Graduate Thesis Or Dissertation

Teachers' perceptions of the concept of limit, the role of limits and the teaching of limits in advanced placement calculus

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  • The main goal of the study was to investigate high school advanced placement calculus teachers' subject matter and pedagogical perceptions by examining the following questions: What are the teachers' perceptions of the concept of limit, the role of limits, and the teaching of limits in calculus? Additionally, the sampling technique used shed some light on the question: Are these teachers' perceptions associated with their participation in a calculus reform project focused on staff development? A multi-case study approach involving detailed examination of six teachers (three had participated in a calculus reform project and three had not participated in any calculus reform project) was used. The data collected and analyzed included questionnaires, interviews, observational fieldnotes, videotapes of classroom instruction, journals, and written instructional documents. Upon completion of the data collection and analysis, detailed teacher profiles were created with respect to the questions above. The results of this study were then generated by searching for similarities and differences across the entire sample as well as comparing and contrasting the group of project teachers and the independent teachers. The teachers in this study perceived calculus as a linearly ordered set of topics in which the concept of limit formed the backbone for appreciating and understanding all other calculus topics. The teachers felt the intuitive understanding of limits was essential to further understanding of calculus. Nevertheless, little classtime was devoted to developing an intuitive understanding. Furthermore, little emphasis was given to drawing connections between limits and subsequent calculus topics. The independent teachers devoted considerable time to discussing formal epsilon-delta definition and arguments. The complex relationship between teachers' perceptions and classroom practice appeared to be affected by the significant influence of the teachers' goals of preparing students for the advanced placement exam and college calculus and the authority given to the calculus textbook. Differences between the group of independent teachers and the group of project teachers were found related to the following factors: (a) commitment to the textbook, (b) planning, (c) use of multiple representations, (d) attitude toward graphing technology, (e) classroom atmosphere, (f) examinations, (g) appropriate level of mathematical rigor needed for teaching calculus, and (h) the stability of perceptions. These factors, however, were not fully attributed to participation in the calculus reform project.
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