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引文資料
題名:
中年級學童「部份-全體」運思的發展:文字題選圖與解題作業表現的差異
書刊名:
中華心理學刊
作者:
蔣治邦
作者(外文):
Chiang, Chi-pang
出版日期:
2001
卷期:
43:2
頁次:
頁239-254
主題關鍵詞:
部份-全體運思發展
;
圖形表徵
;
加減文字題
;
Development of part-whole operation
;
Pictorial representation
;
Addition and subtraction word problems
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被引用次數:期刊(
6
) 博士論文(0) 專書(0) 專書論文(0)
排除自我引用:
6
共同引用:
23
點閱:74
在數學教材中,常見使用圖形來說明抽象概念或問題解法的教學建議。本研究在加減運算範圍,探討圖形表徵理解能力的發展,透過選擇題作業,實驗一觀察916名二至四年級學童對文字題與圖徵表徵轉譯的辨識表現。實二觀察466名三、四年級學童對文字題與線段圖轉譯的辨識要現,來探討學童概念的發展,以及圖形型式對學童轉譯辨識表現的影響。實驗三透過236名三、四年級學童解題作業上的表現,探討附加線段圖在解題過程中所扮演的角色。綜合三個實驗的結果,各項作業上皆呈現年級效果,顯示「部份-全體」關係的掌握,在中年級仍持續的發展。圖形型式並未影響選圖表現,學童選擇圖形表徵時的困難,與各數量間的關係有關,而與各個數舉的本身無關,問題語意與線段圖型式的契合假設亦尚未獲得支持。比較實驗二、三的結果,顯示學童解題表現優於圖形選擇表現。在文字題上附加線段圖,有時能增加學童正確解題的機會,但是,效果相當有限或不穩定可靠。在「部份-全體」運思發現的架構下,進一步討論實驗結果的意涵,以及可能的數學教學建議。
以文找文
With addition and subtraction word problems, this study was to explore students’ abilities of text picture translation in their middle grades, and to explore the effects of drawings in the problem solving processes. In Experiment 1, there were 916 second, third, or fourth graders who were observed on multiple choice task. Two forms of drawings were used: square and bar graph. Students were asked to choose a correct drawing that agreed with the word problem specified. In Experiment 2, there were 466 third or fourth graders who were examined on multiple choice task. Two different sets of drawings were chosen: single-line-segment and double-line-segment drawings. In Experiment 3, there 236 third or fourth graders who were tested on problem solving task. The same word problems as in the Experiment 2 were used, and half of them were presented with additional line-segment drawings. Grade effects were found in all three experiments. There was no effect of drawing forms. The results suggested that the difficulties on choosing correct drawings were related to the translation of the relations of quantities but not the quantities themselves. The findings also did not support the matching hypotheses between situations and drawings. By comparing the results in the last two experiments, it is clear that the performance on problem solving task was better than that on drawing choice task. Finally, the additional line-segment drawing on problem presentation had little effect on students’ performance. All results were discussed in the framework of the development of part-whole operation.
以文找文
期刊論文
1.
蔣治邦(19930900)。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(2),189-212。
延伸查詢
2.
蔣治邦、鍾思嘉(19910800)。低年級學童加減概念的發展。教育與心理研究,14,35-68。
延伸查詢
3.
Cobb, P.、Yackel, E.、Wood, T.、Nicholas, J.、Wheatley, G.、Trigatti, B.、Perlwitz, M.(1992)。A constructivist alternative to the representational view of mind in mathematics education。Journal for Research in Mathematics Education,23(1),2-33。
4.
Cummins, D. D.(1991)。Children's interpretations of arithmetic word problems。Cognition and Instruction,8,261-289。
5.
Carpenter, T. P.、Hiebert, J.、Moser, J. M.(1983)。The effect of instruction on children's solutions of addition and subtraction word problems。Education Studies in Mathematics,14,55-72。
6.
Fuson, K. C.、Carroll, W. M.、Landis, J.(1996)。Levels in conceptualizing and solving addition and subtraction compare word problems。Cognition and Instruction,14,345-371。
7.
Cohen, S. A.、Stover, G.(1981)。Effects of teaching six-grades students to modify format variables of math word problems。Reading Research Quarterly,16,175-200。
8.
Gutstein, E.、Romberg, T. A.(1995)。Teaching children to add and subtract。Journal of Mathematical Behavior,14,283-324。
9.
Lesh, R.(1981)。Applied mathematical problem solving。Education Studies in Mathematics,12,235-264。
10.
Moyer, J. C.、Sowder, L.、Threadgill-Sewder, J.、Moyer, M. B.(1984)。Story problem formats: Drawn versus verbal versus telegraphic。Journal for Research in Mathematics Education,15,342-351。
11.
Nesher, P.、Greeno, J. G.、Riley, M. S.(1982)。The development of semantic categories for addition and subtraction。Educational Studies in Mathematics,13,373-394。
12.
Thompson, A. G.、Silver, E. A.(1984)。Research perspectives on problem solving in elementary school mathematics。The Elementary School Journal,84,529-545。
會議論文
1.
翁嘉英、鄭昭明(1988)。國小兒童解數學應用題的認知歷程。臺北縣。
延伸查詢
2.
蔣治邦、葉淑儀(1995)。二、三年級學童使用算式表徵文字題的能力-數學成就、算式類型、文字題題型對算式判斷作業及推理過程的影響。沒有紀錄。
延伸查詢
研究報告
1.
朱建正、吳昭容(1993)。國小兒童使用數學圖示之發展研究 (計畫編號:NSC-82-0111-S-002-004)。
延伸查詢
學位論文
1.
吳昭容(1990)。圖示對國小兒童解數學應用題之影響(博士論文)。國立臺灣大學。
延伸查詢
2.
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(碩士論文)。國立嘉義師範學院。
延伸查詢
3.
王逸文(1984)。臺北市幼稚園兒童解答簡單算術故事問題能力及其相關因素的研究,0。
延伸查詢
圖書
1.
Pólya, George(1945)。How to solve it: A new aspect of mathematical method。Princeton, NJ:Princeton University Press。
2.
Bruner, J. S.(1966)。Toward a theory of instruction。New York, NY:W. W. Norton and Company。
3.
Schoenfeld, A. H.(1985)。Mathematical problem solving。Orlando, Florida。
4.
National Council of Teachers of Mathematics(1989)。Curriculum and evaluation standards for school mathematics。Reston, VA:National Council of Teachers of Mathematics。
5.
Carpenter, T. P.(1985)。Learning to add and subtract: An exercise in problem solving。Teaching and Learning Mathematical Problem Solving: Multiple Research Perspectives。Hillsdale, NJ。
6.
蔣治邦(1994)。由表徵觀點探討新教材數與計算活動的設計。國民小學數學科新課程概說(低年級)。臺北縣板橋市。
延伸查詢
7.
Carpenter, T. P.、Moser, J. M.(1982)。The development of addition and subtraction problem-solving skill。Addition and subtraction: A cognitive perspective。Hillsdale, NJ。
8.
Haylock, D.、Cockburn, A.(1989)。Understanding early years mathematics。Understanding early years mathematics。London, UK。
9.
(1987)。Problems of representation in the teaching and learning of mathematics。Problems of representation in the teaching and learning of mathematics。Hillsdale, NJ。
10.
Mayer, R. E.、Lewis, A. B.、Hegarty, M.(1992)。Mathematical misunderstandings: Qualitative reasoning about quantitative problems。The nature and origins of mathematical skills。New York, NY。
圖書論文
1.
Riley, M. S.、Greeno, J. G.、Heller, J. I.(1983)。Development of children's problem-solving ability in arithmetic。The Development of Mathematical Thinking。Pittsburgh, Pennsylvania:Learning Research and Development Center, University of Pittsburgh。
2.
Lesh, R.、Post, T.、Behr, M.(1987)。Representations and translations among representations in mathematics learning and problem solving。Problems of Representation in the Teaching and Learning of Mathematics。Hillsdale, New Jersey:Lawrence Erlbaum Associates。
3.
Lesh, R.、Landau, M.、Hamilton, E.(1983)。Conceptual models in applied mathematical problem solving。Acquisition of mathematics concepts and processes。New York:Academic Press。
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