A case study of students' knowledge of functions in an online college algebra course
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This study investigated college students’ knowledge of the concept of function in an online environment and explored the difficulties they might have encountered with the notion of function in the areas of recognition, interpretation, and translation. Research on students’ knowledge and difficulties with the concept of function in an online domain is in its infancy. This case study focused on four students from two sections of online college algebra courses at a two-year college. Data were collected from a pretest, three reflections, two interviews, a test, a quiz, a comprehensive final examination, and written responses from the interviews. I used a constant comparative method (Glaser & Strauss, 1967) to give meaning to the collected data. One of the goals of this study was to examine college students’ knowledge in recognition of relations as functions and non-functions given in different representations. They were able to recognize relations in numerical and graphical forms more frequently than relations in algebraic form. Findings revealed most participants were more knowledgeable about interpretation of the graphical representation of functions in which one of the variables was time. Here they were able to construct answers, as they were able to logically connect to the functional reasoning. On the other hand, most students showed difficulty interpreting (a) functions given in algebraic format, and (b) some global features of the graphical representations of functions The results indicated that all students achieved a better overall knowledge of functions in the area of translation from numerical to graphical form, than from symbolic to graphical description. The task of translating functions from verbal description to algebraic representation was the most difficult task for the majority of students. Translation of functions from graphical to algebraic was easier for the participants than vice versa.