Math self-concept, grades, and achievement test scores: Long-term reciprocal effects across five waves and three achievement tracks

Journal of Educational Psychology

Volumn 109, Issue 5, 2017, Pages 621-634

  Katrin, Arens ^a   Marsh, Herbert W ^b,c   Pekrun, Reinhard ^b,d   Lichtenfeld, Stephanie ^d   Murayama, Kou ^e,f   Vom Hofe, Rudolf ^g  

^a GERMAN INSTITUTE FOR INTERNATIONAL EDUCATIONAL RESEARCH   (Germany)

^b AUSTRALIAN CATHOLIC UNIVERSITY   (Australia)

^c UNIVERSITY OF OXFORD   (United Kingdom)

^d UNIVERSITY OF MUNICH   (Germany)

^e UNIVERSITY OF READING   (United Kingdom)

^f KOCHI UNIVERSITY OF TECHNOLOGY   (Japan)

^g BIELEFELD UNIVERSITY   (Germany)

Author keywords

Math achievement; Math self concept; Reciprocal effects; School tracks

Indexed keywords

EID: 85001122928     PISSN: 00220663     EISSN: 19392176     Source Type: Journal    
DOI: 10.1037/edu0000163     Document Type: Article

References (108)

1. Arens, A. K., Marsh, H. W., Craven, R. G., Yeung, A. S., Randhawa, E., Hasselhorn, M. (2016). Math self-concept in preschool children: Structure, achievement relations, and generalizability across gender. Early Childhood Research Quarterly, 36, 391-403. http://dx.doi.org/10 .1016/j.ecresq.2015.12.024
2. Arens, A. K., Yeung, A. S., Craven, R. G., Hasselhorn, M. (2011). The twofold multidimensionality of academic self-concept: Domain specificity and separation between competence and affect components. Journal of Educational Psychology, 103, 970-981. http://dx.doi.org/10 .1037/a0025047
3. Baumert, J., Watermann, R., Schümer, G. (2003). Disparitäten der Bildungsbeteiligung und des Kompetenzerwerbs: Ein institutionelles und individuelles Mediationsmodell [Disparity of educational participation and acquisition of skills: An institutional and individual model of mediation]. Zeitschrift für Erziehungswissenschaft, 6, 46-71. http://dx .doi.org/10.1007/s11618-003-0004-7
4. Becker, M., Lüdtke, O., Trautwein, U., Baumert, J. (2006). Leistungszuwachs in Mathematik: Evidenz für einen Schereneffekt im mehrgliedrigen Schulsystem? [Achievement gains in mathematics: Evidence for differential trajectories in a tracked school system]. Zeitschrift fur Padagogische Psychologie, 20, 233-242. http://dx.doi.org/10.1024/ 1010-0652.20.4.233
5. Bergan, J. R. (2013). Rasch versus Birnbaum: New arguments in an old debate. Tucson, AZ: Assessment Technology.
6. Bradley, R. H., Corwyn, R. F. (2002). Socioeconomic status and child development. Annual Review of Psychology, 53, 371-399. http://dx.doi .org/10.1146/annurev.psych.53.100901.135233
7. Brookhart, S. (1993). Teachers' grading practices: Meaning and values. Journal of Educational Measurement, 30, 123-142. http://dx.doi.org/10.1111/j.1745-3984.1993.tb01070.x
8. Browne, M. W., Cudeck, R. (1993). Alternative ways of assessing model fit. In K. A. Bollen J. S. Long (Eds.), Testing structural equation models (pp. 136-162). Newbury Park, CA: SAGE.
9. Brunner, M., Krauss, S., Kunter, M. (2008). Gender differences in mathematics: Does the story need to be rewritten? Intelligence, 36, 403-421. http://dx.doi.org/10.1016/j.intell.2007.11.002
10. 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, 136 -145. http://dx.doi.org/10.1037/0022-0663.69.2.136
11. Chapman, J. W., Tunmer, W. E. (1997). A longitudinal study of beginning reading achievement and reading self-concept. The British Journal of Educational Psychology, 67, 279-291. http://dx.doi.org/10.1111/j.2044-8279.1997.tb01244.x
12. Chen, F. F. (2007). Sensitivity of goodness of fit indices to lack of measurement invariance. Structural Equation Modeling, 14, 464-504. http://dx.doi.org/10.1080/10705510701301834
13. Chen, S.-K., Yeh, Y.-C., Hwang, F.-M., Lin, S. S. J. (2013). The relationship between academic self-concept and achievement: A multicohort-multioccasion study. Learning and Individual Differences, 23, 172-178. http://dx.doi.org/10.1016/j.lindif.2012.07.021
14. Cheung, G. W., Rensvold, R. B. (2002). Evaluating goodness-of-fit indexes for testing measurement invariance. Structural Equation Modeling, 9, 233-255. http://dx.doi.org/10.1207/S15328007SEM0902_5
15. Chmielewski, A. K., Dumont, H., Trautwein, U. (2013). Tracking effects depend on tracking type: An international comparison of students' mathematics self-concept. American Educational Research Journal, 50, 925-957. http://dx.doi.org/10.3102/0002831213489843
16. Craven, R. G., Marsh, H. W., Burnett, P. (2003). Cracking the selfconcept enhancement conundrum. A call and blueprint for the next generation of self-concept enhancement research. In H. W. Marsh, R. G. Craven, D. M. McInerney (Eds.), International advances in self research: Speaking to the future (pp. 91-126). Greenwich, CT: Information Age.
17. Curran, P. J., Bollen, K. A. (2001). The best of both worlds: Combining autoregressive and latent curve models. In L. M. Collins A. G. Sayer (Eds.), New methods for the analysis of change (pp. 105-136). Washington, DC: American Psychological Association. http://dx.doi.org/10 .1037/10409-004
18. De Fraine, B., Van Damme, J., Onghena, P. (2007). A longitudinal analysis of gender differences in academic self- concept and language achievement: A multivariate multilevel latent growth approach. Contemporary Educational Psychology, 32, 132-150. http://dx.doi.org/10.1016/ j.cedpsych.2006.10.005
19. Diamantopoulos, A., Siguaw, J. A. (2000). Introducing LISREL. London, UK: SAGE. http://dx.doi.org/10.4135/9781849209359
20. Enders, C. K. (2010). Applied missing data analysis. New York, NY: Guilford Press.
21. Erikson, R., Goldthorpe, J. H., Portocarero, L. (1979). Intergenerational class mobility in three Western European societies. The British Journal of Sociology, 30, 415-441. http://dx.doi.org/10.2307/589632
22. Fredricks, J. A., Eccles, J. S. (2002). Children's competence and value beliefs from childhood through adolescence: Growth trajectories in two male-sex-typed domains. Developmental Psychology, 38, 519-533. http://dx.doi.org/10.1037/0012-1649.38.4.519
23. Fredricks, J. A., Eccles, J. S. (2002). Children's competence and value beliefs from childhood through adolescence: Growth trajectories in two male-sex-typed domains. Developmental Psychology, 38, 519-533. http://dx.doi.org/10.1037/0012-1649.38.4.519
24. Frenzel, A. C., Goetz, T., Lüdtke, O., Pekrun, R., Sutton, R. (2009). Emotional transmission in the classroom: Exploring the relationship between teacher and student enjoyment. Journal of Educational Psychology, 101, 705-716. http://dx.doi.org/10.1037/a0014695
25. Frenzel, A. C., Pekrun, R., Dicke, A. L., Goetz, T. (2012). Beyond quantitative decline: Conceptual shifts in adolescents' development of interest in mathematics. Developmental Psychology, 48, 1069-1082. http://dx.doi.org/10.1037/a0026895
26. Frey, M. C., Detterman, D. K. (2004). Scholastic Assessment or g? The relationship between the Scholastic Assessment Test and general cognitive ability. Psychological Science, 15, 373-378. http://dx.doi.org/10.1111/j.0956-7976.2004.00687.x
27. Furnham, A., Monsen, J. (2009). Personality traits and intelligence predict academic school grades. Learning and Individual Differences, 19, 28-33. http://dx.doi.org/10.1016/j.lindif.2008.02.001
28. Graham, J. W. (2009). Missing data analysis: Making it work in the real world. Annual Review of Psychology, 60, 549-576. http://dx.doi.org/10.1146/annurev.psych.58.110405.085530
29. Guay, F., Marsh, H. W., Boivin, M. (2003). Academic self-concept and academic achievement: A developmental perspective on their causal ordering. Journal of Educational Psychology, 95, 124-136. http://dx.doi.org/10.1037/0022-0663.95.1.124
30. Hamaker, E. L., Kuiper, R. M., Grasman, R. P. P. P. (2015). A critique of the cross-lagged panel model. Psychological Methods, 20, 102-116. http://dx.doi.org/10.1037/a0038889
31. Hanushek, E., Wößmann, L. (2006). Does educational tracking affect performance and inequality? Differences-in-differences evidence across countries. The Economic Journal, 116, 63-76. http://dx.doi.org/10.1111/j.1468-0297.2006.01076.x
32. Heller, K. A., Perleth, C. (2000). Kognitiver Fähigkeitstest für 4. bis 12. Klassen, Revision. Göttingen, the Netherlands: Beltz Test GmbH.
33. Helmke, A., van Aken, M. A. G. (1995). The causal ordering of academic achievement and self-concept of ability during elementary school: A longitudinal study. Journal of Educational Psychology, 87, 624-637. http://dx.doi.org/10.1037/0022-0663.87.4.624
34. Hox, J. J., Maas, C. J. M., Brinkhuis, M. J. S. (2010). The effect of estimation method and sample size in multilevel structural equation modeling. Statistica Neerlandica, 64, 157-170. http://dx.doi.org/10.1111/j.1467-9574.2009.00445.x
35. Hu, L., Bentler, P. M. (1999). Cutoff criteria for fit indexes in covariance structure analysis: Conventional criteria versus new alternatives. Structural Equation Modeling, 6, 1-55. http://dx.doi.org/10.1080/1070551 9909540118
36. Huang, C. (2011). Self-concept and academic achievement: A metaanalysis of longitudinal relations. Journal of School Psychology, 49, 505-528. http://dx.doi.org/10.1016/j.jsp.2011.07.001
37. Hyde, J. S., Fennema, E., Lamon, S. J. (1990). Gender differences in mathematics performance: A meta-analysis. Psychological Bulletin, 107, 139-155. http://dx.doi.org/10.1037/0033-2909.107.2.139
38. Jacobs, J. E., Lanza, S., Osgood, D. W., Eccles, J. S., Wigfield, A. (2002). Changes in children's self-competence and values: Gender and domain differences across grades one through twelve. Child Development, 73, 509-527. http://dx.doi.org/10.1111/1467-8624.00421
39. Jelicíc, H., Phelps, E., Lerner, R. M. (2009). Use of missing data methods in longitudinal studies: The persistence of bad practices in developmental psychology. Developmental Psychology, 45, 1195-1199. http://dx.doi.org/10.1037/a0015665
40. Kenny, D. A. (1975). Cross-lagged panel correlation: A test for spuriousness. Psychological Bulletin, 82, 887-903. http://dx.doi.org/10.1037/ 0033-2909.82.6.887
41. Klieme, E., Rakoczy, K. (2003). Unterrichtsqualität aus Schülerperspektive: Kulturspezifische Profile, regionale Unterschiede und Zusammenhänge mit Effekten von Unterricht. In J. Baumert, C. Artelt, E. Klieme, J. Neubrand, M. Prenzel, U. Schiefele, K.-J. Tillmann (Eds.), PISA
42. Ein differenzierter Blick auf die Länder der Bundesrepublik Deutschland (pp. 334-359). Opladen, Germany: Leske + Budrich.
43. Köller, O., Baumert, J. (2001). Leistungsgruppierungen in der sekundarstufe I. Ihre konsequenzen für die mathematikleistung und das mathematische selbstkonzept der begabung [Ability grouping at secondary level 1: Consequences for mathematics achievement and the selfconcept of mathematical ability]. Zeitschrift fur Padagogische Psychologie, 15, 99-110.
44. Kunter, M., Brunner, M., Baumert, J., Klusmann, U., Krauss, S., Blum, W., Neubrand, M. (2005). Der Mathematikunterricht der PISASchülerinnen und -Schüler. Schulformunterschiede in der Unterrichtsqualität [Quality of mathematics instruction across school types: Findings from PISA 2003]. Zeitschrift für Erziehungswissenschaft, 4, 502-520. http://dx.doi.org/10.1007/s11618-005-0156-8
45. Leahey, E., Guo, G. (2001). Gender differences in mathematical trajectories. Social Forces, 80, 713-732. http://dx.doi.org/10.1353/sof.2001 .0102
46. LeTendre, G. K., Hofer, B. K., Shimizu, H. (2003). What is tracking? Cultural expectations in the United States, Germany, and Japan. American Educational Research Journal, 40, 43-89. http://dx.doi.org/10 .3102/00028312040001043
47. Lietz, P. (2006). A meta-analysis of gender differences in reading achievement at the secondary school level. Studies in Educational Evaluation, 32, 317-344. http://dx.doi.org/10.1016/j.stueduc.2006.10.002
48. Lindberg, S. M., Hyde, J. S., Petersen, J. L., Linn, M. C. (2010). New trends in gender and mathematics performance: A meta-analysis. Psychological Bulletin, 136, 1123-1135. http://dx.doi.org/10.1037/ a0021276
49. Little, R., Rubin, D. (2002). Statistical analysis with missing data. New York, NY: Wiley. http://dx.doi.org/10.1002/9781119013563
50. Liu, X. (2010). Using and developing measurement instruments in science education: A Rasch modeling approach. Charlotte, NC: Information Age Publishing.
51. Marsh, H. W. (1990). The causal ordering of academic self-concept and academic achievement: A multiwave, longitudinal panel analysis. Journal of Educational Psychology, 82, 646-656. http://dx.doi.org/10.1037/ 0022-0663.82.4.646
52. Marsh, H. W. (2007). Self-concept theory, measurement and research into practice: The role of self-concept in educational psychology. Leicester, UK: British Psychological Society.
53. Marsh, H. W., Abduljabbar, A. S., Abu-Hilal, M., Morin, A. J. S., Abdelfattah, F., Leung, K. C., Parker, P. (2013). Factor structure, discriminant and convergent validity of TIMSS math and science motivation measures: A comparison of USA and Saudi Arabia. Journal of Educational Psychology, 105, 108-128. http://dx.doi.org/10.1037/a0029907
54. Marsh, H. W., Byrne, B. M., Yeung, A. S. (1999). Causal ordering of academic self-concept and achievement: Reanalysis of a pioneering study and revised recommendations. Educational Psychologist, 34, 155-167. http://dx.doi.org/10.1207/s15326985ep3403_2
55. 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, 133-163. http://dx.doi.org/10.1111/j.1745-6916.2006.00010.x
56. Marsh, H. W., Craven, R. G., Parada, R. H., Guo, J., Dicke, T., Abduljabbar, A. S. (2016). Temporal ordering effects of adolescent depression, relational aggression and victimization over six waves: Fully latent teciprocal rffects models. Developmental Psychology. Advance online publication. http://dx.doi.org/10.1037/dev0000241
57. Marsh, H. W., Dowson, M., Pietsch, J., Walker, R. (2004). Why multicollinearity matters: A reexamination of relations between selfefficacy, self-concept, and achievement. Journal of Educational Psychology, 96, 518-522. http://dx.doi.org/10.1037/0022-0663.96.3.518
58. Marsh, H. W., Gerlach, E., Trautwein, U., Lüdtke, O., Brettschneider, W.-D. (2007). Longitudinal study of preadolescent sport self-concept and performance: Reciprocal effects and causal ordering. Child Development, 78, 1640 -1656. http://dx.doi.org/10.1111/j.1467-8624.2007.01094.x
59. Marsh, H. W., Hau, K.-T. (1996). Assessing goodness of fit: Is parsimony always desirable? Journal of Experimental Education, 64, 364-400. http://dx.doi.org/10.1080/00220973.1996.10806604
60. Marsh, H. W., Hau, K.-T., Grayson, D. (2005). Goodness of fit evaluation in structural equation modeling. In A. Maydeu-Olivares J. McArdle (Eds.), Contemporary psychometrics. A Festschrift for Roderick P. McDonald. Mahwah, NJ: Lawrence Erlbaum.
61. Marsh, H. W., Hau, K.-T., Kong, K. W. (2002). Multilevel causal ordering or academic self-concept and achievement: Influence of language of instruction (English vs. Chinese) for Hong Kong students. American Educational Research Journal, 39, 727-763. http://dx.doi.org/10.3102/00028312039003727
62. Marsh, H. W., Hau, K.-T., Wen, Z. (2004). In search of golden rules: Comment on hypothesis-testing approaches to cutoff values for fit indexes and dangers in overgeneralizing Hu Bentler's (1999). Structural Equation Modeling, 11, 320 -341. http://dx.doi.org/10.1207/s15328007sem1103_2
63. Marsh, H. W., Kuyper, H., Seaton, M., Parker, P. D., Morin, A. J. S., Möller, J., Abduljabbar, A. S. (2014). Dimensional comparison theory: An extension of the internal/external frame of reference effect on academic self-concept formation. Contemporary Educational Psychology, 39, 326-341. http://dx.doi.org/10.1016/j.cedpsych.2014.08.003
64. Marsh, H. W., O'Mara, A. (2008a). Reciprocal effects between academic self-concept, self-esteem, achievement, and attainment over seven adolescent years: Unidimensional and multidimensional perspectives of self-concept. Personality and Social Psychology Bulletin, 34, 542-552. http://dx.doi.org/10.1177/0146167207312313
65. Marsh, H. W., O'Mara, A. J. (2008b). Self-concept is as multidisciplinary as it is multidimensional. In H. W. Marsh, R. G. Craven, D. M. McInerney (Eds.), Self-processes, learning, and enabling human potential. Dynamic new approaches (pp. 87-115). Charlotte, NC: InformationAge.
66. Marsh, H. W., Pekrun, R., Lichtenfeld, S., Guo, J., Arens, A. K., Murayama, K. (2016). Breaking the double-edged sword of effort/trying hard: Developmental equilibrium and longitudinal relations among effort, achievement, and academic self-concept. Developmental Psychology, 52, 1273-1290. http://dx.doi.org/10.1037/dev0000146
67. Marsh, H. W., Pekrun, R., Parker, P. D., Murayama, K., Guo, J., Dicke, T., Lichtenfeld, S. (2016). Long-term positive effects of repeating a year in school: Six-year longitudinal study of self-beliefs, anxiety, social relations, school grades, and test scores. Journal of Educational Psychology. Advance online publication. http://dx.doi.org/10.1037/edu0000144
68. Marsh, H. W., Trautwein, U., Lüdtke, O., Köller, O., Baumert, J. (2005). Academic self-concept, interest, grades, and standardized test scores: Reciprocal effects models of causal ordering. Child Development, 76, 397-416. http://dx.doi.org/10.1111/j.1467-8624.2005.00853.x
69. Marsh, H. W., Yeung, A. S. (1998). Longitudinal structural equation models of academic self-concept and achievement: Gender differences in the development of math and English constructs. American Educational Research Journal, 35, 705-738. http://dx.doi.org/10.3102/00028312035004705
70. Marshall, S. L., Parker, P. D., Ciarrochi, J., Heaven, P. C. L. (2014). Is self-esteem a cause or consequence of social support? A 4-year longitudinal study. Child Development, 85, 1275-1291. http://dx.doi.org/10.1111/cdev.12176
71. Matteucci, M., Mignani, S. (2011). Gender differences in performance in mathematics at the end of lower secondary school in Italy. Learning and Individual Differences, 21, 543-548. http://dx.doi.org/10.1016/j.lindif.2011.03.001
72. McMillan, J. H., Myran, S., Workman, D. (2002). Elementary teachers' classroom assessment and grading practices. The Journal of Educational Research, 95, 203-213. http://dx.doi.org/10.1080/00220670209596593
73. Millsap, R. E. (2011). Statistical approaches to measurement invariance. New York, NY: Routledge.
74. Möller, J., Pohlmann, B., Köller, O., Marsh, H. W. (2009). Meta-analytic path analysis of the internal/external frame of reference model of academic achievement and academic self-concept. Review of Educational Research, 79, 1129 -1167. http://dx.doi.org/10.3102/0034654309337522
75. Möller, J., Retelsdorf, J., Köller, O., Marsh, H. W. (2011). The reciprocal internal/external frame of reference model: An integration of models of relations between academic achievement and self-concept. American Educational Research Journal, 48, 1315-1346. http://dx.doi.org/10.3102/0002831211419649
76. Möller, J., Zimmermann, F., Köller, O. (2014). The reciprocal internal/ external frame of reference model using grades and test scores. The British Journal of Educational Psychology, 84, 591-611. http://dx.doi.org/10.1111/bjep.12047
77. Mullis, I. V. S., Martin, M. O., Kennedy, A. M., Foy, P. (2007). PIRLS international report: IEA's progress in international reading literacy study in primary schools in 40 countries. Chestnut Hill, MA: Boston College.
78. Murayama, K., Pekrun, R., Lichtenfeld, S., Vom Hofe, R. (2013). Predicting long-term growth in students' mathematics achievement: The unique contributions of motivation and cognitive strategies. Child Development, 84, 1475-1490. http://dx.doi.org/10.1111/cdev.12036
79. Murayama, K., Pekrun, R., Suzuki, M., Marsh, H. W., Lichtenfeld, S. (2016). Don't aim too high for your kids: Parental over-aspiration undermines students' learning in mathematics. Journal of Personality and Social Psychology, 111, 766 -779. http://dx.doi.org/10.1037/pspp0000079
80. Muthén, B., Satorra, A. (1995). Complex sample data in structural equation modeling. In P. V. Marsden (Ed.), Sociological methodology (pp. 267-316). Washington, DC: American Sociological Association. http://dx.doi.org/10.2307/271070
81. Muthén, L. K., Muthén, B. O. (1998 -2015). Mplus user's guide (7th ed.). Los Angeles, CA: Author.
82. Nguyen, H. H., Ryan, A. M. (2008). Does stereotype threat affect test performance of minorities and women? A meta-analysis of experimental evidence. Journal of Applied Psychology, 93, 1314-1334. http://dx.doi .org/10.1037/a0012702
83. Niepel, C., Brunner, M., Preckel, F. (2014). The longitudinal interplay of students' academic self-concepts and achievements within and across domains: Replicating and extending the reciprocal internal/external frame of reference model. Journal of Educational Psychology, 106, 1170-1191. http://dx.doi.org/10.1037/a0036307
84. Nowell, A., Hedges, L. V. (1998). Trends in gender differences in academic achievement from 1960 to 1994: An analysis of differences in mean, variance, and extreme scores. Sex Roles, 39, 21-43. http://dx.doi .org/10.1023/A:1018873615316
85. O'Mara, A. J., Marsh, H. W., Craven, R. G., Debus, R. L. (2006). Do self-concept interventions make a difference? A synergistic blend of construct validation and meta-analysis. Educational Psychologist, 41, 181-206. http://dx.doi.org/10.1207/s15326985ep4103_4
86. Pekrun, R. (2006). The control-value theory of achievement emotions: Assumptions, corollaries, and implications for educational research and practice. Educational Psychology Review, 18, 315-341. http://dx.doi .org/10.1007/s10648-006-9029-9
87. Pekrun, R., Lichtenfeld, S., Marsh, H. W., Murayama, K., Goetz, T. (in press). Achievement emotions and academic performance: Longitudinal models of reciprocal effects. Child Development.
88. Pekrun, R., vom Hofe, R., Blum, W., Frenzel, A. C., Goetz, T., Wartha, S. (2007). Development of mathematical competencies in adolescence: The PALMA longitudinal study. In M. Prenzel (Ed.), Studies on the educational quality of schools (pp. 17-37). Münster, Germany: Waxmann.
89. Raykov, T. (2009). Evaluation of scale reliability for unidimensional measures using latent variable modeling. Measurement Evaluation in Counseling Development, 42, 223-232. http://dx.doi.org/10.1177/0748175609344096
90. Retelsdorf, J., Köller, O., Möller, J. (2014). Reading achievement and reading self-concept. Testing the reciprocal effects model. Learning and Instruction, 29, 21-30. http://dx.doi.org/10.1016/j.learninstruc.2013.07.004
91. Seaton, M., Parker, P., Marsh, H. W., Craven, R. G., Yeung, A. S. (2014). The reciprocal relations between self-concept, motivation and achievement: Juxtaposing academic self-concept and achievement goal orientations for mathematics success. Educational Psychology, 34, 49-72. http://dx.doi.org/10.1080/01443410.2013.825232
92. Shavelson, R. J., Hubner, J. J., Stanton, G. C. (1976). Self-concept: Validation of construct interpretations. Review of Educational Research, 46, 407-441. http://dx.doi.org/10.3102/00346543046003407
93. Sirin, S. R. (2005). Socioeconomic status and academic achievement: A meta-analytic review of research. Review of Educational Research, 75, 417-453. http://dx.doi.org/10.3102/00346543075003417
94. Skaalvik, S., Skaalvik, E. M. (2004). Gender differences in math and verbal self-concept, performance expectations, and motivation. Sex Roles, 50, 241-252. http://dx.doi.org/10.1023/B:SERS.0000015555.40976.e6
95. Spinath, F. M., Spinath, B., Plomin, R. (2008). The nature and nurture of intelligence and motivation in the origins of sex differences in elementary school achievement. European Journal of Personality, 22, 211-229. http://dx.doi.org/10.1002/per.677
96. Steele, C. M. (1997). A threat in the air. How stereotypes shape intellectual identity and performance. American Psychologist, 52, 613-629. http://dx.doi.org/10.1037/0003-066X.52.6.613
97. Trautwein, U., Lüdtke, O., Schnyder, I., Niggli, A. (2006). Predicting homework effort: Support for a domain-specific, multilevel homework model. Journal of Educational Psychology, 98, 438-456. http://dx.doi.org/10.1037/0022-0663.98.2.438
98. Valentine, J. C., DuBois, D. L., Cooper, H. (2004). The relation between self-beliefs and academic achievement: A meta-analytic review. Educational Psychologist, 39, 111-131. http://dx.doi.org/10.1207/s15326985ep3902_3
99. Van de Gaer, E., Pustjens, H., Van Damme, J., De Munter, A. (2008). Mathematics participation and mathematics achievement across secondary school: The role of gender. Sex Roles, 59, 568-585.
100. Vom Hofe, R., Kleine, M., Blum, W., Pekrun, R. (2005). On the role of "Grundvorstellungen" for the development of mathematical literacy. First results of the longitudinal study PALMA. Mediterranean Journal for Research in Mathematics Education, 4, 67-84.
101. Vom Hofe, R., Pekrun, R., Kleine, M., Götz, T. (2002). Projekt zur Analyse der Leistungsentwicklung in Mathematik (PALMA): Konstruktion des Regensburger Mathematikleistungstests für 5.-10. Klassen [Project for the Analysis of Learning and Achievement in Mathematics (PALMA): Development of the Regensburg Mathematics Achievement Test for grades 5 to 10]. Zeitschrift fur Padagogik, 45, 83-100.
102. Wang, J., Wang, X. (2012). Structural equation modeling: Applications using Mplus. Chichester, UK: Wiley. http://dx.doi.org/10.1002/9781118356258
103. Watt, H. M. G. (2004). Development of adolescents' self-perceptions, values, and task perceptions according to gender and domain in 7ththrough 11th-grade Australian students. Child Development, 75, 1556-1574. http://dx.doi.org/10.1111/j.1467-8624.2004.00757.x
104. Widaman, K. F., Ferrer, E., Conger, R. D. (2010). Factorial invariance within longitudinal structural equation models: Measuring the same construct across time. Child Development Perspectives, 4, 10-18. http:// dx.doi.org/10.1111/j.1750-8606.2009.00110.x
105. Wigfield, A., Karpathian, M. (1991). Who am I and what can I do? Children's self- concepts and motivation in achievement solutions. Educational Psychologist, 26, 223-261. http://dx.doi.org/10.1080/ 00461520.1991.9653134
106. Wright, B. D. (1999). Fundamental measurement for psychology. In S. E. Embretson S. I. Hershberger (Eds.), The new rules of measurement: What every educator and psychologist should know. Hillsdale, NJ: Lawrence Erbaum.
107. Wu, M. L., Adams, R. J., Wilson, M. R., Haldane, S. A. (2007). ACERConQuest Version 2: Generalised item response modelling software. Camberwell, Australia: Australian Council for Educational Research.
108. Zimmermann, F., Schütte, K., Taskinen, P., Köller, O. (2013). Reciprocal effects between adolescent externalizing problems and measures of achievement. Journal of Educational Psychology, 105, 747-761. http://dx.doi.org/10.1037/a0032793