Browsing by Author "Ron Tzur, Committee Member"

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    The Effects of Multi-Representational Methods on Students' Knowledge of Function Concepts in Developmental College Mathematics
    (2004-03-19) Rider, Robin Lynn; Ron Tzur, Committee Member; Hollylynne Stohl, Committee Co-Chair; Lee V. Stiff, Committee Co-Chair; Jason Osborne, Committee Member
    The purpose of this study was to investigate the potential benefits of a multi-representational curriculum on students' understanding of and connections among graphical, tabular, and symbolic representations of algebraic concepts. The participants of the study were 313 college students enrolled in developmental college algebra at two southern universities. This study utilized a quasi-experimental design in which instructors at one university (control) taught the course from a traditional algebraic perspective while instructors at the other university (treatment) taught the course from a functional approach simultaneously introducing multiple representations. The effect of a multi-representational curriculum on student success and representational preference was assessed with a pretests and posttests of five problems, each with three representations; graphic, tabular, and symbolic. The problems were chosen because of their prevalence in most developmental college algebra curricula. Although both curricula were successful in increasing student achievement, students from the multi-representational curriculum scored significantly higher and were significantly more adept in using representational methods other than algebraic to solve the problems. Qualitative interviews were also conducted with eight participants from each school to examine the connections that students were making and their ability to move flexibly among the graphical, tabular, and algebraic representations. The interviews were analyzed using Biggs and Collis's SOLO Taxonomy. This research showed that a multi-representational curriculum could be effective in expanding students' web of connected knowledge of algebraic and functional concepts. The SOLO Taxonomy and rubric defined in this research gives teachers an effective way of measuring student learning.
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    Roles of Metaphor in the Growth of Mathematical Understanding
    (2004-04-22) Droujkova, Maria Alexandrovna; Ron Tzur, Committee Member; Hollylynne Stohl, Committee Member; Sarah B. Berenson, Committee Chair; Mladen A. Vouk, Committee Member; Glenda S. Carter, Committee Member
    The purpose of this qualitative study was to investigate roles of metaphor in the growth of mathematical understanding in the area of proportionality. To this end, the task of designing software that would help other people learn about proportions was offered to six children ages 13 to 16 during individual interviews. The process of software design helped to access metaphors students developed for thinking about proportionality. A conceptual framework for the study was based on enactivist perspective. Data analysis was based on the study of sources and targets of metaphors, as represented in learners' actions. The Pirie-Kieren Model for the Growth of Mathematical Understanding, in combination with a model for proportional reasoning development that was created for the study, were used to map learners' knowing actions. Microworlds created by learners supported metaphoric systems, which in turn helped to coordinate the process of knowledge development in proportionality domain. The model used for mapping this process included the notions of equivalence class, relation and invariance. Findings indicate that each of these notions may be developed, during local and context-specific growth of understanding, through actions in additive, multiplicative and qualitative analogy worlds. Metaphors serve as a tool for coordination of collecting in these worlds. Moreover, metaphor is a way new understanding grows out of old knowing. In metaphoric structures, sources fade away, and formalized targets become independent entities. This extended process of metaphorising is supported by open-ended, extended tasks.