Reasoning on simultaneous changes of variables: A qualitative study

Despite variety of research studies that emphasized the effects of students? understanding of rate of change on students? understanding in calculus concepts such as limit, derivative, integrals, there is little information about how college students? reason about continuously changing functional relationships. Aim of this study is to explore, describe and analyze the high performing prospective mathematics teachers? covariational reasoning abilities. Case study design and techniques were used in this study to provide a thick description about thinking and reasoning processes in order to understand covariational reasoning comprehensively. Data were obtained from a detailed examination of a prospective mathematics teacher?s thinking and reasoning processes through the task based in-depth clinical interviews. 15 open ended questions were asked to student in this study. Data obtained from student?s verbal expressions and graphical representations were analyzed in light of the theoretical lens developed by Carlson (2002). Analysis of data disclosed that conceiving of a functional situation statically leads to difficulties in coordinating the continuously changing rate of change over entire domain. This study suggests educators and curriculum developers to introduce functions by focusing on features of defining change in earlier grades. Thus students may develop conceptual understanding rather than memorizing rules and formulas and they may also relate functions with real world situations.Keywords: Covariational reasoning, change, simultaneous changes, dynamic events.