Keywords
Student misconceptions of functions, teacher expectations, transition from high school to university mathematics, diagnostic assessment, error analysis, conceptual understanding, procedural fluency
Abstract
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.
Notes
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Graduation Date
2013
Semester
Summer
Advisor
Ortiz, Enrique
Degree
Doctor of Philosophy (Ph.D.)
College
College of Education and Human Performance
Degree Program
Education; Mathematics Education
Format
application/pdf
Identifier
CFE0004809
URL
http://purl.fcla.edu/fcla/etd/CFE0004809
Language
English
Release Date
August 2014
Length of Campus-only Access
1 year
Access Status
Doctoral Dissertation (Open Access)
Subjects
Dissertations, Academic -- Education, Education -- Dissertations, Academic
STARS Citation
Avila, Cheryl, "Secondary And Postsecondary Calculus Instructors' Expectations Of Student Knowledge Of Functions: A Multiple-case Study" (2013). Electronic Theses and Dissertations. 2837.
https://stars.library.ucf.edu/etd/2837