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Pre-Service Elementary Teachers' Use Of Spatial Diagrams: Investigations Of Unbounded Shearing On Solid Figures, Camden G. Bock
Pre-Service Elementary Teachers' Use Of Spatial Diagrams: Investigations Of Unbounded Shearing On Solid Figures, Camden G. Bock
Electronic Theses and Dissertations
Mithala and Balacheff (2019) describe three difficulties with two-dimensional representations of three-dimensional geometrical objects: “it is no longer possible to confuse the representation with the object itself,” visually observed relationships can be misleading, and analysis of the representation requires the use of lower-dimensional theoretical properties. Despite these difficulties, students are routinely expected to learn about three-dimensional figures through interacting with two-dimensional inscriptions. Three-dimensional alternatives include diagrams realized through various spatial inscriptions (e.g., Dimmel & Bock, 2019; Gecu-Parmaksiz & Delialioglu, 2019; Lai, McMahan, Kitagawa & Connolly, 2016; Ng and Sinclair, 2018). Such diagrams are three-dimensional in the sense that they occupy …
Student Understanding Of Limit And Continuity At A Point: A Look Into Four Potentially Problematic Conceptions, Miriam Lynne Amatangelo
Student Understanding Of Limit And Continuity At A Point: A Look Into Four Potentially Problematic Conceptions, Miriam Lynne Amatangelo
Theses and Dissertations
Mathematics students and teachers are familiar with the difficulty of learning and teaching concepts of continuity and limits. Research has expanded our knowledge of how students think about these concepts, including different conceptions and metaphors students use to reason about continuity and limits at a point. From the literature I have identified four potentially problematic conceptions (PPCs) students may use when reasoning about limit and continuity at a point. Questionnaires were administered to 861 BYU students in various mathematics courses to determine how prevalent and persistent the PPCs are among the students in each course. Interviews were conducted with nine …