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- All Subjects: Frame of Reference
- Genre: Doctoral Dissertation
- Creators: Joshua, Surani Ashanthi
- Creators: Puckett, Kathleen
- Member of: ASU Electronic Theses and Dissertations
Description
This dissertation reports three studies about what it means for teachers and students to reason with frames of reference: to conceptualize a reference frame, to coordinate multiple frames of reference, and to combine multiple frames of reference. Each paper expands on the previous one to illustrate and utilize the construct of frame of reference. The first paper is a theory paper that introduces the mental actions involved in reasoning with frames of reference. The concept of frames of reference, though commonly used in mathematics and physics, is not described cognitively in any literature. The paper offers a theoretical model of mental actions involved in conceptualizing a frame of reference. Additionally, it posits mental actions that are necessary for a student to reason with multiple frames of reference. It also extends the theory of quantitative reasoning with the construct of a ‘framed quantity’. The second paper investigates how two introductory calculus students who participated in teaching experiments reasoned about changes (variations). The data was analyzed to see to what extent each student conceptualized the variations within a conceptualized frame of reference as described in the first paper. The study found that the extent to which each student conceptualized, coordinated, and combined reference frames significantly affected his ability to reason productively about variations and to make sense of his own answers. The paper ends by analyzing 123 calculus students’ written responses to one of the tasks to build hypotheses about how calculus students reason about variations within frames of reference. The third paper reports how U.S. and Korean secondary mathematics teachers reason with frame of reference on open-response items. An assessment with five frame of reference tasks was given to 539 teachers in the US and Korea, and the responses were coded with rubrics intended to categorize responses by the extent to which they demonstrated conceptualized and coordinated frames of reference. The results show that the theory in the first study is useful in analyzing teachers’ reasoning with frames of reference, and that the items and rubrics function as useful tools in investigating teachers’ meanings for quantities within a frame of reference.
ContributorsJoshua, Surani Ashanthi (Author) / Thompson, Patrick W (Thesis advisor) / Carlson, Marilyn (Committee member) / Roh, Kyeong Hah (Committee member) / Middleton, James (Committee member) / Culbertson, Robert (Committee member) / Arizona State University (Publisher)
Created2019
Description
A mixed methods action research study was designed to answer three research questions based on inter-rater reliability (IRR) in compliance calls for transition at a state education agency, perceived confidence levels in making and discussing compliance calls, and perceived confidence in sharing transition resources. An innovation based on andragogy and frame of reference training (FOR) was designed and implemented with twelve participants to answer these questions. To measure the effects of the innovation, participants completed a pre-and post-innovation review of five student files, analyzing the IRR for the group as compared with a gold standard (GS) both before and after the innovation. Additionally, a smaller group sample for the same five files post-innovation was collected to compare group results for IRR with the GS to the combined individual results. A retrospective survey was also utilized in which participants rated their confidence in each component pre- and post-innovation. Based upon analyses of these data, several key findings were identified. Higher inter-rater reliability was noted when participants reviewed files within small groups and in the area of annual Individualized Education Program (IEP) goals aligned with measurable post-secondary goals. Lower IRR was reported in nuanced files, files for students with low-incidence disabilities, and files with more instances of non-compliance. Results indicated that participant confidence in making and discussing transition files in the field improved post-innovation. Lastly, participants indicated higher confidence in sharing best practices in transition with the field post-innovation. Implications for this research include training suggestions, additional practice with low-incidence and nuanced files at the state agency, and group review of files in other state monitoring systems.
ContributorsRaithel, Heather (Author) / Puckett, Kathleen (Thesis advisor) / Mathur, Sarup (Committee member) / Ross, Lydia (Committee member) / Arizona State University (Publisher)
Created2023