Examination of the Concept Images of Pre-service Teachers for Single-Variable and Multi-Variable
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Asian Institute of Research, Journal Publication, Journal Academics, Education Journal, Asian Institute
Asian Institute of Research, Journal Publication, Journal Academics, Education Journal, Asian Institute

Education Quarterly Reviews

ISSN 2621-5799

asia institute of research, journal of education, education journal, education quarterly reviews, education publication, education call for papers
asia institute of research, journal of education, education journal, education quarterly reviews, education publication, education call for papers
asia institute of research, journal of education, education journal, education quarterly reviews, education publication, education call for papers
asia institute of research, journal of education, education journal, education quarterly reviews, education publication, education call for papers
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Published: 15 December 2022

Examination of the Concept Images of Pre-service Teachers for Single-Variable and Multi-Variable

Bahar Dinçer

Izmir Demokrasi University, Turkey

asia institute of research, journal of education, education journal, education quarterly reviews, education publication, education call for papers
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doi

10.31014/aior.1993.05.04.660

Pages: 788-798

Keywords: Concept Image, Single Variable Function, Multivariable Function

Abstract

This study aims to examine the concept images of pre-service mathematics teachers for the concepts of single-variable and multivariable functions. In the present research, which was conducted with the case study method, a test consisting of three open-ended questions was used to obtain data about the definition of the concept of function and the concept images of the single and multivariate functions of the pre-service teachers. The data obtained were coded with the descriptive analysis method and analyzed qualitatively. Each coding was given as a theme with frequency and percentage values and the answers given by the pre-service teachers were presented as examples. The findings obtained in this study showed that the pre-service teachers' concept images about function consisted of different representations of the concept of a function and concept images were generally classified as matching, transformation and equation. The pre-service teachers' concept images of the concept of function also had incomplete learning and misconceptions. That definition and value sets, which are important components of the concept of function, were not included in the answers. The pre-service teachers defined the functions as f(x) in multivariate function examples, and they ignored that x represents the only variable in the function. In addition, pre-service teachers who had misconceptions in single-variable function examples (equation and algebraic expression) made the same mistake in multivariable functions and could not make a correct representation although they used two variables in their expressions. It was determined that misinformation and misconceptions in concept images for multivariable functions were caused by incomplete information and mislearning in the function definition and single-variable function examples. The findings suggest that supporting the course designs on single and multivariable functions with examples and concept knowledge would be beneficial for an effective learning process.

References

  1. Aydın, M. & Köğce, D. (2008). The perceptions of teacher candidates about “equation and function” concepts. Van Yuzuncu Yil University Journal of Education, 5, 46-58

  2. Carlson, M., Oehrtman, M., & Thompson, P. W. (2005). Key aspects of knowing and learning the concept of function. Mathematical Association of America Research Sampler, 9.

  3. Christou, C., Elia, I., & Gagatsis, A. (2004). The nature of multiple representations in developing mathematical relationships. Quaderni di Ricerca in Didattica, 14, 150-159.

  4. Ergün, S. (2010). 7th grade students' perception, definition and classification of the polygons [Master thesis]. Dokuz Eylul University.

  5. Fujita, T. & Jones, K. (2007). Learners’ understanding of the definitions and hierarchical classification of quadrilaterals: Towards a theoretical framing, Research in Mathematics Education, 9 (1-2), 3-20.

  6. Fujita, T. (2012). Learners’ level of understanding of the ınclusion relations of quadrilaterals and prototype phenomen. The Journal of Mathematical Behavior, 31, 60- 72

  7. Johnson, B., & Christensen, L. (2014). Educational research: quantitative, qualitative and mixed approaches. SAGE Publications.

  8. Kabael, T. U. (2010). Concept of the functıon: hıstorıcal development, understandıng process, mısconceptıon and the teachıng strategıes, Tübav Journal of Science, 3 (1), 128-136.

  9. Lobato, J., & Bowers, J. (2000, April). Three Perspectives in Research on Functions: Multi-Representational, Quantitative, and Phenomenological. Annual meeting of the American educational research association, New Orleans, LA.

  10. Macit, E., & Nacar, S. (2019). Concept images for rational number and fraction of the students at the elementary mathematics education department. Inonu University Journal of the Graduate School of Education, 6(11), 50-62.

  11. Mayes, R. (2001). Using Information technology in mathematics education. (ed: D. James Tooke and Norma Enderson (Eds.),  CAS Applied in a Functional Perspective College Algebra Curriculum, The Haworth Press, In

  12. Miles, M., & Huberman, A. M. (1994). Qualitative data analysis: an expanded sourcebook. Thousand Oaks, CA: Sage

  13. Monaghan, F. (2000). What difference does it make? children’s views of the differences between some quadrilaterals. Educational Studies in Mathematics, 42(2),179-196.

  14. Nakahara, T. (July, 1995). Children’s construction process of the concepts of basic quadrilaterals in Japan. Proceedings of the 19th Conference of the International Group for the Psychology of Mathematics Education (Vol:3). Brazil: Universidade Federal de Pernanbuco

  15. National Council of Teachers of Mathematics (NCTM) (1989). Curriculum and Evaluation Standards for School Mathematics, Reston, Virginia: NCTM.

  16. Rösken, B., & Rolka, K. (2007). Integrating intuition: The role of concept image and concept definition for students’ learning of integral calculus. The Montana Mathematics Enthusiast, 3, 181-204.

  17. Sierpinska, A. (1992). On understanding the notion of function. Aspects of Epistemology and Pedagogy, 25, 23-58.

  18. Tall, D. & Vinner, S. (1981). Concept image and concept definition in mathematics with particular reference to limits and continuity. Educational Studies in Mathematics, 12(2), 151-169

  19. Tavşancıl, E. ve Aslan, E.A. (2001). Content analysis and application examples for verbal, written and other materials. Epsilon Publishing

  20. Vinner, S. & Dreyfus, T. (1989). Images and definitions for the concept of function. Journal for Research in Mathematics Education. 20(4), 356-366.

  21. Vinner, S. (1983). Concept definition, concept image and the notion of function. Internetional Journal of Matematical Education in Science and Technology, 14(3), 293-305.

  22. Vinner, S. (2002). The role of definitions in the teaching and learning of mathematics. In Advanced Mathematical Thinking (pp. 65-81).

  23. Ward, R. A. (2004). An investigation of K-8 preservice teachers’ concept images and mathematical definitions of polygons. Issues in Teacher Education, 13(2), 39-56.

  24. Wilson, P.S. (1990). Inconsistent ideas related to definitions and examples. Focus on Learning Problems in Mathematics, 12(3), 31-47

  25. Yerushalmy, M. (1997). Designing representations: reasoning about functions of two-variables. Journal for Research in Mathematics Education, 28, 431-466.

  26. Şimşek, H., & Yıldırım, A. (2011). Qualitative research methods in the social sciences. Seçkin Pub.

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