Author: Jamshid Nejad, Masomeh
Trigonometry is one of the fundamental topics taught in high school and university curricula. However, it is considered as one of the most challenging subjects for teaching and learning. Contributing to research on learning trigonometry, this dissertation sheds light on aspects of undergraduate students’ understanding of transformations of sinusoidal functions. Six undergraduate students participated in the study. Two types of tasks – (A) Identifying sinusoidal functions and (B) Assigning coordinates – were presented to participants in a clinical interview.To analyze the collected data, three theoretical frameworks, Mason’s theory of shifts of attention, Presmeg’s visual imagery and Carlson, Jacobs, Coe, Larsen, and Hsu covariational reasoning were used in this dissertation. Mason’s theory provided opportunity to study the critical role of attention and awareness in learning and understanding mathematics, and in particular the concept of transformation of sinusoidal functions. Presmeg’s classification of visual imagery was applied for investigating students’ visual mental constructs since the participants applied their imagery on different occasions when they completed the interview tasks. Lastly, participants’ solution approaches were evaluated using covariational reasoning, focusing on Carlson’s et al. description of mental actions associated with developmental levels. The results of this research show that undergraduate students participating in this study experienced difficulty in identifying a phase shift/ horizontal transformation of the sinusoidal functions. They, in fact, determined “BC” as phase shift instead of “C” when they relied on the representation of sinusoids as f(x)= A sin/cos((B(x+C))+D. Some participants were also unable to complete tasks in which coefficient of x was a fraction. I conclude this dissertation with some pedagogical suggestions in terms of learning and teaching transformations of sinusoidal functions.
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Thesis advisor: Zazkis, Rina
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