The purpose of this study is to assess object and schema conceptions of transformations of functions for undergraduate level students of Mongolian National University. The research participants were 37 undergraduate students who attended the Calculus course of the third author. To achieve our purpose two of the authors analyzed students’ project work independently based on the pre-developed rubrics and further analyses were made. Students’ project work included recognition of simple and complicated transformation of functions visually, expressing algebraic forms of such transformations and drawing a doll using transformations of a half circle of radius one. The research results show that students’ object and schema conception of transformations of functions were poor. Finding the reason for these poor results is a subject for future research. Moreover, students who were able to recognize more complicated transformations visually could draw a doll using the half circle while the ones who could express transformations of both simple and complicated transformations in algebraic form were able to construct a doll using transformations of the half circle.
Arnon, I., Cottrill, J., Dubinsky, E., Oktaç, A., Roa Fuentes, S., Trigueros, M., Weller, K. (2014). APOS Theory: A Framework for Research and Curriculum Development in Mathematics Education. New York: Springer.10.1007/978-1-4614-7966-6Search in Google Scholar
Asiala, M., Brown, A., De Vries, D. J., & Dubinsky, E. (1996). A framework for research and development in undergraduate mathematics education. Research in Collegiate Mathematics Education, 2, 1-32.10.1090/cbmath/006/01Search in Google Scholar
Baker, B., Hemenway, C., & Trigueros, M. (2001). On transformations of functions. In R. Speiser, C. N. Walter, & C. A. Maher (Eds.), Proceedings of 23rd Annual meeting of the North American Chapter of the International Group for Psychology of Mathematics, 1, pp. 91-98. Snowbird, Utah.Search in Google Scholar
Daher, W. M., & Anabousi, A. A. (2015). Students’ recognition of function transformations’ themes associated with the algebraic representation. REDIMAT, 4(2), 179-194.10.17583/redimat.2015.1110Search in Google Scholar
Dubinsky, E. (1991). Reflective abstraction in advanced mathematical thinking. In D. Tall, Advanced mathematical thinking (pp. 95-123). Dordrecht, The Netherlands: Kluwer.Search in Google Scholar
Eisenberg, T., & Dreyfus, T. (1994). On understanding how students learn to visualize function transformations. Research in collegiate mathematics education, 1, 45-68.10.1090/cbmath/004/03Search in Google Scholar
Hollebrands, K. F. (2003). High school students’ understandings of geometric transformations in the context of a technological environment. The Journal of Mathematical Behavior, 22, 55-72.10.1016/S0732-3123(03)00004-XSearch in Google Scholar
Lage, A. E., & Gaisman, M. T. (2006). An Analysis of Students’ Ideas About Transformations of Functions. Proceedings of the 28th North American Chapter of the International Group for the Psychology of Mathematics Education, 2, pp. 23-31. Mérida, México.Search in Google Scholar
Piaget, J and Garcia, R. (1989). Psychogenesis and the history of science. (H. Feider, Trans.). New York: Columbia University Press.Search in Google Scholar
Zazkis, R., Liljedahl, P., & Gadowsky, K. (2003). Conceptions of function translation: obstacles, intuitions, and rerouting. Journal of Mathematical Behavior, 22(4), 437-450.10.1016/j.jmathb.2003.09.003Search in Google Scholar
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