The Teaching of Calculus in High Schools in the United States
Williams, John Bernard
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https://hdl.handle.net/2142/69225
Description
Title
The Teaching of Calculus in High Schools in the United States
Author(s)
Williams, John Bernard
Issue Date
1988
Doctoral Committee Chair(s)
Travers, Kenneth J.
Department of Study
Education
Discipline
Education
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Education, Mathematics
Abstract
This thesis utilized data from the Second International Mathematics Study to characterize U.S. high school calculus classes and to identify aspects of teachers and teaching of calculus that accounted for differences in class achievement. The factors examined were (a) the degree to which teachers' presentations of mathematics were process oriented, (b) the degree to which teachers used formal methods of instruction, (c) the extent to which teachers relied on the textbook, (d) the percent of time that the class spent working in small groups, and (e) the percent of time that students spent working alone. A detailed profile of high school calculus teachers and classes was developed, including such variables as teacher background, curriculum content, manner of teacher presentations, and decisions regarding the teaching of the target class.
Of the five factors and their interactions, none showed a significant relationship with achievement. Exploratory analyses suggested that classes which spent less time in small groups showed a greater achievement in comprehension accompanied by a higher variance in overall achievement. The data suggested that greater teacher reliance on the textbook coupled with more time spent in small groups was associated with lower achievement at both the computation and comprehension levels. Finally, teacher presentations containing formal proofs were associated with greater variance among classes at the higher cognitive levels of achievement. Implications for future development of the high school curriculum in calculus is included.
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