Student misconceptions of functions, teacher expectations, transition from high school to university mathematics, diagnostic assessment, error analysis, conceptual understanding, procedural fluency
This multiple-case study examines the explicit and implicit assumptions of six veteran calculus instructors from three types of educational institutions, comparing and contrasting their views on the iteration of conceptual understanding and procedural fluency of pre-calculus topics. There were three components to the research data recording process. The first component was a written survey, the second component was a "think-aloud" activity of the instructors analyzing the results of a function diagnostic instrument administered to a calculus class, and for the third component, the instructors responded to two quotations. As a result of this activity, themes were found between and among instructors at the three types of educational institutions related to their expectations of their incoming students’ prior knowledge of pre-calculus topics related to functions. Differences between instructors of the three types of educational institutions included two identifiable areas: (1) the teachers’ expectations of their incoming students and (2) the methods for planning instruction. In spite of these differences, the veteran instructors were in agreement with other studies’ findings that an iterative approach to conceptual understanding and procedural fluency are necessary for student understanding of pre-calculus concepts.
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Doctor of Philosophy (Ph.D.)
College of Education and Human Performance
Education; Mathematics Education
Length of Campus-only Access
Doctoral Dissertation (Open Access)
Dissertations, Academic -- Education, Education -- Dissertations, Academic
Avila, Cheryl, "Secondary And Postsecondary Calculus Instructors' Expectations Of Student Knowledge Of Functions: A Multiple-case Study" (2013). Electronic Theses and Dissertations. 2837.