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題名 加減應用問題中多餘資訊的辨識
作者 陳文寬
貢獻者 蔣治邦
陳文寬
關鍵詞 多餘資訊
加減應用題
兩步驟問題
國小三年級
日期 2006
上傳時間 17-Sep-2009 13:23:20 (UTC+8)
摘要 Littlefield與Rieser(1993)曾提出語意區辨模型,來解釋多餘資訊特性對多餘資訊辨識的影響,本研究則以Kintsch與Greeno(1985)的閱讀理解模型為基礎,重新探討多餘資訊的辨識。與問題中的問句相比較,多餘資訊句的語意特徵相似度可分為高低兩個水準,多餘資訊句的位置則可能出現在題目中間或後面,本研究由這兩個特性編製出四類多餘資訊句,分別加入六類兩步驟加減應用問題中,要求國小三年級的學童圈選出解題需用到的數字,來探討多餘資訊特性對辨識的影響。
研究結果發現:整體而言,語意特徵相似度低時,學童的辨識表現較好,所犯的錯誤主要為只圈選兩個相關資訊;語意特徵相似度高時,學童的辨識表現下降,較容易圈選多餘資訊句中的數字。而位置變項的效果並不顯著,且語意特徵相似度與位置變項的交互作用也不明顯。
進一步分析學童在六類兩步驟問題中的表現,本研究建議閱讀理解模型比語意區辨模型更能合理地解釋學童的辨識表現,而記憶可能是值得進一步探討的因素。此外,部分學童會以問句中的主角為線索,判斷擁有相同主角的句子與解題有關,而造成辨識錯誤。
參考文獻 丁春蘭(2003)。國小學童乘除問題的解題表現、後設認知與認知型式之分析研究。未出版之碩士論文,國立台中師範學院數學教育研究所,台中市。
林美惠(1997)。題目表徵型式與國小二年級學生加減法解題之相關研究。未出版之碩士論文,國立嘉義師範學院國民教育研究所,嘉義縣。
洪義德(2002)。不同表徵面積題目對國小六年級學生解題表現之探討。未出版之碩士論文,國立台北師範學院數理教育研究所,台北市。
陳立倫(2000)。兒童解答數學文字題的認知歷程。未出版之碩士論文,國立中正大學心理研究所,嘉義縣。
教育部國民小學及國民中學教科圖書印製標準規格(民93)。
黃敏晃(1997)。國小數學新課程下評量改革的一些想法。國民小學數學科新課程概說(中年級)。民95年3月1日,取材自國立教育研究院籌備處網頁:http:// 203.71.239.3/study/math/newmath3/15.htm
蔣治邦(1993)。中年級學童解決加減文字題能力之探討:多餘資訊與兩步驟問題。科學教育學刊,1,189-212。
Babbitt, B. C. (1990, October). Error patterns in problem solving. Paper presented at the International Conference of the Council for Learning Disabilities, Austin, TX.
Blankenship, C. S., & Lovitt, T. C. (1976). Story problems: Merely confusing or downright befuddling. Journal for Research in Mathematics Education, 7, 290-298.
Blessing, S. B., & Ross, B. H. (1996). Content effects in problem categorization and problem solving. Journal of Experimental Psychology, 22, 792-810.
Cohen, S. A., & Stover, G. (1981). Effects of teaching sixth-grade students to modify format variables of math word problems. Reading Research Quarterly, 16, 175-200.
Cook, J. L., & Rieser, J. J. (2005). Finding the critical facts: Children’s visual scan patterns when solving story problems that contain irrelevant information. Journal of Educational Psychology, 97, 224-234.
Cummins, D. D., Kintsch, W., Reusser, K., & Weimer, R. (1988). The role of understanding in solving word problems. Cognitive Psychology, 20, 405-438.
De Corte, E., Verschaffel, L., & DeWinn, L. (1985). Influence of rewording verbal problems on children’s problem representations and solutions. Journal of Educational Psychology, 77, 460-470.
Fuchs, L. S., Fuchs, D., Compton, D. L., Powell, S. R., Seethaler, P. M., Capizzi, A. M., Schatschneider, C., & Fletcher, J. M. (2006). The cognitive correlates of third-grade skill in arithmetic, algorithmic computation, and arithmetic word problems. Journal of Educational Psychology, 98, 29-43.
Hayes, J. R. (1989). The complete problem solver. Hillsdale, NJ: Lawrence Erlbaum Associates.
Hinsley, D. A., Hayes, J. R., & Simon, H. A. (1977). From words to equations meaning and representation in algebra word problems. In P. Carpenter & M. Just (Eds.), Cognitive processes in comprehension (pp. 89-106). Hillside, NJ: Erlbaum.
Kintsch, W., & Greeno, J. G. (1985). Understanding and solving word arithmetic problems. Psychological Review, 92, 109-129.
Lester, F. K. (1980). Research on mathematical problem solving. In R. J. Shumway(Ed.),Research in mathematics education. NCTM.
Littlefield, J., & Rieser, J. J. (1993). Semantic features of similarity and children’s strategies for identifying relevant information in mathematical story problems. Cognition and instruction, 11, 133-188.
Low, R., & Over, R. (1989). Detection of missing and irrelevant information within algebraic story problems. British Journal of Educational Psychology, 59, 296-305.
Low, R., Over, R., Doolan, L., & Michell, S. (1994). Solution of algebraic word problems following training in identifying necessary and sufficient information within problems. American Journal of Psychology, 107, 423-439.
Marzocchi, G. M., Lucangeli, D., De Meo, T., Fini, F., & Cornoldi, C. (2002). The disturbing effect of irrelevant information on arithmetic problem solving in inattentive children. Developmental Neuropsychology, 21, 73-92.
Masson, M. E. J. (1995). A distributed memory model of semantic priming. Journal of Experimental Psychology: Learning, Memory, and Cognition, 21, 3-23.
Mayer, R. E. (1982). Memory for algebra story problems. Journal of Educational Psychology, 74, 199-216.
Mayer, R. E. (1992). Thinking, problem solving, cognition. (2nd ed). NY: W. H. Freeman and Company.
McKenna, F. P. (1984). Measures of field dependence: Cognitive style or cognitive ability. Journal of Personality and Social Psychology, 47, 593-603.
Muth, K. D. (1991). Effects of cuing on middle-school students’ performance on arithmetic word problems containing extraneous information. Journal of Educational Psychology, 83, 173-174
Muth, K. D. (1992). Extraneous information and extra steps in arithmetic word problems. Contemporary Educational Psychology, 17, 278-285.
Nathan, M. J., & Kintsch, W. (1992). A theory of algebra-word-problem comprehension and its implications for the design of learning environments. Cognition and Instruction, 9, 329-389.
Nesher, P. (1992). Solving multiplication word problem. In G. Leinhardt, R. Putnam, & R. A. Hattrup(Eds.), Analysis of arithmetic for mathematics teaching(pp. 189-219). Hillsdale, NJ: L. Erlbaum Associates.
Ng Li, F. L. (1990). The effect of superfluous information on children’s solution of story arithmetic problems. Educational Studies in Mathematics, 21, 509-520.
Passolunghi, M. C., Cornoldi, C., & De Liberto, S. (1999). Working memory and intrusions of irrelevant information in a group of specific poor problem solvers. Memory and Cognition, 27, 779-790.
Passolunghi, M. C., & Siegel, L. S. (2001). Short-term memory, working memory and inhibitory control in children with difficulties in arithmetic problem solving. Journal of Experimental Child Psychology, 80, 44-57.
Polya, G. ( 1945 ). How to solve it. Princeton, New Jersey:Princeton University Press.
Reusser, K. (1990). From text to situation to equation: Cognitive simulation of understanding and solving mathematical word problem. In H. Mandl, E. De Corte, N. Bennett, & H. F. Friendrich(Eds.), Learning and instruction: Vol.2.2. Analysis of complex skills and complex knowledge domains(pp. 477- 498). Elmsford, NY: Pergamon Press.
Riley, M. S., Greeno, J. G., & Heller, J. I.(1983). Development of children’s problem-solving ability in arithmetic. In H. P. Ginsburg(Ed.), The development of mathematical thinking(pp. 153-196). New York : Academic Press.
Schoenfeld, A. H. (1985 ). Mathematical problem solving. New York: Academic Press.
Swanson, H. L., Cooney, J. B., & Brock, S. (1993). The influence of working memory and classification ability on children’s word problem solution. Journal of Experimental Child Psychology, 55, 374-395.
Tiedmann, J. (1989). Measures of cognitive styles: A critical review. Educational Psychologist, 24, 261-275.
van Dijk, T. A., & Kintsch, W. (1983). Strategies of discourse comprehension. New York: Academic Press.
描述 碩士
國立政治大學
心理學研究所
92752020
95
資料來源 http://thesis.lib.nccu.edu.tw/record/#G0927520201
資料類型 thesis
dc.contributor.advisor 蔣治邦zh_TW
dc.contributor.author (Authors) 陳文寬zh_TW
dc.creator (作者) 陳文寬zh_TW
dc.date (日期) 2006en_US
dc.date.accessioned 17-Sep-2009 13:23:20 (UTC+8)-
dc.date.available 17-Sep-2009 13:23:20 (UTC+8)-
dc.date.issued (上傳時間) 17-Sep-2009 13:23:20 (UTC+8)-
dc.identifier (Other Identifiers) G0927520201en_US
dc.identifier.uri (URI) https://nccur.lib.nccu.edu.tw/handle/140.119/32548-
dc.description (描述) 碩士zh_TW
dc.description (描述) 國立政治大學zh_TW
dc.description (描述) 心理學研究所zh_TW
dc.description (描述) 92752020zh_TW
dc.description (描述) 95zh_TW
dc.description.abstract (摘要) Littlefield與Rieser(1993)曾提出語意區辨模型,來解釋多餘資訊特性對多餘資訊辨識的影響,本研究則以Kintsch與Greeno(1985)的閱讀理解模型為基礎,重新探討多餘資訊的辨識。與問題中的問句相比較,多餘資訊句的語意特徵相似度可分為高低兩個水準,多餘資訊句的位置則可能出現在題目中間或後面,本研究由這兩個特性編製出四類多餘資訊句,分別加入六類兩步驟加減應用問題中,要求國小三年級的學童圈選出解題需用到的數字,來探討多餘資訊特性對辨識的影響。
研究結果發現:整體而言,語意特徵相似度低時,學童的辨識表現較好,所犯的錯誤主要為只圈選兩個相關資訊;語意特徵相似度高時,學童的辨識表現下降,較容易圈選多餘資訊句中的數字。而位置變項的效果並不顯著,且語意特徵相似度與位置變項的交互作用也不明顯。
進一步分析學童在六類兩步驟問題中的表現,本研究建議閱讀理解模型比語意區辨模型更能合理地解釋學童的辨識表現,而記憶可能是值得進一步探討的因素。此外,部分學童會以問句中的主角為線索,判斷擁有相同主角的句子與解題有關,而造成辨識錯誤。
zh_TW
dc.description.tableofcontents 第一章 緒論……………………………………………………… 1
多餘資訊題………………………………………………………… 1
閱讀理解歷程……………………………………………………… 3
多餘資訊的語意特徵相似度……………………………………… 5
多餘資訊的位置…………………………………………………… 12
研究問題…………………………………………………………… 13
第二章 文獻探討……………………………………………………… 15
第一節 解題歷程………………………………………………… 15
第二節 多餘資訊………………………………………………… 23
第三節 研究目的及假設………………………………………… 36
第三章 研究方法……………………………………………………… 39
受試………………………………………………………………… 39
工具………………………………………………………………… 39
實驗程序…………………………………………………………… 45
資料分析…………………………………………………………… 45
第四章 研究結果………………………………………………………… 47
前置分析…………………………………………………………… 47
語意特徵相似度及位置的效果…………………………………… 48
兩步驟應用題題型的影響………………………………………… 50
圈選位置分析……………………………………………………… 55
第五章 討論與建議……………………………………………………… 59
兩階段語意區辨模型與閱讀理解模型…………………………… 59
位置………………………………………………………………… 64
本研究的限制及建議……………………………………………… 66
參考文獻………………………………………………………………… 68

表 目 錄
表一: 改變類型問題的表徵………………………………………… 20
表二: 單步驟加減應用題類型……………………………………… 40
表三: 六種基本題型範例…………………………………………… 41
表四: 多餘資訊題範例……………………………………………… 42
表五: 題本設計……………………………………………………… 43
表六: 題目順序……………………………………………………… 44
表七: 三種作答結果的平均題數表………………………………… 49
表八: 三大類題型…………………………………………………… 52
表九: 六種題型的作答結果………………………………………… 53
表十: 各題型位置效果表…………………………………………… 54
表十一: 兩個常被圈選的相關資訊位置及圈選人數比率………… 56
表十二: 問句圈選策略的作答型態…………………………………… 58
表十三: 三類題型多餘資訊句和相關資訊句的語意關係…………… 61

圖 目 錄
圖一: 兩步驟多餘資訊題集合關係圖……………………………… 8-11
圖二: 改變問題的基模表徵圖…………………………………… 17
圖三: 比較動作基模………………………………………………… 18
圖四: 情境問題解決者SPS………………………………………… 22


附 錄 目 錄
附錄一 施測題本…………………………………………………………… 72
附錄二 施測手冊…………………………………………………………… 82
附錄三 不同性別的平均答對題數表……………………………………… 85
附錄四 答對題數的「題本×區組×性別」
變異數分析摘要表………………………………………………… 86
附錄五 不同成就水準的平均答對題數表………………………………… 87
附錄六 答對題數的「題本×區組×成就水準」
變異數分析摘要表………………………………………………… 88
附錄七 答對題數的「題本×區組」
變異數分析摘要表………………………………………………… 89
附錄八 選兩相關題數的「題本×區組」
變異數分析摘要表………………………………………………… 90
附錄九 多選題數的「題本×區組」
變異數分析摘要表………………………………………………… 91
附錄十 六種題型的八種反應……………………………………………… 92
zh_TW
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dc.source.uri (資料來源) http://thesis.lib.nccu.edu.tw/record/#G0927520201en_US
dc.subject (關鍵詞) 多餘資訊zh_TW
dc.subject (關鍵詞) 加減應用題zh_TW
dc.subject (關鍵詞) 兩步驟問題zh_TW
dc.subject (關鍵詞) 國小三年級zh_TW
dc.title (題名) 加減應用問題中多餘資訊的辨識zh_TW
dc.type (資料類型) thesisen
dc.relation.reference (參考文獻) 丁春蘭(2003)。國小學童乘除問題的解題表現、後設認知與認知型式之分析研究。未出版之碩士論文,國立台中師範學院數學教育研究所,台中市。zh_TW
dc.relation.reference (參考文獻) 林美惠(1997)。題目表徵型式與國小二年級學生加減法解題之相關研究。未出版之碩士論文,國立嘉義師範學院國民教育研究所,嘉義縣。zh_TW
dc.relation.reference (參考文獻) 洪義德(2002)。不同表徵面積題目對國小六年級學生解題表現之探討。未出版之碩士論文,國立台北師範學院數理教育研究所,台北市。zh_TW
dc.relation.reference (參考文獻) 陳立倫(2000)。兒童解答數學文字題的認知歷程。未出版之碩士論文,國立中正大學心理研究所,嘉義縣。zh_TW
dc.relation.reference (參考文獻) 教育部國民小學及國民中學教科圖書印製標準規格(民93)。zh_TW
dc.relation.reference (參考文獻) 黃敏晃(1997)。國小數學新課程下評量改革的一些想法。國民小學數學科新課程概說(中年級)。民95年3月1日,取材自國立教育研究院籌備處網頁:http:// 203.71.239.3/study/math/newmath3/15.htmzh_TW
dc.relation.reference (參考文獻) 蔣治邦(1993)。中年級學童解決加減文字題能力之探討:多餘資訊與兩步驟問題。科學教育學刊,1,189-212。zh_TW
dc.relation.reference (參考文獻) Babbitt, B. C. (1990, October). Error patterns in problem solving. Paper presented at the International Conference of the Council for Learning Disabilities, Austin, TX.zh_TW
dc.relation.reference (參考文獻) Blankenship, C. S., & Lovitt, T. C. (1976). Story problems: Merely confusing or downright befuddling. Journal for Research in Mathematics Education, 7, 290-298.zh_TW
dc.relation.reference (參考文獻) Blessing, S. B., & Ross, B. H. (1996). Content effects in problem categorization and problem solving. Journal of Experimental Psychology, 22, 792-810.zh_TW
dc.relation.reference (參考文獻) Cohen, S. A., & Stover, G. (1981). Effects of teaching sixth-grade students to modify format variables of math word problems. Reading Research Quarterly, 16, 175-200.zh_TW
dc.relation.reference (參考文獻) Cook, J. L., & Rieser, J. J. (2005). Finding the critical facts: Children’s visual scan patterns when solving story problems that contain irrelevant information. Journal of Educational Psychology, 97, 224-234.zh_TW
dc.relation.reference (參考文獻) Cummins, D. D., Kintsch, W., Reusser, K., & Weimer, R. (1988). The role of understanding in solving word problems. Cognitive Psychology, 20, 405-438.zh_TW
dc.relation.reference (參考文獻) De Corte, E., Verschaffel, L., & DeWinn, L. (1985). Influence of rewording verbal problems on children’s problem representations and solutions. Journal of Educational Psychology, 77, 460-470.zh_TW
dc.relation.reference (參考文獻) Fuchs, L. S., Fuchs, D., Compton, D. L., Powell, S. R., Seethaler, P. M., Capizzi, A. M., Schatschneider, C., & Fletcher, J. M. (2006). The cognitive correlates of third-grade skill in arithmetic, algorithmic computation, and arithmetic word problems. Journal of Educational Psychology, 98, 29-43.zh_TW
dc.relation.reference (參考文獻) Hayes, J. R. (1989). The complete problem solver. Hillsdale, NJ: Lawrence Erlbaum Associates.zh_TW
dc.relation.reference (參考文獻) Hinsley, D. A., Hayes, J. R., & Simon, H. A. (1977). From words to equations meaning and representation in algebra word problems. In P. Carpenter & M. Just (Eds.), Cognitive processes in comprehension (pp. 89-106). Hillside, NJ: Erlbaum.zh_TW
dc.relation.reference (參考文獻) Kintsch, W., & Greeno, J. G. (1985). Understanding and solving word arithmetic problems. Psychological Review, 92, 109-129.zh_TW
dc.relation.reference (參考文獻) Lester, F. K. (1980). Research on mathematical problem solving. In R. J. Shumway(Ed.),Research in mathematics education. NCTM.zh_TW
dc.relation.reference (參考文獻) Littlefield, J., & Rieser, J. J. (1993). Semantic features of similarity and children’s strategies for identifying relevant information in mathematical story problems. Cognition and instruction, 11, 133-188.zh_TW
dc.relation.reference (參考文獻) Low, R., & Over, R. (1989). Detection of missing and irrelevant information within algebraic story problems. British Journal of Educational Psychology, 59, 296-305.zh_TW
dc.relation.reference (參考文獻) Low, R., Over, R., Doolan, L., & Michell, S. (1994). Solution of algebraic word problems following training in identifying necessary and sufficient information within problems. American Journal of Psychology, 107, 423-439.zh_TW
dc.relation.reference (參考文獻) Marzocchi, G. M., Lucangeli, D., De Meo, T., Fini, F., & Cornoldi, C. (2002). The disturbing effect of irrelevant information on arithmetic problem solving in inattentive children. Developmental Neuropsychology, 21, 73-92.zh_TW
dc.relation.reference (參考文獻) Masson, M. E. J. (1995). A distributed memory model of semantic priming. Journal of Experimental Psychology: Learning, Memory, and Cognition, 21, 3-23.zh_TW
dc.relation.reference (參考文獻) Mayer, R. E. (1982). Memory for algebra story problems. Journal of Educational Psychology, 74, 199-216.zh_TW
dc.relation.reference (參考文獻) Mayer, R. E. (1992). Thinking, problem solving, cognition. (2nd ed). NY: W. H. Freeman and Company.zh_TW
dc.relation.reference (參考文獻) McKenna, F. P. (1984). Measures of field dependence: Cognitive style or cognitive ability. Journal of Personality and Social Psychology, 47, 593-603.zh_TW
dc.relation.reference (參考文獻) Muth, K. D. (1991). Effects of cuing on middle-school students’ performance on arithmetic word problems containing extraneous information. Journal of Educational Psychology, 83, 173-174zh_TW
dc.relation.reference (參考文獻) Muth, K. D. (1992). Extraneous information and extra steps in arithmetic word problems. Contemporary Educational Psychology, 17, 278-285.zh_TW
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