Progress in Learning Disabilities (pp.235-264). New York : Stratton.
Baum, S. (1994). Meeting the needs of gifted/learning disabled students. The Journal of Secondary Gifted Mathematics, 5(3), 6-16.
Branca, N. A. (1990). Problem solving as a goal, process, and basic skill. In S. Krulik, & R. E. Reys (Eds.), Problem Solving in School Mathematics, 3-8.
Brown, A.L.(1978). Knowing when, and how to remember: A problem of matacognition. In R. Glaser, Advance in Instructional Psychology (pp77-165). Hillsdale, NJ: Lawrence Erlbaum.
Cawley, J. F., & Miller, J. H. (1989). Cross-section comparison of the mathematics performance of children with learning disabilities: Are we on the right tract toward comprehensive programming, Journal of Learning Disabilities, 22, 250-259.
Czepiel, J.,& Esty, J. M.(1980).Mathematics in the newspaper .Mathematics Teacher, 73, 582-586.
Davydov, V. V. (1991). A psychological analysis of the operation of multiplication. In L. P. Steffe (Ed.), Psychological ability of primary school children in learning mathematics.9-85.Soviet Studies in Mathematics Education Series, volume 6, (J. Teller trans.). Reston, VA: NCTM.
Deshler, D. D. (1993). Strategy mastery by at-risk students: Not a simple matter. Elementary School Journal, 94, 153-67.
Ericsson, K. A., & Simon, H. A. (1993). Protocol analysis: verbal reports as data (rev. ed.). Cambridge, MA: The MIT Press.
Fischbein, E., Deri, M., Nello, M.S., & Marino, M. S. (1985). The role of implicit models in solving decimal problem in multiplication and division. Journal for Research in Mathematics Education, 16, 3-17.
Gagne, E. D., Yekovich, C.W., &Yekovich, F. R. (1993). The cognitive psychology of school learning (2nd ed.). New York, NY: HarperCollins College Publishers.
Garofalo, J., & Lester, F. K. (1985). Matacognition, cognitive monitoring and mathematics performance. Journal for Research in Mathematics Education, 16 (3), 163-176.
Greer, B. (1992). Multiplication and division as models of situations. In D. Grouws (Eds.). Handbook of research on mathematics teaching learning. 276- 295. Reston, VA: NCTM.
Hallahan, D. P., Kauffman, J. M., & Lloyd, J. W. (1999). Introduction to Learning Disabilities. (2nd ed.). Needham Heights, Mass: Allyn & Bacon.
Hiebert, J., & Behr, M. (1988). Introduction capturing the major themes. In J. Hiebert & M. Behr (Eds.), Number concepts and operations in the middle grades. Pp.1-18. Reston VA: NCTM.
Kouba, V. L., Brown, C. A., Carprnter, T. P., Lindquist, M. M., Silver, E. A.& Swafford, M. M.(1988). Results of the forth NAEP assessment of mathematics: Number, operations, and word problems. Arithmetic Teacher, 35,14-19.
Koubo, V. L. (1989). Children’s solution strategies for equivalent set multiplication and division word problems. Journal for Research in Mathematics Education, 20, 147-158.
Lerner, J. (2000). Learning disabilities: Theories, diagnosis, and teaching strategies(8th ed.). Boston, MA: Houghton Mifflin Co.
Marshall, S. P., Pribe, C. A. &Smith, J. D. (1987). Schema knowledge structure for representing and understanding arithmetic story problem. (Tech. Rep. Ontract No.nooo14-85-k-0661). Arilington, VA: Office of Naval Research.
Mayer, R. E. (1992). Thinking, problem solving, cognition. New York: W. H. Freeman and Company.
McCoy, L. P. (1994). Mathematics problem —solving processes of elementary male and female students. School Science & Mathematics, 94 (5), 266-271.
Miller, S. P., & Mercer, C. D. (1997). Educational aspects of mathematics disabilities. Journal of Learning Disabilities, 30 (1), 47-56.
Montague, M. & Applegate, B. (1993). Middle school students mathematical problem solving: An analysis of think-aloud protocols. Learning Disabilities Quarterly, 16, 19-31.
Montague, M. (1997). Student’s perception, mathematical problem solving and learning disabilities. Remedial and Special Education, 18(1), 46-53.
Mulligan, J. T. (1992). Children’s solutions to multiplication and division word problems: A longitudinal study. Mathematics Education Research Journal,4(1), 24-41.
National Council of Teachers of Mathematics (1989). Curriculum and evaluation standards for school mathematics. Reston, VA: Author.
Nacy, C. J., & Theresa, O. M. (1997). Cognitive arithmetic and problem solving: A comparison of children with special and general mathematics difficulties. Journal of Learning Disabilities,30 (6), 624-634,684.
Nesher, P. (1988). Multiplicative school word problem: Theoretical approaches and empirical findings. In J. Hiebert & M. Behr (Eds.), Number concepts and operations in the middle grades (41-52). Reston, VA: NCTM.
Polya, G., (1945). How to solve it: A new aspect of mathematical method. New Jersey: Princeton University Press.
Quintero, A. H.(1984).Children’s difficulties with two-step word problem. ERIC Document Reproduction, Service No. ED 242535.
Saunters, H. (1980). When are we ever gonna have to use this? Mathematics Teacher, 73, 7-16.
Schoenfeld, A. H. (1985). Making sense of out loud problem-solving protocols. Journal of Mathematical Behavior, 4, 171-191.
Schoenfeld, A.H. (1991). On pure and applied research in mathematics education. Journal of Mathematical Behavior, 10,263-276.
Strang, J. D., & Rourke, B. P. (1985). Adaptive behavior of children who exhibit specific arithmetic disabilities and associated neuropsychological abilities and deficits. In B. P. Rourke (ed.), Neuropsychology of Learning Disabilities. New York: The Guilford Press.
Snyder, R. F.(1998).A clinical study of three high school problem solvers. High School Journal, 81 (3), 167-177.
Swanson, H. L. (1994). Short-term memory and working memory: Do both contribute to our understanding of academic achievement in children and adults with learning disabilities? Journal of Learning Disabilities, 27(1), 34-50.
Vergnaud, G. (1983). Multiplicative structures in acquisition of mathematics concepts and processes. In R. Lesh, & M. Landau (Eds.), Acquisition of mathematics concepts and process. Academic press.
Webster, B. J. (1979). Accounting for variation in science and mathematics achievement. School Effectiveness & School Improvement, 11, 339-360.
QRCODE
 
 
 
 
 
                                                                                                                                                                                                                                                                                                                                                                                                               
第一頁 上一頁 下一頁 最後一頁 top