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A Study of Student Understanding of the Sine Function through Representations and the Process and Object Perspectives

Marchi, Dominic J.

Abstract Details

2012, Master of Arts, Ohio State University, EDU Teaching and Learning.
A major topic that is addressed during the second half of the high school curriculum is the topic of trigonometric functions. In order to analyze how students represent a function like sine and how they connect those representations together, the framework developed by Moschkovich, Schoenfeld, and Arcavi, (1993) will be utilized. Their framework contained two dimensions. The first dealt with the means in which students represent functions and the second dealt with the perspective from which a functions is seen and operated on. 6 students of varying mathematical ability were interviewed to see how they understood sine, represented sine, and connected representations together. Students’ responses were analyzed qualitatively to see depth of understanding by looking at the representations, perspective, and the connections between representations that were used for answering questions. The representations that students utilized were algebraic in the form of an equation, graphical in the form of a sine wave, and geometric in the form of right triangles and the unit circle. Particular attention was paid to if and when a student utilized the Cartesian Connection (Moschkovich et al., 1993). The analysis also attempted to discover where student knowledge is lacking and how this relates to the ability of students to use multiple representation and perspectives. Results indicate that students had some difficulty seeing sine as a function with inputs and outputs. The analysis also revealed that students’ use of the Cartesian Connection was dictated by the context of the question being asked. In addition, students under-utilized the graphical representation during the interview and mostly used the object perspective for this representation. Finally, some implications for teaching are discussed, including getting students to go beyond memorization of facts and more opportunities to use the graphical representation for problem solving and building connections.
Michael Battista, PhD (Committee Chair)
Azita Manouchehri, PhD (Committee Member)
335 p.

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Citations

  • Marchi, D. J. (2012). A Study of Student Understanding of the Sine Function through Representations and the Process and Object Perspectives [Master's thesis, Ohio State University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=osu1343253667

    APA Style (7th edition)

  • Marchi, Dominic. A Study of Student Understanding of the Sine Function through Representations and the Process and Object Perspectives. 2012. Ohio State University, Master's thesis. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=osu1343253667.

    MLA Style (8th edition)

  • Marchi, Dominic. "A Study of Student Understanding of the Sine Function through Representations and the Process and Object Perspectives." Master's thesis, Ohio State University, 2012. http://rave.ohiolink.edu/etdc/view?acc_num=osu1343253667

    Chicago Manual of Style (17th edition)