國中學生數學自我概念與數學學業成就相互效果模式之縱貫研究－性別差異與城鄉差距之觀點

The Longitudinal Reciprocal Effects Model of Junior High School Students' Mathematics Self-Concept and Mathematics Achievement: The Perspectives of Gender and Urban/Rural Differences

10.6173/CJSE.2016.24S.04

龔心怡(Hsin-Yi Kung)；李靜儀(Ching-Yi Lee)

性別差異 ； 相互效果模式 ； 城鄉差距 ； 數學自我概念 ； 數學學業成就 ； Gender Difference ； Reciprocal Effects Model ； Urban/Rural Difference ； Mathematics Self-Concept ； Mathematics Achievement

科學教育學刊

24卷S期（2016 / 12 / 01）

511 - 536

繁體中文

本研究旨在以縱貫研究設計來探究國中學生的數學自我概念與數學學業成就的相互效果模式，再進一步從多元文化的觀點著手，分析在數學自我概念與數學學業成就變項上的性別差異與城鄉差距，及這些差距是否有縱貫的跨時間性。本研究以七年級至九年級三個波次共1,025位國中學生為研究樣本，藉由追蹤資料之結構方程模式分析後，獲致結果如下：一、整體模式所獲得的適配度指標顯示模式可被接受，數學自我概念與數學學業成就相互效果模式獲得支持；二、國中學生的數學自我概念與數學學業成就具有跨時間性的性別差異，男生在三波次的數學自我概念皆顯著地高於女生，但女生的成就表現顯著地高於男生；三、國中學生的數學自我概念與數學學業成就呈現橫跨不同年級的城鄉差距，城市地區學生在三波次的數學自我概念與數學學業成就皆顯著地高於鄉鎮地區學生。最後根據研究結果提出建議，提供數學教育及後續研究之參考。

This study drew on the multidimensional-multifaceted theory of self-concept to examine the relations between mathematics self-concept and mathematics achievement with a three-wave longitudinal design. Using the multicultural perspectives, the study also investigated the gender and urban/rural differences on mathematics self-concept and mathematics achievement over time. Utilizing structural equation modeling, 1,025 junior high school students participated in the three-wave longitudinal study. The results revealed that: 1. A reciprocal effects model between mathematics self-concept and mathematics achievement was proposed and indicated a reasonable goodness-of-fit. 2. There were significant gender differences on mathematics self-concept and mathematics achievement over time. While boys tended to have higher mathematics self-concept, girls tended to have higher mathematics achievement. 3. Student’s mathematics self-concept and mathematics achievement had urban/rural differences over time. Urban students tended to have higher mathematics self-concept and mathematics achievement than their rural counterparts. Implications and suggestions were discussed and provided to enhance students’ mathematics learning.

1. 吳春慧(2010)。數學和科學領域I/E模式的探討：跨性別之研究。屏東教育大學學報─教育類，34，67-82。
   連結：
2. 巫博瀚、陸偉明(2010)。延宕交叉相關與二階層線性成長模式在臺灣青少年自尊的發現。測驗學刊，57(4)，541-565。
   連結：
3. 李俊豪(2010)。解釋學生基測成績差異之個人因素與地區因素。地理學報，60，67-102。
   連結：
4. 教育部統計處(2016)。教育統計查詢網。查詢日期：2016年12月15日，檢自https://stats.moe.gov.tw/
5. Mullis, I. V. S., Martin, M. O., Foy, P., & Hooper, M. (2016). TIMSS 2015 international results in mathematics. Retrieved September 17, 2016, from http://timssandpirls.bc.edu/timss2015/international-results/timss-2015/mathematics/student-achievement/
6. Abu-Hilal, M. M.,Abdelfattah, F. A.,Shumrani, S. A.,Dodeen, H.,Abduljabber, A. S.,Marsh, H. W.(2014).Mathematics and science achievements predicted by self-concept and subject value among 8th grade Saudi students: Invariance across gender.International Perspectives in Psychology: Research, Practice, Consultation,3(4),268-283.
7. Ajai, J. T.,Imoko, B. I.(2015).Gender differences in mathematics achievement and retention scores: A case of problem-based learning method.International Journal of Research in Education and Science,1(1),45-50.
8. Alordiah, C. O.,Akpadaka, G.,Oviogbodu, C. O.(2015).The influence of gender, school location and socio-economic status on students' academic achievement in mathematics.Journal of Education and Practice,6(17),130-136.
9. Archambault, I.,Eccles, J. S.,Vida, M. N.(2010).Ability self-concepts and subjective value in literacy: Joint trajectories from grades 1 through 12..Journal of Educational Psychology,102(4),804-816.
10. Bagozzi, R. P.,Yi, Y.(1988).On the evaluation of structural equation models.Journal of the Academy of Marketing Science,16(1),74-94.
11. Bassey, S. W.,Joshua, M. T.,Asim, A. E.(2011).Gender differences and mathematics achievement of rural senior secondary students in Cross River State, Nigeria.Mathematics Connection,10,56-60.
12. Beaton, A. E.,Mullis, I. V. S.,Martin, M. O.,Gonzalez, E. J.,Kelly, D. L.,Smith, T. A.(1996).Mathematics achievement in the middle school years: IEA's third international mathematics and science study (TIMSS).Chestnut Hill, MA:TIMSS International Study Center..
13. Bollen, K. A.(ed.),Long, J. S.(ed.)(1993).Testing structural equation models.Newbury Park, CA:Sage.
14. Butt, I. H.,Dogar, A. H.(2014).Gender disparity in mathematics achievement among the rural and urban high school students in Pakistan.Pakistan Journal of Social Sciences,34(1),93-100.
15. Calsyn, R. J.,Kenny, D. A.(1977).Self-concept of ability and perceived evaluation of others: Cause or effect of academic achievement?.Journal of Educational Psychology,69(2),136-145.
16. Cvencek, D.,Kapur, M.,Meltzoff, A. N.(2015).Math achievement, stereotypes, and math selfconcepts among elementary-school students in Singapore.Learning and Instruction,39,1-10.
17. Cvencek, D.,Meltzoff, A. N.,Greenwald, A. G.(2011).Math-gender stereotypes in elementary school children.Child Development,82(3),766-779.
18. Dare, E. A.,Roehrig, G. H.(2016)."If I had to do it, then I would": Understanding early middle school students' perceptions of physics and physics-related careers by gender.Physical Review Physics Education Research,12(2),1-11.
19. Dramanu, B. Y.,Balarabe, M.(2013).Relationship between academic self-concept and academic performance of junior high school students in Ghana.European Scientific Journal,9(34),93-104.
20. Durik, A. M.,Vida, M.,Eccles, J. S.(2006).Task values and ability beliefs as predictors of high school literacy choices: A developmental analysis.Journal of Educational Psychology,98(2),382-393.
21. Fan, X.,Sivo, S. A.(2009).Using ΔGoodness-of-Fit indexes in assessing mean structure invariance.Structural Equation Modeling: A Multidisciplinary Journal,16(1),54-69.
22. Festinger, L.(1954).A theory of social comparison processes.Human Relations,7,117-140.
23. Ganley, C. M.,Lubienski, S. T.(2016).Mathematics confidence, interest, and performance: Examining gender patterns and reciprocal relations.Learning and Individual Differences,47,182-193.
24. Gold, M. S.,Bentler, P. M.(2000).Treatments of missing data: A Monte Carlo comparison of RBHDI, iterative stochastic regression imputation, and expectation-maximization.Structural Equation Modeling: A Multidisciplinary Journal,7(3),319-355.
25. Goldman, A. D.,Penner, A. M.(2016).Exploring international gender differences in mathematics self-concept.International Journal of Adolescence and Youth,21(4),403-418.
26. Guo, J.,Marsh, H. W.,Parker, P. D.,Morin, A. J. S.,Yeung, A. S.(2015).Expectancy-value in mathematics, gender and socioeconomic background as predictors of achievement and aspirations: A multi-cohort study.Learning and Individual Differences,37,161-168.
27. Hair, J. F.,Black, W. C.,Babin, B. J.,Anderson, R. E.(2009).Multivariate data analysis.Upper Saddle River, NJ:Prentice-Hall.
28. Hoelter, J. W.(1983).The analysis of covariance structures: Goodness-of-fit indices.Sociological Methods & Research,11(3),325-344.
29. Hoge, D. R.,Smit, E. K.,Crist, J. T.(1995).Reciprocal effects of self-concept and academic achievement in sixth and seventh grade.Journal of Youth and Adolescence,24(3),295-314.
30. Kline, R. B.(2005).Principles and practice of structural equation modeling.New York:The Guilford Press.
31. Kung, H.-Y.(2009).Perception or confidence? Self-concept, self-efficacy and achievement in mathematics: A longitudinal study.Policy Futures in Education,7(4),387-398.
32. Leung, F. K. S.(2002).Behind the high achievement of East Asian students..Educational Research and Evaluation: An International Journal on Theory and Practice,8(1),87-108.
33. Li, Q.(2007).Mathematics, science, and technology in secondary schools: Do gender and region make a difference?.Canadian Journal of Learning and Technology,33(1),41-57.
34. Little, R. J. A.(1998).A test of missing completely at random for multivariate data with missing values.Journal of the American Statistical Association,83(404),1198-1202.
35. Marsh, H. W.(1990).SDQ II manual: Self-description questionnaire II.Campbelltown, Australia:University of Western Sydney.
36. Marsh, H. W.(1990).Causal ordering of academic self-concept and academic achievement: A multiwave, longitudinal panel analysis.Journal of Educational Psychology,82(4),646-656.
37. Marsh, H. W.,Byrne, B. M.,Shavelson, R. J.(1988).A multifaceted academic self-concept: Its hierarchical structure and its relation to academic achievement.Journal of Educational Psychology,80(3),366-380.
38. Marsh, H. W.,Craven, R. G.(2006).Reciprocal effects of self-concept and performance from a multidimensional perspective: Beyond seductive pleasure and unidimensional perspectives.Perspectives on Psychological Science,1(2),133-163.
39. Marsh, H. W.,Martin, A. J.(2011).Academic self-concept and academic achievement: Relations and causal ordering.British Journal of Educational Psychology,81(1),59-77.
40. Marsh, H. W.,Trautwein, U.,Lüdtke, O.,Köller, O.,Baumert, J.(2005).Academic selfconcept, interest, grades, and standardized test scores: Reciprocal effects models of causal ordering.Child Development,76(2),397-416.
41. Marsh, H. W.,Yeung, A. S.(1997).Causal effects of academic self-concept on academic achievement: Structural equation models of longitudinal data.Journal of Educational Psychology,89(1),41-54.
42. Mullis, I. V. S.,Martin, M. O.,Foy, P.,Arora, A.(2012).TIMSS 2011 international results in mathematics.Chestnut Hill, MA:TIMSS & PIRLS International Study Center.
43. Pinxten, M.,Marsh, H. W.,De Fraine, B.,Van Den Noortgate, W.,Van Damme, J.(2014).Enjoying mathematics or feeling competent in mathematics? Reciprocal effects on mathematics achievement and perceived math effort expenditure.British Journal of Educational Psychology,84(1),152-174.
44. Retelsdorf, J.,Schwartz, K.,Asbrock, F.(2015)."Michael can't read!" Teachers' gender stereotypes and boys' reading self-concept.Journal of Educational Psychology,107(1),186-194.
45. Rinn, A. N.,Miner, K.,Taylor, A. B.(2013).Family context predictors of math self-concept among undergraduate STEM majors: An analysis of gender differences.Journal of the Scholarship of Teaching and Learning,13(2),116-132.
46. Rubin, D. B.(1987).Multiple imputation for nonresponse in surveys.New York:Wiley.
47. Sáinz, M.,Eccles, J.(2012).Self-concept of computer and math ability: Gender implications across time and within ICT studies.Journal of Vocational Behavior,80(2),486-499.
48. Sáinz, M.,Upadyaya, K.(2016).Accuracy and bias in Spanish secondary school students' self-concept of math ability: The influence of gender and parental educational level.International Journal of Educational Research,77,26-36.
49. Schumacker, R. E.,Lomax, R. G.(2015).A beginner's guide to structural equation modeling.London:Routledge.
50. Shaffer, D. R.,Kipp, K.(2014).Developmental psychology: Childhood and adolescence.Belmont, CA:Wadsworth Cengage Learning.
51. Shavelson, R. J.,Hubner, J. J.,Stanton, G. C.(1976).Self-concept: Validation of construct interpretations.Review of Educational Research,46(3),407-441.
52. Shen, C.(2005).How American middle schools differ from schools of five Asian countries: Based on cross-national data from TIMSS 1999.Educational Research and Evaluation,11(2),179-199.
53. Sirin, S. R.(2005).Socioeconomic status and academic achievement: A meta-analytic review of research.Review of Educational Research,75(3),417-453.
54. Skaalvik, E. M.,Valås, H.(1999).Relations among achievement, self-concept, and motivation in mathematics and language arts: A longitudinal study.The Journal of Experimental Education,67(2),135-149.
55. Wu, P.-C.,Kung, H.-Y.,Wey, S.-C.(2008).Construct validation of the Chinese version of self-description questionnaire.the 47th Taiwanese Psychological Association Meeting,Taipei, Taiwan:
56. 余民寧(2006)。潛在變項模式：SIMPLIS的應用。臺北市:高等教育文化。
57. 邱嘉品(2016)。縮小城鄉教育差距之建議與成功案例。臺灣教育評論月刊，5(2)，38-42。
58. 張芳全(2008)。數學成就的城鄉差距探討：以TIMSS 2003為例。國民教育，48(6)，22-29。
59. 張美瑤(2009)。多元文化教育改革之省思。正修通識教育學報，6，321-340。
60. 莊勝義(2009)。從多元文化觀點省思「弱勢者」的教育「問題」與「對策」。教育與多元文化研究，12(1)，17-56。
61. 陳吉仲、郭曉怡、李佩倫(2007)。影響國中基本學力測驗分數的因素之分析。教育政策論壇，10(4)，119-142。
62. 黃志偉(2002)。多元文化對數學課程的衝擊─民族數學的剝奪與回歸。師友，415，38-41。

1. 陳麒,高台茜(2019)。翻轉教學應用於偏鄉網路課輔國小高年級數學之成效。當代教育研究季刊，27(2)，1-37。
2. 龔心怡,孫俊傑,李靜儀(2023)。包容性評鑑取向運用於偏鄉國民中學學習扶助方案之探究。教育科學研究期刊，68(3)，141-178。
3. 郭文金,徐偉民(2023)。國小學生「數學心向量表」之發展。測驗學刊，70(1)，1-32。
4. 劉玉玲,沈淑芬(2019)。國中生數學自我概念、數學學習策略與數學學業成就之模式建構。課程與教學，22(3)，187-214。
5. 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。
6. 張凌嘉(2021)。學習興趣和自信對中年級學生數學成就成長率的影響。臺灣數學教育期刊，8(2)，77-106。
7. 趙珮晴,曾建銘,曾招文(2020)。小六數學素養表現分析之研究。測驗學刊，67(4)，333-353。