Abstract:

Science, Technology, Engineering, and Mathematics (STEM) fields are required functional thinking to understand functions of many variables in the real world situations. However, the development of functional thinking do not only take place in secondary or university grades. Development of students’ functional thinking commence in the elementary grades and proceed gradually [1]. Therefore, the function concept plays an important role in mathematics curriculums for all grades [2]. When considering the middle school mathematics teachers’ functional thinking abilities have an effect on the development of functional thinking in middle grades, the purpose of this study which is to investigate pre-service middle school mathematics teachers’ functional thinking abilities in the context of problem solving gains importance. This is a qualitatively designed study in which ten participants were purposively selected from pre-service middle school mathematics teachers attending Analysis II course to conduct clinical interviews. For clinical interviews, three real world problems were prepared in the context of one variable function by the researchers of the study. Obtained data from clinical interviews was analyzed by using three-phase qualitative data analysis method [3]. According to the results, it was seen that most of the participants could determine independent and dependent variables, but they had difficulties in representation of the function as the solution of the problem mathematically. It was seen that the participants represented the independent variable’s interval verbally. Moreover, although the participants were able to access their concept knowledge of function, they could not represent the solution as function correctly without any prompt by the interviewer.

References:
[1] Warren, E. A., Cooper, T. J., & Lamb, J. T. (2006). Investigating functional thinking in the elementary classroom: Foundations of early algebraic reasoning. Journal of Mathematical Behavior, 25, 208-223.
[2] Clement, L. (2001). What do students really know about functions? The National Council of Teachers of Mathematics, 94(9), 745-748.
[3] Miles, M., & Huberman, A. M. (1994). Qualitative data analysis: an expanded sourcebook. Thousand Oaks, CA: Sage.

Keywords:

Functional thinking, pre-service teachers, function concept.