徑路搜尋方法之加減法文字題知識結構分析

The Pathfinder Analysis on Knowledge Structure of Addition and Subtraction Word Problems

10.6773/JRMS.200706.0029

林原宏(Yuan-Horng Lin)；黃美盼(Mei-Pan Huang)；易正明(Jenq-Ming Yih)

加減法文字題 ； 知識結構 ； 徑路搜尋 ； 試題反應理論 ； addition and subtraction word problems ； knowledge structure ； pathfinder ； item response theory

測驗統計年刊

15期_上（2007 / 06 / 01）

29 - 57

繁體中文

本研究旨在進行國小學童的加減法文字題知識結構之徑路搜尋分析，以二年級學童為研究對象。利用試題反應理論和概念類似係數的計算，可獲得不同能力值下的加減法文字題知識結構。 「加減法文字題解題測驗」，根據實證資料之徑路搜尋分析，主要發現如下： 一、三個相似性指數均能對能力值做有效之預測，且GTD指數預測效果最高。 二、高能力值組知識結構圖與標準參照知識結構圖較為相似，中低能力值組知識結構圖與標準參照知識結構圖較不相似。 三、以集群分析方法將受試者分群，各群的知識結構有其特殊性。 四、高分群學童知識結構圖很接近標準參照知識結構圖，教師可進行充實活動。中分群學童答對率較低的概念位於同一區，教師應進行該區概念的補救教學。低分群學童在概念1和概念11有多餘鏈結，可能對概念不甚了解，教師須利用課外時間校正學生的錯誤概念。 根據結果，研究者提出未來知識結構方法論研究之建議，以及有關加減法概念的診斷及教學的參考。

The purpose of this study is to analyze addition and subtraction word problems knowledge structure by pathfinder. There are 324 pupils in this research. According to the response of addition and subtraction on word problems, the researcher wants to investigate the knowledge structure of addition and subtraction. Another methodologies, item response theory, factor analysis and cluster analysis, are applied so that the features of varied knowledge structure are discussed. The main results of this research are as follows: 1. All the three proximity indexes can explain the ability of pupils effectively. Moreover, the most effective index is GTD index. 2. The knowledge structure of high ability group is similar to the that of criterion-referenced one. On the contrary, the knowledge structure of middle and low ability group is relatively dissimilar to that of criterion-referenced one. 3. The method of cluster analysis can help group examinees effectively. There are lots of similarities on knowledge structure between each group. 4. Pupils in high score group have knowledge structures which are very close to that of criterion-referenced one. Therefore, teachers can carry out substantial activities. Pupils in middle scored group have low rate of correct responses and conception in the same area. Hence, teachers can carry out conceptual remedial instruction in that area. Pupils in low scored group have redundant links in concept 1 and concept 11. It is likely that they have no any idea with concepts so that teachers should design extracurricular to correct students' unpracticed section. Based on the findings and results, some suggestions for practical teaching and future research are discussed.

1. 黃湃翔(2002)。徑路搜尋法在高中學生物理學科知識結構測量上之應用。教育與社會研究，4，1-33。
   連結：
2. Acton, W. H.,Johnson, P. J.,Goldsmith, T. E.(1994).Structural knowledge assessment: Comparison of referent structures.Journal of Educational Psychology,86,303-311.
3. Anderson, J. R.(1990).Cognitive psychology and its implications.New York:Freeman.
4. Carpenter, T. P.,Moser, J. M.,R. Lesh,M. Landau (Eds.)(1983).Acquisition of mathematics concepts and processes.New York:Academic Press.
5. Cooke, N. J.,Durso, F. T.,Schvaneveldt, R. W.(1986).Recall and measures of memory organization.Journal of Experimental: Learning, Memory and Cognition,12,538-549.
6. Fuson, K. C.,D. Grouws (Ed.)(1992).Handbook of research on mathematics teaching and learning.New York:Macmillan.
7. Goldsmith, T. E.,Johnson, P. J.,Acton, H. W.(1991).Assessing structural knowledge.Journal of Educational Psychology,83,88-96.
8. Gomez, R.,Hadfield, O. D.,Housner, L. D.(1995).Manuscript from Computing Research Laboratory.Las Cruces:New Mexico State University.
9. Gomez, R.,Housner, L.D.(1992).Pedagogical knowledge structures in prospective teachers.Paper presented at the annual meeting of the American Educational Research Association,Austin, TX:
10. Greeno, J. G.,R. E. Snow,P. A. Federico,W. E. Montague (Eds.)(1980).Aptitude, learning, and instruction: Cognitive process analysis.Hillsdale, NJ:Lawrence Erlbaum Associates.
11. Houliham, D. M.,Ginsburg, H. P.(1981).The addition methods of first and second grade children.Journal for Research in Mathematics Education,12,95-106.
12. Johnson, P. J.,Goldsmith, T. E.,Teague, K. W.(1994).Locus of the predictive advantage in pathfinder-based representations of classroom knowledge.Journal of Educational Psychology,86,617-626.
13. Jonassen, D. H.,Beissner, K.,Yacci, M.(1993).Structural knowledge: Techniques for representing, conveying, and acquiring structural knowledge Hillsdale.NJ:Lawrence Erlbaum Associates.
14. Koubek, R. J.,Mountjoy, D. N.(1991).Toward a model of knowledge structure and a comparative analysis of knowledge structure of knowledge structure measurement techniques.Wright State Univ., Dayton, OH. Dept. of Biomedical and Human Factors Engineering.
15. Lewis, A. B.,Mayer, R. E.(1987).Students' miscomprehension of relational statements in arithmetic word problems.Journal of Educational Psychology,76,1382-1385.
16. Marshall, S. P.,Pribe, C. A.,Smith, J. D.(1987).Schema knowledge structure for representing and understanding arithmetic story problems.Arlington, VA:Office of Naval Research.
17. Mitchell, A. A.,Chi, M. T.,P. Nagy (Ed.)(1984).The representation of cognitive structure.Toronto, Canada:Ontario Institute for Studies in Education.
18. Riley, M. S.(1981).Unpublished master`s thesis.University of Pittsburgh.
19. Rumelhart, D. E.,Norman, D. A.,A.M. Aitkenhead,,J.M. Slack (Ed.)(1985).Issues in cognitive modeling.Hillsdale, NJ:Lawrence Erlbaum Associates.
20. Schvaneveldt, R. W.(Ed.)(1990).Pathfinder associative networks: Studies in knowledge organization.Norwood, NJ:Ablex.
21. Yancy, A. V.(1981).Specialist in Education Degree Thesis.University of Louisville.
22. 山下元、勝又保雄、津田榮(1994)。ファジィ理論を應用した教材構造分析－多值テストデータを用いた近似構造解析。科學教育研究，18(1)，23-29。
23. 江淑卿(1997)。國立臺灣師範大學教育心理與輔導研究所博士論文（未出版）。
24. 余民寧、林曉芳、蔡佳燕(2001)。國小學生數學知識結構認知診斷評量之研究。國立政治大學教育與心理研究，24，263-302。
25. 呂玉琴(1997)。國小低年級學生對加減法文字題的了解。中華民國第十三屆科學教育學術研討會論文集
26. 呂玉琴譯、Thomas P. Carpenter著(1988)。加、減法文字題的分類、解題策略及影響因素。國民教育，28(8, 9)，17-29。
27. 林原宏(1996)。知識結構分析－徑路搜尋、多向度量尺和集群分析的方法論探討。測驗統計年刊，4，47-69。
28. 林曉芳、余民寧(2001)。國中生在代數概念學習之評量研究－以二元一次方程式為例。國立政治大學教育與心理研究，24，303-326。
29. 涂金堂(2001)。國立政治大學教育研究所博士論文（未出版）。
30. 許淑貞(2003)。國立臺中師範學院數學教育學系碩士班理學碩士論文（未出版）。
31. 許琇皙(1999)。國立中正大學教育學研究所碩士論文（未出版）。
32. 蔣治邦(2001)。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。中華心理學刊，43(2)，239-254。
33. 蔣治邦、鍾思嘉(1991)。低年級學童加減概念的發展。國立政治大學教育與心理研究，14，35-68。
34. 蔡佳燕(2000)。國立政治大學教育研究所碩士論文（未出版）。
35. 鍾聖校(1990)。認知心理學。臺北市:心理出版社。