Abstract

One of the critical tasks in early mathematical education is teaching the concept of function and its different representations through diverse examples and dynamic tasks. This task is meant to enable students to develop meaningful and powerful constructions between functional concepts and procedures, to conceptualize a function as a generalized process that accepts input and produces output and, therefore, to build essential conceptual and analytical thinking of functions that are necessary to form a covariational conception of function. This is particularly useful for College level students enrolled in Calculus courses who need a strong covariational conception of function to further succeed in mathematics courses.
My thesis reveals that, from a sample group of college level students enrolled in Calculus courses at Concordia University, many participants do not have a strong conceptual or/and analytical thinking of functions that is essential in meaningfully modeling dynamic situations. Majority of students, who have obstacle(s) or/and pseudo-thought(s) or/and misconception(s) due to them having weak analytical/conceptual understanding of functions, do not move flexibly between different representations of functions and fail to view a function as a process that maps values of one variable to values of another variable. Consequently, these students generally do not reason dynamic functional situations covariationally at a higher level. This outcome questions the readiness of Calculus students for subsequent mathematics courses, as well as the effectiveness of prior school curriculum in mathematics education.