開展個體數學解題檢核能力之動態評量研究

The Research of Applying Multi-Stage Dynamic Assessment to Facilitate the Learning Potential of Checking Performance on Mathematical Problem Solving for First Graders

10.6251/BEP.20050119

許家驊(Chia-Hua Hsu)

可能發展區間(ZPD) ； 動態評量 ； 鷹架教學中介 ； 後設認知 ； 數學解題錯誤偵測 ； dynamic assessment (DA) ； error detection performance on mathematical problem solving (MPS) ； metacognition ； intervention of scaffolding instruction ； zone of proximal development (ZPD)

教育心理學報

36卷3期（2005 / 03 / 01）

287 - 309

繁體中文

本研究係結合動態評量與錯誤偵測作業來試探及評估個體的數學解題檢核能力，並探求其與解題表現間之關係。篩選後正式對象共26人，採組間實驗設計，處理組接受中介評量程序，而參照組則給予自我練習機會。結果發現處理組解題檢核學習進步表現顯著優於參照組，且具大幅度效果值與關聯強度。處理組內標準群表現優於連續群，連續群非標準化中介表現又較標準化中介表現為佳，透過組合指標可再區分出兩群內個體間的學習潛力。之後藉由不同中介階段解題檢核表現的診斷分析，針對個體找出相對應之各項問題。此外個體檢核與解題表現間具中度正向關聯，處理組解題表現有隨檢核學習進步而呈正向改變之現象。

The researcher combines Multi-Stage Dynamic Assessment (MSDA) model with error detection tasks to facilitate the learning potential of MPS checking performance for first graders, and investigates the interrelationships between solving with checking performance. Taking the between grouping experimental design to proceed study. The screened samples are 26 by pre-testing, and subject matching 13 to each group. One group is mediated by multi session dynamic assessment, the other take self-practice. Then two groups accept needed testing. Next the data are analyzed by adequate statistical methods. The simple gain scores of treatment group on checking performance are better than counterpart significantly. The effectiveness of cumulative facilitation, potential discrimination, deficiency diagnosis and prescription for multi session dynamic assessment are found in treatment group. There is medium positive correlation existed between solving and checking performance also.

1. 許家驊、邱上真、張新仁(2003)。多階段動態評量對國小學生數學學習促進與補救效益之分析研究。教育心理學報，2(35)，141-166。
   連結：
2. Brown, A. L.、Campione, J. C.(1990)。Toward a scientific practice of science education。Jersey, New York:Lawrence Eribaum Associates, Publishers。
3. Campione, J. C.,Brown, A. L.(1987).Dynamic assessment: An interactional approach to evaluating learning potential.New York:The Guilford Press.
4. Cohen, J.(1988).Statistical power analysis for the behavioral sciences.Hillsdale, New Jersey:Lawrence Eribaum Associates.
5. Embretson, S. E.(1987).Dynamic assessment: An interactional approach to evaluating learning potential.New York:The Guilford Press.
6. Feuerstein, R.,Rand, Y,,Jensen, M. R.,Kaniel, S.,Tzuriel, D.(1987).Dynamic assessment: An interactional approach to evaluating learning potential.New York:The Guilford Press.
7. Fuson, K. C.(1992).Handbook of research on mathematics teaching and learning: A project of the national council of teachers of mathematics.New York:Macmillan.
8. Garner, R.(1988).Metacogniton and reading comprehension.Norwood, New Jersey:Ablex.
9. Garofalo, J.,Lester, F. K.(1985).Metacogniton.cognitive monitoring, and mathematical performance.Journal for Reaserch in Mathematics Education,16（3）,163-176.
10. Haywood, H. C.,Tzuriel, D.,Vaught, S.(1992).Interactive assessment.New York:Springer-Verlag.
11. Hutchinson, N. L.(1992).The challenges of componential analysis : Cognitive and metacognitive instruction in mathematical problem solving.Journal of Learning Disabilities,25（4）,249-252＆257.
12. Jitendra, A. K.,Kameenul, E. J.(1993).An exploratory study of dynamic assessment involving two strategies on experts and novices' performance in solving part-whole mathematical word problems.Diagnostique,18（4）,305-325.
13. Kintsch, W.,Greeno, J. G.(1985).Understanding and solving word arithmetic problems.Psychological Review,92（1）,109-129.
14. Kirk, R. E.(1995).Experimental design: Procedures for the behavioral sciences.Pacific Grove, CA:Brooks/Cole Publishing Company.
15. Krulik, S. K.,Rudnick, J. A.(1989).Problem solving: A handbook for senior high school teachers.Boston, MA:Allyn & Bacon.
16. Lester, F. K.,Garofalo, J.,Kroll, D. L.(1989).The role ofmetacognition in mathematical problem solving: A study of two grade seven classes.Bloomington:Indiana University, School of Education, Mathematics Education Development Center.
17. Lidz, C. S.(1991).Practitioner's guide to dynamic assessment.New York:The Guilford Press.
18. Mayer, R. E.(1993).Understanding individual differences in mathematical problem solving: Towards a research agenda.Journal Disability Quarterly,16（1）,3-5.
19. Mayer, R. E.(1989).Introduction to the special section.Journal of Educational Psychology,81（4）,452-456.
20. Montague, M.(1992).The effects of cognitive and metacognitive strategy instruction on the mathematical problem solving of middle school students with learning disabilities.Journal of Learning disabilities,25（4）,230-248.
21. Montague, M.,Warger, C.,Morgan, T. H.(2000).Solve it! strategy instruction to improve mathematical problem solving.Learning Disabilities Research and Practice,15（2）,110-116.
22. Paris, S. G.,Paris, A. H.(2001).Educational Psychologist.
23. Polya, G.(1957).How to solve it.Princeton NJ:Princeton University Press.
24. Pugalee, D. K.(2001).Writing, mathematics, and metacognition: looking for connections through students' work in mathematical problem solving.School Science and Mathematics,101（5）,236-244.
25. Schoenfeld, A. H.(1992).Handbook of research on mathematics teaching and learning: A project of the national council of teachers of mathematics.New York:Macmillan.
26. Schurter, W. A.(2002).Comprehension monitoring: An aid to mathematical problem solving.Journal of Developmental Education,26（2）,22-33.
27. Swanson, H. L.,Lussier, C. M.(2001).A selective synthesis of experimental literature on dynamic assessment.Review of Educational Research,71（2）,321-363.
28. Van Haneghan, J. P.(1990).Third and fifth graders' use of multiple standards of evaluation to detect errors in word problems.Journal of Educational Psychology,82（2）,352-358.
29. Van Haneghan, J. P.,Baker, L.(1989).Cognitive strategy research: From basic research to educational applications.New York:Springer-Verlag.
30. Vye, N. J.,Burns, M. S.,Delclos, V. R.,Bransford, J. D.(1987).Dynamic assessment: An interactional approach to evaluating learning potential.New York:The Guilford Press.
31. Vygotsky, L. S.(1978).Mind in society: The development of higher psychological processes.Cambridge, MA:Harvard University Press.
32. 古明鋒(1998)。加減法應用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。
33. 朱經明、蔡玉瑟(2000)。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。
34. 吳國銘、洪碧霞、邱上真(1995)。國小學童在動態評量中數學解題學習歷程與遷移效益之探討。測驗年刊，42，61-84。
35. 康軒文化事業股份有限公司(2003)。一下國小數學課本及教學手冊。台北市:康軒文化事業股份有限公司。
36. 教育部(2003)。國民中小學九年一貫課程網要。台北市:教育部。
37. 許家驊(1999)。高雄市政府公教人力資源發展中心學術教育叢書，新典範數學。高雄:高雄市政府公教人力資源發展中心。
38. 許家驊(1995)。中華民國第十一屆科學教育學術研討會論文集。
39. 許家驊(1998)。從社會互動認知建構觀點探討動態評量在評估及促發認知監控潛能上的應用性。初等教育學報(台南師範學院)，11，335-364。
40. 許家驊(1994)。中華民國第十屆科學教育學術研討會論文集。
41. 許家驊(2003)。從鷹架教學中介觀點探討動態評量在促進及評估個體學習潛能上之基礎與設計。彰化師大教育學報，5，87-113。
42. 許家驊(2001)。國小三年級數學多階段動態評量之研究。國立高雄師範大學教育學系。
43. 陳密桃(1990)。後設認知(metacognition)的評估方法。教育文粹，20，196-209。

1. 許家驊(2008)。不同策略教學及鷹架中介設計對個體數學文字題解題學習潛能開展效益影響之動態評量研究。教育心理學報，39(4)，513-532。
2. 許家驊(2011)。國小中低年級學生解題檢核能力與自我調節表現之關係研究。教育學誌，25，91-137。
3. 許家驊(2011)。歷程導向設計及學習策略中介教導對個體不同層次數學解題學習潛能開展效益影響之動態評量研究。教育心理學報，43(1)，127-154。
4. 薛岳、劉玉玲(2013)。國中生數學學業自我概念及數學學習策略與數學學業成就之研究-自我提升模式觀點。課程與教學，16(1)，179-208。
5. 鍾怡臻、蕭輔萱、蕭劭芬、張芸瑄、張云綺、王文伶(2014)。非標準化學習潛能中介模式動態評量對國中資源班學生數學學習成效初探。特殊教育季刊，131，23-32。