The Influence of Proof Understanding Strategies and Negative Self-concept on Undergraduate Afghan Students’ Achievement in Modern Algebra

• Autores: Ahmad S. Khalil, Naiqing Song, Yang Xinrong, Pei Changgen
• Localización: International Electronic Journal of Mathematics Education, ISSN-e 1306-3030, Vol. 15, Nº. 1, 2020
• Idioma: inglés
• Enlaces
  • Texto completo (pdf)
• Resumen

  • This study explored the influence of proof understanding strategies and negative self-concept on undergraduate Afghan students’ achievement in modern algebra1. To examine the relationships among proof understanding strategies, negative self-concept and achievement in modern algebra1, we used structural equation modeling on data collected from three classes of students taking modern algebra in two consecutive years of 2016 and 2017. Participants of this study included 139 sophomore Afghan students, 40.29% male and 59.71% female. Conducting SEM analysis resulted the following findings: firstly, negative self-concept had significant negative influence over students’ achievement in modern algebra1; secondly, proof understanding strategies had significant positive influence over students’ achievement in modern algebra1; thirdly, negative self-concept had significant negative influence over proof understanding strategies; finally, the data fitted very well the SEM model, implying that proof understanding strategies and negative self-concept significantly influence students’ achievement in modern algebra1.

• Referencias bibliográficas
  • Alcock, L. (2009). E-proofs: Students experience of online resources to aid understanding of mathematical proofs. In Proceedings of the 12th...
  • Alcock, L., & Weber, K. (2005). Proof validation in real analysis: inferring and evaluating warrants. Journal of Mathematical Behavior,...
  • Browne, M. W., & Cudeck, R. (1993). Alternative ways of assessing model fit. In K. A. Bollen, & J. S. Long (Eds.), Testing structural...
  • Byrne, B. M. (1996). Academic self-concept: Its structure, measurement, and relation to academic achievement. In B. A. Bracken (Ed.), Handbook...
  • Casey, M. B., Nuttall, R. L., & Pezaris, E. (2001). Spatial-mechanical reasoning skills versus mathematics self-confidence as mediators...
  • Chapman, J. W. (1988). Learning disabled children self-concept. Review of Educational Research, 58(3), 347-371. https://doi.org/10.3102/00346543058003347
  • Conradie, J., & Frith, J. (2000). Comprehension tests in mathematics. Educational Studies in Mathematics, 42(3), 225-235. https://doi.org/10.1023/A:1017502919000
  • Cronbach, L. J. (1951) Coefficient alpha and the internal structure of tests. Psychometrika, 16(3), 297-334. https://doi.org/10.1007/BF02310555
  • Curran, P. J., West, S. G., & Finch, J. F. (1996). The robustness of test statistics to nonnormality and specification error in confirmatory...
  • Davis, P. J, & Hersh, R. (1981). The mathematical experience. New York: Viking Penguin Inc. https://doi.org/10.1007/BF01967935
  • Dreyfus, T. (1991). Advanced mathematical thinking processes. In D. Tall (Eds.), Advanced Mathematical Thinking (pp. 25-41). Dordrecht: Kluwer....
  • Ercikan, L., McCreith, T., & Lapointe, V. (2005). Factors associated with mathematics achievement and participation in advanced mathematics...
  • Hair, J. H., Tatham, R. L., & Anderson, R. E. (1998). Multivariate Data Analysis. NY: Prentice Hall International.
  • Hair, J., Black, W., Babin, B., & Anderson, R. (2010). Multivariate Data Analysis (7th ed). New Jersey: Prentice-Hall. https://doi.org/10.1016/j.jmva.2009.12.014
  • Harel, G., & Sowder, L., (1998). Students’ proof schemes: Results from exploratory studies. In A. Schoenfeld, J. Kaput, & E. Dubinsky...
  • Healy, L., & Hoyles, C. (2000). A study of proof conceptions in algebra. Journal for Research in Mathematics Education, 31, 398-428. https://doi.org/10.2307/749651
  • Hox, J. J., & Bechger, T. M. (1995). An introduction to structural equation modeling. Family Science Review, 2, 354-373. https://doi.org/10.1080/10705519509539996
  • Ignacio, N. G., Nieto, L. J. B., & Barona, E. G. (2006). The affective domain in mathematics learning. International Journal of Mathematic...
  • Inglis, M., Alcock, L. (2012). Expert and novice approaches to reading mathematical proofs. Journal for Research in Mathematics Education,...
  • Jöreskog, K. G., & Sorbom, D. (1993). LISREL 8: Structural equation modeling with the SIMPLIS command language. Chicago, IL: Scientific...
  • Ko, Y., & Knuth, E. (2012). Validating proofs and counterexamples across domains: practices of importance for mathematics majors. Journal...
  • Kung, H.-Y. (2009). Perception or confidence? Self-concept, self-efficacy and achievement in mathematics: A longitudinal study. Policy Futures...
  • Mardia, K. V. (1970). Measures of multivariate skewness and kurtosis with applications. Biometrika, 57, 519-530. https://doi.org/10.1093/biomet/57.3.519
  • Marsh, H. W. (1993). Academic self-concept: Theory measurement and research. In J. Suls (Ed.), Psychological perspectives on the self (pp....
  • Marsh, H. W., & Yeung, A. S. (1997). Causal effects of academic self-concept on academic achievement: Structural equation models of longitudinal...
  • Marsh, H. W., Trautwein, U., Lüdtke, O., Köller, O., & Baumert, J. (2005). Academic self-concept, interest, grades, and standardized test...
  • Martin, W. G., & Harel, G. (1989). Proof frames of pre-service elementary teachers. Journal for Research in Mathematics Education, 20(1),...
  • McDonald, R. P., & Ho, M. R. (2002). Principles and practices in reporting structural equation analysis. Psychological Methods, 7(1),...
  • McLeod, D. B. (1992). Research on affect and mathematics learning in the JRME: 1970 to the present. Journal for Research in Mathematics Education,...
  • Mejia-Ramos, J. P., Fuller, E., Weber, K., Rhoads, K., & Samkoff, A. (2012). An assessment model for proof comprehension in undergraduate...
  • Möller, J., Streblow, L., & Pohlmann, B. (2009). Achievement and self-concept of students with learning disabilities. Social Psychological...
  • Porteous, K. (1986). Children’s appreciation of the significance of proof. In Proceedings of the Tenth International Conference for the Psychology...
  • Raykov, T., & Marcoulides, G. A. (2008). An Introduction to Applied Multivariate Analysis. New York: Taylor and Francis.
  • Ross, J. A., Scott, G., & Bruce, C. D. (2012). The gender confidence gap in fractions knowledge: Gender differences in student belief-achievement...
  • Rowland, T. (2001). Generic proofs in number theory. In S. Campbell & R. Zazkis (Eds.), Learning and teaching number theory: Research...
  • Sarouphim, K. M., & Chartouny, M. (2017). Mathematics education in Lebanon: Gender differences in attitudes and achievement. Education...
  • Schumacker, R. E., & Lomax, R. G. (2015). A beginner’s guide to structural equation modeling (4th ed.). Mahwah, NJ: Lawrence Erlbaum Associates.
  • Selden, A. (2012). Transitions and proof and proving at the tertiary level. In G. Hanna & M. de Villiers (Eds.), Proof and proving in...
  • Selden, A., & Selden, J. (2003). Validations of proofs considered as texts: can undergraduates tell whether an argument proves a theorem?...
  • Skaalvik, E. M., & Valås, H. (1999). Relations among achievement, self-concept, and motivation in mathematics and language arts: A longitudinal...
  • Tabachnick, B. G., & Fidell, L. S. (2007). Using Multivariate Statistics (5th ed). Boston: Pearson Education. Tall, D. (2013). How humans...
  • Temel, S., Sen, S., & Yilmaz, A. (2015). Validity and reliability analysis for chemistry self-concept inventory. Journal of Baltic Science...
  • Wang, J. (2007). A trend study of self-concept and mathematics achievement in a cross-cultural context. Mathematics Education Research Journal,...
  • Weber, K. (2015). Effective proof reading strategies for comprehending mathematical proofs. International Journal of Research in Undergraduate...
  • Yilmaz, V., Celik, H. E., & Ekiz, E. H. (2006). Investigation of the factors that affect the authority’s commitment with structural equation...