Skip to content
BY 4.0 license Open Access Published by De Gruyter Open Access January 29, 2021

Student’s Conceptions of Function Transformation

Davaanyam Tumenbayar , Amartuvshin Amarzaya EMAIL logo and Tserendorj Navchaa
From the journal Open Education Studies


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

Received: 2020-07-30
Accepted: 2020-12-20
Published Online: 2021-01-29

© 2021 Davaanyam Tumenbayar et al., published by De Gruyter

This work is licensed under the Creative Commons Attribution 4.0 International License.

Downloaded on 28.1.2023 from
Scroll Up Arrow