研究生: |
林淑玲 |
---|---|
論文名稱: |
國小數學學習障礙學生對比較類加減應用題解題表徵之研究 |
指導教授: | 陳美芳 |
學位類別: |
碩士 Master |
系所名稱: |
特殊教育學系 Department of Special Education |
畢業學年度: | 87 |
語文別: | 中文 |
論文頁數: | 167 |
中文關鍵詞: | 數學學習障礙 、比較類加減應用題 、解題表徵 、表徵提示 |
英文關鍵詞: | mathematics learning disabilities, addtion and subtraction compare problem, problem solving representation, representation promotion |
論文種類: | 學術論文 |
相關次數: | 點閱:236 下載:0 |
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 |
本研究的主要目的在探討國小數學學障學生在解差異量未知、被比較量未知、與參照量未知等三種比較類加減應用題的解題表徵正確率、所應用的解題表徵類型,以及產生的解題表徵困難。
本研究利用「比較類加減應用題測驗」進行施測,在施測完畢後,隨即應用「解題表徵晤談記錄表」對學生進行晤談;若學生解題表徵有誤,並以表徵提示給予學生解題協助,期使學生可訂正錯誤表徵方式。本研究對象為目前就讀於台北市7所國小身心障礙資源班3、4年級的數學學障學生,共有25名。25名學生在「國民小學低年級數學診斷測驗」的原始得分,都在該測驗19分的切截點以下。
本研究的資料分析是將25名學生的測驗結果、記錄表內容與錄影所得資料,進行量化與質化的分析。本研究以百分比呈現學生的解題表徵正確率、解題表徵類型,並根據學生的晤談書面資料與行為表現,加以歸納分析,陳列出學生的解題表徵困難類型。
本研究結果發現:(1)學生首次的解題表徵正確率,由高而低為被比較量未知題、差異量未知型與參照量未知題,但若排除解題表徵正確,但解題表徵歷程說明有誤,或無法說明解題表徵歷程者,則解題表徵的正確率,則以差異量未知題最高。(2)學生在比較類加減應用題的解題表徵類型,使用「書寫符號」的類型佔94%以上,至於在解題表徵提示的提示效果上,必須將數學學障學生的解題經驗從文字題的形式中,帶至親身經驗與角色扮演的表徵方式中,方能更正錯誤的解題表徵形式。(3)數學學障學生在比較類加減應用題中,出現解題表徵困難最多的是在解題表徵中「理解」階段,其中尤其以「關鍵字解題」的表徵困難類型居多。
根據上述結果,本研究對數學學障學生在數學解題教學與評量及未來相關研究提出數點建議。
The main purpose of this study was to investigate problem solving representation of addition and subtraction compare word problem on elementary students with mathematics learning disabilities .The problem solving accurate percentage、the problem solving representation types and problem solving representation difficulties were analyzed in the study. 25 elementary students with mathematics learning disabilities served as subjects. 「 Addition and subtraction compare problem test 」and interview were administered to all the subjects.
The major findings were concluded as follows:
1. The accurate percentage of problem solving representation from more to less were: 「compared unknown quality problem」、「discrepancy quality unknown problem」、「referent quality unknown problem」. If eliminate students who could make accurate representation, but had mistakes during the problem solving process or who couldn't explain the problem solving process, the highest problem solving representation accurate percentage was changed to「discrepancy quality unknown problems」.
2. Although above 94﹪ students used「written symbols」to make representations, the effects of repersentations were not satisfied . Experience-based and role-playing could effectively bring subjects into the problem s and therefore revised the problem solving representation mistakes.
3. The most difficulties on addition and subtraction compare problems were found in comprehension stage of problem solving process.
According to the findings, the author proposed suggestion to further research and application of the study to math education .
參考書目
一、 中文部份
何縕琪(民83):表徵策略教學對提昇國小低解題正確率學生解題表現之效果研究。國立台灣師範大學教育心理與輔導研究所碩士論文,未出版。
呂玉琴(民86):國小低年級學生對加減法文字題的瞭解。載於中華民國第十三屆科學教育學術研討會會議手冊及短篇論文彙編(pp. 355-361)。
呂玉琴譯(民77):加減法文字題的解題層次及其數學的表徵。國民教育,29(1、2),53-63。
周筱亭(民83):國民小學教師對數學新課程應有的認識。載於八十二學年度數學教育研討會論文暨會議實錄彙編( pp. 204-228)。
林美和(民76):數學障礙兒童學習問題之研究。國立台灣師範大學社會教育學刊,16 , 43-76。
林素貞(民84):回顧與展望-學習障礙。特殊教育季刊,54,24-25。
林清山(民80):教育心理學-認知取向。台北市:遠流出版社。
柯華崴(民86):國語文低成就學生之閱讀理解能力研究-第二年。國科會專題研究計畫成果報告,未出版。
洪儷瑜(民85):學習障礙者教育。台北市:心理出版社。
紀惠英(民80):國小六年級學生數學應用問題表徵類型與同構性之研究。國立台灣師範大學特殊教育研究所碩士論文,未出版。
徐文鈺(民81):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,未出版。
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。
翁嘉英(民77):國小兒童解數學應用問題的認知歷程。國立台灣師範大學心理學研究所碩士論文,未出版。
張春興(民78):張氏心理學辭典。台北市:東華書局。
教育部(民82):國民小學課程標準。台北市:正中書局。
教育部(民87):身心障礙及資賦優異學生鑑定原則鑑定基準。
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。國立台灣師範大學教育心理與輔導研究所博士論文,未出版。
陳進福(民86):國小輕度智障兒童數學解題動態評量之研究。國立嘉義師範學院國民教育研究所碩士論文,未出版。
曾世杰(民87):算數和數學推理障礙:神經學及神經心理的觀點。載於「數學學習障礙」研究推動研討會會議記錄。
楊美伶、蔣治邦(民81):國民小學數學科加減法教材關鍵字之分析研究。國教學報,4,109-127。
葉雪梅(民78):國小兒童對「比較類」應用問題的解題行為。國立政治大學教育研究所碩士論文,未出版。
詹士宜(民80):國中智能不足學生數學應用問題解題之研究。國立彰化師範大學特殊教育學習系碩士論文,未出版。
蔣治邦(民83):由表徵觀點探討實驗教材數與計算活動的設計。載於八十二學年度數學教育研討會論文暨會議實錄彙編( pp. 132-149)。
蔡宗玫(民84):國小數學學習障礙學生應用問題解題研究。國立彰化師範大學特殊教育學習系碩士論文,未出版。
蔡翠華(民85):國小數學學習障礙學生的學習型態與學習策略之相關研究。國立台灣師範大學特殊教育研究所碩士論文,未出版。
鄧少林、蔣治邦(民83):三、五年級學生對比較應用問題的分類。國教學報,6,97-113。
蕭金土(民84):國小數學學習障礙學生的鑑定、學習問題診斷及學習策略教學效果之研究。國立政治大學教育研究所博士論文,未出版。
二、 英文部份
Brown, A. L.(1987). Metacognition,executive control,selfregulation and other moremysterious mechanisms. In F.E.Weinert & R .H. Kluwe(Eds.), Metacognition,motivation,and understanding. London:Lawrence Erlbaum.
Bruner, J. S.(1966). Toward s theory of instruction. MA: Belknap Harvard.
Bryan, T.(1998). Social competence of studies with learning disabilities.In B. Wong (Ed.)Learning about learning disabilities(pp. 237-275).San Diego, CA:Academic Press.
Carnine, D.,(1997). Instructional design in mathematics for students with learning disabilities. Journal of Learning Disabilities, 30(2), 130-141.
Carpenter, T. P. (1985). Learning to add and subtracst. In E. Silver (Ed.) Teaching and learning mathematical problem solving: Multiple research perspectives (pp. 75-89). Hillsdals, NJ: Lawrance Erllaum Associates.
Carpenter, T. P., & Moser, J. M.(1984). The acqiusition of addition and subtraction concepts in grade one through three. Journal for Research in Mathematics Education, 15, 279-302.
Cawley, J. F.(ED.)(1985).Development teaching of mathematics for learning disabled. Rockville, MD:Aspen System.
Clements, M. A.(1980). Analysis children's errors on written mathematical tasks. Educational Studies in Mathematics,11,1-21.
DeCorte, E., & Verchaffel, L. (1987). Teaching word problem in the primary school. In G. Brain & Mulhern (Eds.). New directions in mathematics education(pp. 85-106). New York: Routlerdge.
Defour-Janvier, B.,Bendnarz, N., & Belanger, M. (1987). Pedagogical considerations concering the problem of representation. In C.Janvier(Ed.), Problems of representation in the teaching and learning of mathematics (pp. 109-122). Hillsdale, NJ: Erlbaum.
Diagonostic and statistical manual of mental disorder (DSM-IV)(4rd ed)(1994): American Psychiatric Association. Washiton DC.,( pp. 50-51).
Dickson, L., Brown, M., & Gibson, O. (1984). Children learning mathematics: A teacher's guide to recent research. Oxford: Alden Press.
Dickstein, E. B., & Warren, D. R. (1980). Role-taking deficits un learning disabled children. Journal of Learning Disabilities, 13, 33-37.
Fleischner, J. E., & Marzola, E. S.(1988). Arithmatic . In K. A. Kavale, S. R. Forness, & M. B. Bender (Eds.), Handbook of learnin disabilities (Vol.II): Methods and interventions (pp.89-110). Boston, MA: College-Hill Publication.
Gagne', E. D. (1985). The cognitive psychology of school learning. Boston: Little, Brown and Company.
Glass, A. L. & Holyoak, K. J.(1986). Cognition ( 2nd ed.). New York: Random House.
Grenno, J. G.(1978). A study of problem solving . In R. Glaser (Ed.). Advances in instructional psychology (vol.1). Hilladale NJ: Lawrance Erlbaum Associates.
Grenno, J. G.(1987).Instructional representations based on research about understanding. In A. H. Schoenfeld(Ed.), Cognitive science and mathematics education (pp. 61-88). Hillsadle, NJ: Erlbaum.
Hallahan, D. P., Kauffman, J. M. & Lloyd, J. W.(1996). Learning Disabilities. Needham Heughts, MA: Allyn & Bacon.
Hart, L. C. (1985), Factors impeding the formating of a useful representation in mathematics problem solving. Chicago, paper presented at the Annual Meeting of the American Educational Research Association. (ERIC Document Reproduction Service, No. ED 254 419).
Kaput, J. J. (1985). Representation and problem solving : Methodological issues related to modeling. In E. A. Silver (Ed.), Teaching and learning mathematical problem solving : Multiple research perspectives (pp.381-398).
Kaput, J. J.(1987). Representation systems and mathematics.In C.Janvier(Ed.), Problems of representation in the teaching and learning of mathematics (pp. 19-26). Hillsdale, NJ: Erlbaum.
Kinstsch, W., & Grenno, J. G.(1985). Understanding and solving word arithmetic problems. Psychology Review, 92, 109-129.
Kintsch, W., & Grenno, J. G.(1985). Understanding and solving word arithmatic problemd . Psycgology review,92, 109-129.
Lerner, J. (1997), Learning disabilities: Theories, diagnosis and teaching strategies, 7th ed., New York: Houghhton Mifflin.
Lesh, R.(1985). Conceptual analysis of problem-solving performance. In E. Silver (Ed.) Teaching and learning mathematical problem solving: Multiple research perspectives (pp. 75-89). Hillsdals, NJ: Lawrance Erllaum Associates.
Lewis, A. B. & Mayer, R. E. (1987). Students' miscpmprehention of relational statementas in arithmatic word problems. Journal of Educational Psychology, 79(4), 363-371.
Marshall, S. P. & Smith, J. D. (1987). Sex difference in learning mathematics : A longutudial study with item and error analysis. Journal of Educational Psychology, 79(4), 372-383.
Marshall, S. P.(1995). Schemas in problem solving. New York: Cambridge press.
Mayer, R. E. (1992). Educational psychology : A cognitive approach. Boston, MA: Little, Brown.
Mayer, R. E.(1992). Thinking, problem solving ,cognition. New York:Freeman.
Mercer, C. D.(1992). Students with learning disabilities. New York: Merrill.
Mercer, C. D., & Mercer, A. R. (1993). Teaching students with learning problems. New York: Macmillan.
Miller, S. P., & Mercer, C. D.,(1997). Educational aspects of mathematics disabilities. Journal of Learning Disabilities, 30(1),47-56.
Montague, M. (1997). Cognitive strategy instruction in mathematics for students with learning disabilities. Journal of Learning Disabilities, 30(2), 164-177.
Montague, M., & Applegate, B.(1993). Middle school students' mathematical problem solving: An analysis of think-aloud protocols. Learning Disability Quuarterly, 16, 19-32.
Nesher, P., Grenno, J. G., & Riley, M. S.(1982). The development of semantic categories for addition and subtraction. Educational Studies in Mathematics , 8, 251-269.
Reid, D. K., Hresko, W. P. & Swanson, H. L.(1996). Cognitive approach to learning disabilities(3rd ed). Austin, Texas: PRO-ED.
Riley, M. S., Grenno, J. G., & Heller, J. E. (1983).Development of children's problem-solving ability in arithmetic. In H. P. Ginsburg (Ed.), The development of mathematical thinking (pp.153-200). New York: Academic Press.
Riley, M. S., Grenno, J. G., & Heller, J. I.(1982). Development of Children's problem-solving ability in arithmatic. In H. P. Ginsburg (Ed.), The development of mathematics thinking. (pp. 153-196). New York: Academic Press.
Rivera, D. P.(1997). Mathematics education and students with learning disabilities: Itroduction to the special education. Journal of Learning Disabilities, 30(1), 2-19,68.
Russel, R. L. & Ginsberg, H. P. (1981). Cognitive analysis of children's mathematics difficulties. Cognition and Instruction,1(2),217-244.
Silver, E. A.(1985). Introduction. In E. A. Silver (Ed.), Teaching and learning mathematical problem solving : Multiple research perspectives. Hillsdals, NJ: Lawrance Erllaum Associates.
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). Hillsadle, NJ: Erlbaum.
Smith, C. R.(1994). Learning Disabilities: The interaction of learning , task, and setting. Needham Heughts, MA: Allyn & Bacon.
Sternberg, R. J.(1996). Cognitive Psychology. Orlando, FL: Harcourt Brace.
Thornton, C. A., Langrall, C. W., & Jones, G.(1997). Mathematics instruction for elementary syudents with learning disabilities. Journal of Learning Disabilities, 30(2), 142-150.
Wallace, G., & Mcloughlin, J. A.(1988). Learning Disabilities: Concepts and characteristics. Columbus, OH: Merrill.
Yackel, E. & Wheatley, G. H.(1985). Caracteristics of problem representation indicative of understanding in mathematics problem solving. Chicago, paper presented at the Annual Meeting of the American Educational Research Association. (ERIC Document Reproduction Service, No. ED 255 376).
Zawaiza, T. R. W., & Gerber, M. M.(1993). Effects of explicit instruction on math word-problem solving by community college students with learning disabilities. Learning Disability Quuarterly, 16, 64-79.