補習與教學型態對數學低成就生之文字題表現的影響

The Impact of Cram Schooling and Teaching Approaches on Mathematics Underachievers' Word-Problem Solving Performance

10.6776/JEPR.201212.0001

白雲霞(Yun-Hsia Pai)

低成就生 ； 補習 ； 數學文字題 ； 閱讀理解 ； cram school ； math word-problem ； reading comprehension ； supplementary school education ； underachievers

教育實踐與研究

25卷2期（2012 / 12 / 01）

1 - 33

繁體中文

本研究主要在探討有無補習之高年級低成就學生在數學文字題學習成就上的差異，與其學校及補習班教師教學型態對數學文字題的影響。本研究之五、六年級低成就生分別接受該年級之數學文字題測驗，該測驗由低、中、高閱讀理解難度文字題組成，有補習低成就生的補習班與學校教師分別接受教學型態量表。研究結果主要發現如下：（一）補習與未補習之五年級數學低成就生在數學文字題測驗總分及其學習保留量皆沒有明顯差異；但有補習的六年級低成就生數學文字題總表現顯著高於沒有補習者，並較具學習保留效果；（二）補習僅對於六年級數學低成就生在低、中閱讀難度文字題得分有顯著的幫助。（三）對五年級低成就生而言，補習班教師愈傾向使用建構教學取向，有補習者的數學文字題成就總分及中、高難度文字題的作答表現則越高，而其直接教學取向對中難度題具有負向預測力；在六年級部分，智力對六年級低成就生的數學文字題總分有正向預測力，而教學型態則不具預測力。但對低閱讀難度的數學文字題而言，智力與學校教師越不採用直接教學取向的程度可共同預測低成就生數學文字題低難度題得分，其解釋力為20%；而補習天數對五、六年級數學低成就生的數學文字題測驗總分皆沒有顯著預測力。

This study investigates differences in mathematics word-problem solving performance among 5th and 6th grade mathematics underachievers with and without cram schooling, and the effect of their elementary school teachers' and cram school teachers' teaching approaches on word-problem solving performance. The word-problem test is comprised of three parts, including problems requiring low, average, and high level of reading comprehension. Participants were given word-problem tests appropriate to their grade level. Students' mathematics teachers in cram schools and elementary schools were given a questionnaire on their teaching approaches. First, there were no significant differences in math word-problem solving performance and learning retention between 5th grade mathematics underachievers with and without cram schooling. However, word-problem solving performance and learning retention of the 6th grade underachievers with cram schooling were significantly better than those without. Regression analysis of math word-problem performance in 5th grade underachievers revealed that the more cram school teachers used a constructivist teaching approach, the higher their scores were on the total, average, and high level math word-problem tests. In contrast, the more cram school teachers used the direct teaching approach, the lower scores math underachievers got on the average level word-problem tests. The 6th grade math underachievers' performance can be explained by their intelligence. Moreover, the direct teaching approach was demonstrated to have a negative effect on underachievers' performance solving low level word-problems. In addition, word-problem solving performance was not related to the number of hours per week they learned mathematics in cram schools.

1. 林大森、陳憶芬(2006)。臺灣高中生參加補習之效益分析。教育研究集刊，52(4)，35-70。
   連結：
2. 林慧敏、黃毅志(2009)。原漢族群、補習教育與學業成績關連之研究：以台東地區國中二年級生為例。當代教育研究，17(3)，41-81。
   連結：
3. 秦麗花、邱上真(2004)。數學本文閱讀理解相關因素探討及其模式建立之研究～以角度單元為例。特殊教育與復健學報，12，99-121。
   連結：
4. 張蓓莉(2006)。啟動建構學習的教學方式對數學低成就聽覺障礙學生二步驟四則運算文字題的教學效果。特殊教育研究學刊，30，75-94。
   連結：
5. 陳俊瑋、黃毅志(2011)。重探學科補習的階層化與效益：Wisconsin模型的延伸。教育研究集刊，57(1)，101-135。
   連結：
6. 黃毅志、陳俊瑋(2008)。學科補習、成績表現與升學結果─以學測成績與上公立大學為例。教育研究集刊，54(1)，117-149。
   連結：
7. 劉正(2006)。補習在臺灣的變遷、效能與階層化。教育研究集刊，52(4)，1-33。
   連結：
8. 關秉寅、李敦義(2010)。國中生數學補的愈久，數學成就愈好嗎？傾向分數配對法的分析。教育研究集刊，56(2)，105-139。
   連結：
9. Esty, W. W. (2003). The language of mathematics. Retrieved October 1, 2009, from http://augustusmath.hypermart.net/
10. Kenny, D. T. (2002). To coach or not to coach: But what is the question? Online International Confederation of Principals' Journal. Retrieved January 10, 2007, from http://www2.fhs.usyd.edu.au/bach/staff/kenny/Documents/Developmental%20Psych/Educational%20Psych/Academic%20Coaching/Coaching_Online%20ICP.pdf
11. 教育部（2012）。全國補習班最近十年成長統計圖表。2012年1月15日，取自http://bsb.edu.tw/afterschool/html/statistics.html
12. Aiken, L. R., Jr.(1976).Update on attitudes and other affective variables in learning mathematics.Review of educational research,46,239-311.
13. Autry, S. L.(2002).Attitude and achievement using two approaches for first-grade mathematics instruction.annual meeting of the Mid-South Educational Research Association,Chattanooga, TN:
14. Bangert-Drowns, R. L.,Kulik, J. A.,Kulik, C. -L. C.(1983).Effects of coaching programs on achievement test performance.Review of Educational Research,53(4),571-585.
15. Bangert-Drowns, R. L.,Kulik, J. A.,Kulik, C. -L. C.(1983).Synthesis of research on the effects of coaching for aptitude and admissions tests.Educational Leadership,41,80-82.
16. Chall, J. S.(1991).Patterns of adult reading.conference on Literacy and Adults with Learning Disabilities,New York:
17. Chung, I.(2004).A comparative assessment of constructivist and traditionalist approaches to establishing mathematical connections in learning multiplication.Education,125(2),271-278.
18. Din, F. S.(1998).Direct instruction in remedial math instructions.National Conference on Creating the High Quality School,Arlington, VA:
19. Dolly, J. P.(1992)."Juku" and the performance of Japanese students: An American Perspective.Annual Meeting of the Japan United States Teacher Education Consortium
20. Durkin, K.(Ed.),Shire, B.(Ed.)(1991).Language in mathematics in mathematical education: Research and practice.Milton Keyes, UK:Open University Press.
21. Ebel, R. L.,Frisbie, D. A.(1979).Essentials of educational measurement.Englewood Cliffs, NJ:Prentice-Hall.
22. Gales, M. J.,Yan, W.(2001).Relationship between constructivist teacher beliefs and instructional practices to students' mathematical achievement: Evidence from TIMMS.annual meeting of the American Educational Research Association,Seattle, WA:
23. Goldin, G. A.(Ed.),McClintock, C. E.(Ed.)(1984).Task variables in mathematics problem solving.Philadelphia, PA:The Franklin Institute Press.
24. Harper, G. F.,Mallette, B.,Macheady, L.,Brennan, G.(1993).Classwide student tutoring teams and direct instruction as a combined instructional program to teach generalizable strategies for mathematics Word Problems.Education and Treatment of Children,16(2),115-134.
25. Harskamp, E. G.,Suhre, C. J. M.(2006).Improving mathematical problem solving: A computerised approach.Computers in Human Behaviour,22,801-815.
26. Hui, H. T.,Naufal, U. I.(2011).,未出版
27. Jitendra, A. K.,Hoff, K. E.(1996).The effects of schema-based instruction on mathematical word problem solving performance of students with learning disabilities.Journal of Learning Disabilities,21(3),242-253.
28. Karaduman, H.,Gultekin, M.(2007).The effect of constructivist learning principles based learning materials to students' attitudes, success and retention in social studies.Turkish Online Journal of Educational Technology,6(3)
29. Kenny, D. T.,Faunce, G.(2004).Effects of academic coaching on elementary and secondary school students.Journal of Educational Research,98(2),115-126.
30. Kim, J. S.(2005).The effects of a constructive teaching approach on student academic achievement, self-concept, and learning strategies.Asia pacific education review,6(1),7-19.
31. Lyons, D.(1981).Report prepared as part of the Humboldt County Labor Market information Project and financed under the provisions of Title VII of the Comprehensive Employment and Training Act of 1973.Report prepared as part of the Humboldt County Labor Market information Project and financed under the provisions of Title VII of the Comprehensive Employment and Training Act of 1973.,未出版
32. Mayer, R. E.(1993).Understanding individual differences in mathematical problem-solving: Towards a research agenda.Learning Disability Quarterly,16,2-5.
33. McNamara, D. S.(2001).Reading both high-coherence and low-coherence texts: Effects of text sequence and prior knowledge.Canadian Journal of Experimental Psychology,55(2),51-62.
34. Miller, S. P.,Mercer, C. D.(1997).Educational aspects of mathematics disabilities.Journal of Learning Disabilities,30,47-56.
35. Montague, M.(2003).Teaching division to students with learning disabilities: A constructivist approach.Exceptionality: A Special Education Journal,11(3),165-175.
36. Morrone, A. S.,Harkness, S. S.,D'Ambrosio, B.,Caulfield, R.(2004).Patterns instructional discourse that promote the perception of mastery goals in a social constructivist mathematics course.Educational Studies in Mathematics,56,19-38.
37. Pólya, G.(1990).Mathematics and plausible reasoning.Princeton, NJ:Princeton University Press.
38. Salend, S. J.(2001).Creating inclusive classrooms: Effective and reflective practices.Columbus, NJ:Merrill Prentice Hall.
39. Smyth, F. L.(1989).Commercial coaching and SAT scores: The effects on college preparatory students in private schools.Journal of College Admission,123,2-9.
40. Tice, T. N.(1994).Japan's cram schools.Education Digest,60(1),42.
41. Wiederholt, J. L.,Bryant, B. R.(1987).Assessing the reading abilities and insturctional needs of students.Austin, TX:ProED.
42. Wilson, C. L.(1991).Direct instruction in math word problems: Students with learning disabilities.Exceptional Children,57(6),512-529.
43. 江芳盛(2006)。國中學生課業補習效果之探討。台北市立教育大學學報，37(1)，131-148。
44. 李敦義(2006)。補習有助於升學嗎？─分析補習、多元入學與教育取得間的關係。教育與心理研究，29(3)，489-516。
45. 林振春(1987)。台北市升大學補習班學生生活狀況調查研究。社會教育學刊，16，191-232。
46. 邱上真、詹士宜、王惠川、吳建志(1995)。解題歷程導向教學對國小四年級數學科低成就學生解題表現之成效研究。特殊教育復健學報，4，75-108。
47. 洪碧霞、邱上真(1997)。國民小學國語文低成就學童篩選工具系列發展之研究。特殊教育研究學刊，15，83-107。
48. 孫清山、黃毅志(1996)。補習教育、文化資本與教育取得。台灣社會學刊，19，95-139。
49. 涂金堂(2007)。國小學生數學文字題問題結構與數學解題表現之相關研究。屏東教育大學學報，26，101-136。
50. 張芳全(2009)。家長教育成度與科學成就之關係：文化資本、補習時間與學習興趣為中介的分析。教育研究與發展期刊，5(4)，39-77。
51. 張春興(1997)。教育心理學。台北:東華書局。
52. 許崇憲(2010)。高中學生參加補習的情境決定因素及對學業成績的影響。教育心理研究，33(3)，77-105。
53. 陳義汶(2009)。國中生學校數學成績與數學補習及數學態度之相關研究。國民教育學報，6，131-161。
54. 黃雅容(2009)。就讀明星高中的學習經驗比就讀一般高中好嗎？檢視上課方式、補習與課外閱讀。教育實踐與研究，22(1)，113-138。
55. 關秉寅、李敦義(2008)。補習數學有用嗎？一個「反事實」的分析。臺灣社會學刊，41，97-148。
56. 蘇秀枝(2008)。東南亞外籍與大陸配偶國小子女參加課後托育與補習才藝之現況與學業成就及行為適應之關係。朝陽人文社會學刊，6(1)，123-175。

1. 顏郁玲,陸偉明(2023)。學校教師因素對國三生數學成就之跨層次影響：考量參與數學補習的國中生個人因素。清華教育學報，40(1)，1-43。
2. (2014)。從建模教學推敲數學補救教學的可能面向。教育研究月刊，242，49-68。