CAUSAL SEM OF MATHEMATICAL COMPETENCES IN ELEMENTARY EDUCATION

Abstract

In this paper, authors defined mathematical competences for 7^th year elementary school. The basic objective was to measure the mathematical competence or mathematical knowledge, skills and abilities in mathematical educations. Mathematical competences were grouped in following areas: Algebra and functions, Space and shapes, Measurements and Data.  Statistical set for the research consisted of 48 children from the Elementary school Dr. Ivan Merz in Zagreb, Croatia. Authors had 15 measuring variables together with the evaluated results of described tasks. With statistical set with variables as measured mathematical competences the authors make the causal structural equation model (SEM) of mathematical competences. The authors use free software Tetrad 5.2.1-3 (Tetrad project 2015). In the results we describe structural equations between the mathematical competitions for 7^th year elementary school children. This paper is a result of our previous research on causal modeling of mathematical competences in kindergarten (Tepeš at. all. 2013, 2014 and 2015)

Keywords

• mathematical competences,structural equation model and causal model

References

1. Boolen, K. A. (2007). An Overview of Equation Models with Latent Variables, Miami University Symposium on Computational Research, March 1-2, 1-51, http://www.units.miamioh.edu/cacr/activities/documents/LatentVariable-tutorial.pdf Hyarinen, A. and Oja, E. (2000). Independent Component Analysis: Algorithms and Applications, Neural Networks, 13(4-5): 411-430 National Curriculum Framework for Pre-school Education and General Compulsory and Secondary Education, (2011), Ministry of Science, Education and Sport of the Republic of Croatia, http://public.mzos.hr/Default.aspx?sec=2497 Paić G., Bošnjak Ž., Čulina B. (2014). Mathematical challenges 7 – textbook with workbook, Alfa, Zagreb, (Croatian), http://www.alfa.hr/artikl/info/53aba7930c45d9da18000850#list-top Paić G., Bošnjak Ž., Čulina B. (2014). Mathematical challenges 7 – worksheets, Alfa, Zagreb, (Croatian), http://www.alfa.hr/artikl/info/4fa0a1d93988ccee67000033#list-top Paić G., Bošnjak Ž., Čulina B. (2014). Mathematical challenges 7 – tests, Alfa, Zagreb Pearl, J. (2000) Causality: Models, Reasoning, and Inference, Cambridge University Press Scheines, R., Ramsey, J., Spirters, P. and Glymor, C. (2015). Causal Model Search, Gentle introduction to Tetrad, http://www.phil.cmu.edu/tetrad/ Shimizu, S. (2014). LiNGAM: Non-Gaussian Methods for Estimating Causal Structures, Behaviormetrika 41(1), 65-98 Tepeš, B. (2009), Statistical Models on Graphs (Croatian). Faculty of Humanities and Social Sciences, bozidartepes.net/ Tepeš, B., Lešin, G & Hrkač,A. (2013). Causal Modelling in Mathematical Education, The 1st International Conference on “Research and Education - Challenges Towards the Future, Schroder, Albania, www.unishk.edu.al./Pub.html Tepeš, B., Šimović V. and Tepeš, K.(2014). Causal Model of Mathematical Competences in Kindergarten, International Teacher Education Conference 2014, Proceeding Book, pp. 102 – 107, UAE Dubai http://www.ite-c.net Tepeš, B., Šimović V. and Tepeš, K. (2015). A Note on Modeling of Mathematical Competences, 14th Hawaii International Conference on Education 2015, Proceeding Book, USA Hawaii, www.hiceducation.org, The Tetrad Project (2015), Launch Tetrad 5.2.1-3, www.phil.cmu.edu/tetrad/