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Description
Previous research discusses students' difficulties in grasping an operational understanding of covariational reasoning. In this study, I interviewed four undergraduate students in calculus and pre-calculus classes to determine their ways of thinking when working on an animated covariation problem. With previous studies in mind and with the use of technology, I devised an interview method, which I structured using multiple phases of pre-planned support. With these interviews, I gathered information about two main aspects about students' thinking: how students think when attempting to reason covariationally and which of the identified ways of thinking are most propitious for the development of an understanding of covariational reasoning. I will discuss how, based on interview data, one of the five identified ways of thinking about covariational reasoning is highly propitious, while the other four are somewhat less propitious.
ContributorsWhitmire, Benjamin James (Author) / Thompson, Patrick (Thesis director) / Musgrave, Stacy (Committee member) / Moore, Kevin C. (Committee member) / Barrett, The Honors College (Contributor) / School of Mathematical and Statistical Sciences (Contributor) / T. Denny Sanford School of Social and Family Dynamics (Contributor)
Created2014-05
Description
Over the past thirty years, research on teachers’ mathematical knowledge for teaching (MKT) has developed and grown in popularity as an area of focus for improving mathematics teaching and students’ learning. Many scholars have investigated types of knowledge teachers use when teaching and the relationship between teacher knowledge and student performance. However, few researchers have studied the sources of teachers’ pedagogical decisions and actions and some studies have reported that advances in teachers’ mathematical meanings does not necessarily lead to a teacher conveying strong meanings to students. It has also been reported that a teacher’s ways of thinking about teaching an idea and actions to decenter can influence the teacher’s interactions with students.This document presents three papers detailing a multiple-case study that constitutes my dissertation. The first paper reviews the constructs researchers have used to investigate teachers’ knowledge base. This paper also provides a characterization of the first case’s mathematical meaning for teaching angle measure and the impact of her meaning on her interactions with students while teaching her angle measure lessons. The second paper examines another instructor’s meaning for an angle and its measure and illustrates the symbiotic relationship between the teacher’s mathematical meanings for teaching and decentering actions. This paper also characterizes how an instructor’s commitment to quantitative reasoning influences the teacher’s instructional orientation and instructional actions. Finally, the third paper includes a cross-case analysis of the two instructors’ mathematical meanings for teaching sine function and their enacted teaching practices, including their choice of tasks, interactions with students, and explanations while teaching their sine function lessons.
ContributorsRocha, Abby (Author) / Carlson, Marilyn P (Thesis advisor) / Thompson, Patrick (Committee member) / Tallman, Michael (Committee member) / O'Bryan, Alan (Committee member) / Strom, April (Committee member) / Apkarian, Naneh (Committee member) / Arizona State University (Publisher)
Created2023