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Secondary and Postsecondary Calculus Instructors' Expectations of Student Knowledge of Functions: A Multiple-case Study

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Date Issued:
2013
Abstract/Description:
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.
Title: Secondary and Postsecondary Calculus Instructors' Expectations of Student Knowledge of Functions: A Multiple-case Study.
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Name(s): Avila, Cheryl, Author
Ortiz, Enrique, Committee Chair
Dixon, Juli, Committee Member
Hynes, Michael, Committee Member
Andreasen, Janet, Committee Member
Mohapatra, Ram, Committee Member
University of Central Florida, Degree Grantor
Type of Resource: text
Date Issued: 2013
Publisher: University of Central Florida
Language(s): English
Abstract/Description: 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.
Identifier: CFE0004809 (IID), ucf:49758 (fedora)
Note(s): 2013-08-01
Ph.D.
Education, Dean's Office EDUC
Doctoral
This record was generated from author submitted information.
Subject(s): Student misconceptions of functions -- Teacher expectations -- Transition from high school to university mathematics -- Diagnostic assessment -- Error analysis -- Conceptual understanding -- Procedural fluency
Persistent Link to This Record: http://purl.flvc.org/ucf/fd/CFE0004809
Restrictions on Access: campus 2014-08-15
Host Institution: UCF

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