Investigating Students' Profiles of Mathematical Modeling: A Latent Profile Analysis in PISA 2012
0
조회
0
다운로드
2
인용
0
참고문헌
키워드
초록
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.
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.
참고문헌 (35)
- Hirotugu Akaike, "Factor analysis and AIC", Psychometrika, 52(3), pp.317~332 (1987), Springer Science and Business Media LLC[DOI]
- Gerhard Arminger, "Mixtures of conditional mean- and covariance-structure models", Psychometrika, 64(4), pp.475~494 (1999), Springer Science and Business Media LLC[DOI]
- 백도현, "수학적 모델링에서 가추적 사고의 역할과 의의", 수학교육학연구, 28(2), pp.221~240 (2018), 대한수학교육학회[DOI]
- Blum, W., "Mathematical modelling : Can it be taught and learnt", Journal of Mathematical Modelling and Application, 1(1), pp.45~58 (2009)
- Blum, W., "Mathematical modelling (ICTMA 12): Education, engineering and economics", pp.222~231 (2007), Horwood
- Werner Blum, "Applied mathematical problem solving, modelling, applications, and links to other subjects ? State, trends and issues in mathematics instruction", Educational Studies in Mathematics, 22(1), pp.37~68 (1991), Springer Science and Business Media LLC[DOI]
- Rita Borromeo Ferri, "Theoretical and empirical differentiations of phases in the modelling process", Zentralblatt für Didaktik der Mathematik, 38(2), pp.86~95 (2006), Springer Science and Business Media LLC[DOI]
- Gilles Celeux, "An entropy criterion for assessing the number of clusters in a mixture model", Journal of Classification, 13(2), pp.195~212 (1996), Springer Science and Business Media LLC[DOI]
- 전경희, "수학과 정의적 성취 특성의 잠재프로파일 분석", 교육과정평가연구, 22(2), pp.319~339 (2019), 한국교육과정평가원[DOI]
- "Relating latent class analysis results to variables not included in the analysis" (2009)[URL]
- Lyn D. English, "Mathematical modelling in the early school years", Mathematics Education Research Journal, 16(3), pp.58~79 (2005), Springer Science and Business Media LLC[DOI]
- Galbraith, P., "Models of modelling : Genres, purposes or perspectives", Journal of Mathematical Modelling and Application, 4(8), pp.3~16 (2012)
- Peter Galbraith, "A framework for identifying student blockages during transitions in the modelling process", Zentralblatt für Didaktik der Mathematik, 38(2), pp.143~162 (2006), Springer Science and Business Media LLC[DOI]
- Koeno Gravemeijer, "Context problems in realistic mathematics education: A calculus course as an example", Educational Studies in Mathematics, 39(1, pp.3) (1999), 111~129[DOI]
- Haines, C., "Modelling and applications in mathematics education: The 14th ICMI Study", pp.417~424 (2007), Springer
- John R. Hipp, "Local solutions in the estimation of growth mixture models.", Psychological Methods, 11(1), pp.36~53 (2006), American Psychological Association (APA)[DOI]
- 황지현, "학생들의 태도 특성 분석을 통한 학생 집단 구분에 대한 연구: TIMSS 2015 결과를 중심으로", 한국학교수학회논문집, 21(3), pp.207~225 (2018), 한국학교수학회[DOI]
- 황성환, "잠재프로파일을 활용한 중학생의 수학 학습동기 유형 분석 및 영향요인 탐색", 교육연구, 80, pp.275~294 (2021), 교육문제연구소[DOI]
- Andrew Iverson, "Understanding School Truancy: Risk–Need Latent Profiles of Adolescents", Assessment, 25(8), pp.978~987 (2016), SAGE Publications[DOI]
- David Jonassen, "Supporting Problem Solving in PBL", Interdisciplinary Journal of Problem-Based Learning, 5(2), pp.95~119 (2011), Purdue University (bepress)[DOI]
- Gabriele Kaiser, "A global survey of international perspectives on modelling in mathematics education", Zentralblatt für Didaktik der Mathematik, 38(3), pp.302~310 (2006), Springer Science and Business Media LLC[DOI]
- 김선희, "수학적 모델링 과정에 포함된 추론의 유형 및 역할 분석", 학교수학, 6(3), pp.283~299 (2004), 대한수학교육학회
- Richard Lesh, "Models and Modeling Perspectives on the Development of Students and Teachers", Mathematical Thinking and Learning, 5(2-3), pp.109~129 (2003), Informa UK Limited[DOI]
- Lesh, R., "Second handbook of research on mathematics teaching and learning", pp.763~804 (2007), Information Age Publishing
- Y. Lo, "Testing the number of components in a normal mixture", Biometrika, 88(3), pp.767~778 (2001), Oxford University Press (OUP)[DOI]
- Maaß, K., "Trends in teaching and learning of mathematical modelling", pp.629~639 (2011), Springer
- Herbert W. Marsh, "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: A Multidisciplinary Journal, 16(2), pp.191~225 (2009), Informa UK Limited[DOI]
- Muthén, L. K., (1998), Muthén & Muthén
- OECD, "PISA 2012 assessment and analytical framework: Mathematics, reading, science, problem solving and financial literacy" (2012), OECD Publishing
- Schwarz, G., "Estimating the dimension of a model", The Annals of Statistics, 6(2), pp.461~464 (1978)
- Stanley L. Sclove, "Application of model-selection criteria to some problems in multivariate analysis", Psychometrika, 52(3), pp.333~343 (1987), Springer Science and Business Media LLC[DOI]
- Sriraman, B., "Modeling conceptions revisited", Zentralblatt für Didaktik der Mathematik, 38(3), pp.247~254 (2006)[DOI]
- Verschaffel, L., "Symbolizing, modeling and tool use in mathematics education", pp.257~276 (2002), Springer Netherlands
- 이현숙, "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(1), pp.23~39 (2017), 교육연구소
- Caroline Yoon, "Grounded blends and mathematical gesture spaces: developing mathematical understandings via gestures", Educational Studies in Mathematics, 78(3), pp.371~393 (2011), Springer Science and Business Media LLC[DOI]
