Research in Mathematical Education (한국수학교육학회지시리즈D:수학교육연구)

Korean Society of Mathematical Education (한국수학교육학회)
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Investigating Students' Profiles of Mathematical Modeling: A Latent Profile Analysis in PISA 2012

  • SeoJin Jeong (Department of Mathematics Gifted Education, Korea National University of Education) ;
  • Jihyun Hwang (Department of Mathematics Education, Korea National University of Education) ;
  • Jeong Su Ahn (Department of Mathematics Education, Korea National University of Education)
  • Received : 2023.06.03
  • Accepted : 2023.06.17
  • Published : 2023.09.30
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Abstract

We investigated the classification of learner groups for students' mathematical modeling competency and analyzed the characteristics in each profile group for each country and variable using PISA 2012 data from six countries. With a perspective on measuring sub-competency, we applied the latent profile analysis method to student achievement for mathematical modeling variables - Formulate, Employ, Interpret. The findings showed the presence of 4-6 profile groups, with the variables exhibiting high and low achievement within each profile group varying by country, and a hierarchical structure was observed in the profile group distribution in all countries, interestingly, the Formulate variable showed the largest difference between high-achieving and low-achieving profile groups. These results have significant implications. Comparison by country, variable, and profile group can provide valuable insights into understanding the various characteristics of students' mathematical modeling competency. The Formulate variable could serve as the most suitable predictor of a student's profile group and the score range of other variables. We suggest further studies to gain more detailed insights into mathematical modeling competency with different cultural contexts.

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References

  1. Akaike, H. (1987). Factor analysis and AIC. Psychometrika, 52(3), 317-332. https://doi.org/10.1007/BF02294359
  2. Arminger, G., Stein, P., & Wittenberg, J. (1999). Mixtures of condition mean- and covariance-structure models. Psychometrika, 64, 475-494. https://doi.org/10.1007/BF02294568
  3. Baek, D., & Lee, K. (2018). Role and significance of abductive reasoning in mathematical modeling. Journal of Educational Research in Mathematics, 28(2), 221-240. https://doi.org/10.29275/jerm.2018.05.28.2.221
  4. Blum, W., & Ferri, R. B. (2009). Mathematical modelling: Can it be taught and learnt? Journal of Mathematical Modelling and Application, 1(1), 45-58.
  5. Blum, W., & Leiss, D. (2007). How do students and teachers deal with modelling problems? In C. Haines, P. Galbraith, W. Blum, & S. Khan (Eds.), Mathematical modelling (ICTMA 12): Education, engineering and economics (pp. 222-231). Horwood. https://doi.org/10.1533/9780857099419.5.221
  6. Blum, W., & Niss, M. (1991). Applied mathematical problem solving, modelling, applications, and links to other subjects-State, trends and issues in mathematics instruction. Educational Studies in Mathematics, 22(1), 37-68. https://doi.org/10.1007/BF00302716
  7. Borromeo Ferri, R. (2006). Theoretical and empirical differentiations of phases in the modelling process. Zentralblatt fur Didaktik der Mathematik, 38(2), 86-95. https://doi.org/10.1007/BF02655883
  8. Celeux, G., & Soromenho, G. (1996). An entropy criterion for assessing the number of clusters in a mixture model. Journal of Classification, 13, 195-212. https://doi.org/10.1007/BF01246098
  9. Chon, K., & Kim, S. (2019). A latent profile analysis of math attitudes. Journal of Curriculum and Evaluation, 22(2), 319-339. https://doi.org/10.29221/jce.2019.22.2.319
  10. Clark, S. L., & Muthen, B. (2009). Relating latent class analysis results to variables not included in the analysis. Retrieved from http://www.statmodel.com/download/relatinglca.pdf.
  11. English, L., & Watters, J. (2005). Mathematical modelling in the early school years. Mathematics Education Research Journal, 16(3), 58-79. https://doi.org/10.1007/BF03217401
  12. Galbraith, P. (2012). Models of modelling: Genres, purposes or perspectives. Journal of Mathematical Modelling and Application, 4(8), 3-16.
  13. Galbraith, P., & Stillman, G. (2006). A framework for identifying student blockages during transitions in the modelling process. Zentralblatt fur Didaktik der Mathematik, 38(2), 143-162. https://doi.org/10.1007/BF02655886
  14. Gravemeijer, K., & Doorman, M. (1999). Context problems in realistic mathematics education: A calculus course as an example. Educational Studies in Mathematics 39, 111-129. https://doi.org/10.1023/A:1003749919816
  15. Haines, C., & Crouch, R. (2007). Mathematical modelling and applications: Ability and competence frameworks. In W. Blum, P. L. Galbraith, H.-W. Henn, & M. Niss (Eds.), Modelling and applications in mathematics education: The 14th ICMI Study (pp. 417-424). Springer. https://doi.org/10.1007/978-0-387-29822-1_46
  16. Hipp, J. R., & Bauer, D. J. (2006). Local solutions in the estimation of growth mixture models. Psychological Methods, 11(1), 36-53. https://doi.org/10.1037/1082-989x.11.1.36
  17. Hwang, J., & Ko, E. (2018). Investigating Korean students' different profiles of affective constructs and engagements: a latent profile analysis on TIMSS 2015. Journal of the Korean School Mathematics Society, 21(3), 207-225. http://dx.doi.org/10.30807/ksms.2018.21.3.001
  18. Hwang, S., & Son, T. (2021). Exploring middle school students' mathematics learning motivation and influential factors using latent profile analysis. Educational Research, 80, 275-294. https://doi.org/10.17253/swueri.2021.80..013
  19. Iverson, A., French, B. F., Strand, P. S., Gotch, C. M., & McCurley, C. (2018). Understanding school truancy: Risk-need latent profiles of adolescents. Assessment, 25(8), 978-987. https://doi.org/10.1177/1073191116672329
  20. Jonassen, D. (2011). Supporting problem solving in PBL. Interdisciplinary Journal of Problem-Based Learning, 5(2). 95-119. https://doi.org/10.7771/1541-5015.1256
  21. Kaiser, G., & Sriraman, B. (2006). A global survey of international perspectives on modelling in mathematics education. Zentralblatt fur Didaktik der Mathematik, 38(3), 302-310. https://doi.org/10.1007/BF02652813
  22. Kim, S., & Kim, K. (2004). Analysis on types and roles of reasoning used in the mathematical modeling process. School Mathematics, 6(3), 283-299.
  23. Lesh, R., & Lehrer, R. (2003). Models and modeling perspectives on the development of students and teachers. Mathematical Thinking and Learning, 5(2-3), 109-129. https://doi.org/10.1080/10986065.2003.9679996
  24. Lesh, R., & Zawojewski, J. (2007). Problem solving and modeling. In F. Lester (Ed.), Second handbook of research on mathematics teaching and learning (pp. 763-804). Information Age
  25. Lo, Y., Mendell, N., & Rubin, D. (2001). Testing the number of components in a normal mixture. Biometrika, 88(3), 767-778. https://doi.org/10.1093/biomet/88.3.767
  26. Maass, K., & Gurlitt, J. (2011). LEMA-Professional development of teachers in relation to mathematical modelling. In G. Kaiser, W. Blum, R. Borromeo Ferri, & G. A. Stillman (Eds.), Trends in teaching and learning of mathematical modelling (pp. 629-639). Springer. https://doi.org/10.1007/978-94-007-0910-2_60
  27. Marsh, H. W., Luedtke, O., Trautwein, U., & Morin, J.S.A. (2009). Classical latent profile analysis of academic self-concept dimensions: Synergy of person- and variable-centered approaches to theoretical models of self-concept. Structural Equation Modeling, 16, 191-225. https://doi.org/10.1080/10705510902751010
  28. Muthen, L. K., & Muthen, B. O. (1998). Mplus (version 8.8) [Computer software]. Muthen & Muthen.
  29. OECD. (2013). PISA 2012 assessment and analytical framework: Mathematics, reading, science, problem solving and financial literacy. OECD Publishing. https://doi.org/10.1787/9789264190511-en
  30. Schwarz, G. (1978). Estimating the dimension of a model. The Annals of Statistics, 6(2), 461-464. https://doi.org/10.1214/aos/1176344136
  31. Sclove, S. L. (1987). Application of model-selection criteria to some problems in multivariate analysis. Psychometrika, 52(3), 333-343. https://doi.org/10.1007/BF02294360
  32. Sriraman, B., & Lesh, R. A. (2006). Modeling conceptions revisited. Zentralblatt fur Didaktik der Mathematik, 38(3), 247-254. https://doi.org/10.1007/BF02652808
  33. Verschaffel, L., Greer, B., & De Corte, E. (2002). Everyday knowledge and mathematical modeling of school word problems. In K. Gravemeijer, R. Lehrer, B. Van Oers, & L. Verschaffel (Eds.), Symbolizing, modeling and tool use in mathematics education (pp. 257-276). Springer Netherlands. https://doi.org/10.1007/978-94-017-3194-2_16
  34. Yi, H., & Lee, Y. (2017). A latent profile analysis and structural equation modeling of the instructional quality of mathematics classrooms based on the PISA 2012 results of Korea and Singapore. Asia Pacific Education Review, 18, 23-39. https://doi.org/10.1007/s12564-016-9455-4
  35. Yoon, C., Thomas, M., & Dreyfus, T. (2011). Grounded blends and mathematical gesture spaces: developing mathematical understandings via gestures. Educational Studies in Mathematics, 78(3), 371-393. https://doi.org/10.1007/s10649-011-9329-y