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ERIC Number: ED530149
Record Type: Non-Journal
Publication Date: 2009
Pages: 192
Abstractor: As Provided
Reference Count: 0
ISBN: ISBN-978-1-1094-6325-5
Measuring Knowledge of Mathematical Functions: Validity of Scores and Profiles of Participants
Higley, Kelli
ProQuest LLC, Ph.D. Dissertation, The Pennsylvania State University
Knowledge of mathematical functions is expected of university students. This knowledge was measured in this dissertation using two previously untested instruments. The aim of this dissertation was to validate the scores from these measures. The first instrument measured function knowledge in its declarative, procedural, or conditional form. The second instrument measured student ability to translate among representations of linear and quadratic functions. These instruments were intended to measure knowledge of functions in an efficient and effective manner such that deficits of knowledge could be clearly determined, along with clear directions for improving that knowledge. As an essential correlate with knowledge, beliefs about mathematics were also measured, using the Conceptions of Mathematics Scale (Crawford et al., 1998b) and a modified Teachers Epistemic Beliefs Instrument (Hennessey, 2007). The instruments were administered to 640 undergraduate students. The scores on the instruments were submitted to exploratory and confirmatory factor analyses in order to ascertain the structure of the scores; then profiles were established through latent class analysis. The instruments did not measure knowledge as expected. Instead the results indicate that mathematical knowledge of functions must be understood through the lens of representations, specifically their overall format of visual or symbolic representations. The beliefs measures did not substantially add to understanding of student proficiency in mathematics. Four profiles were identified, based primarily on total scores. The profiles provided a possible theory for acquisition of knowledge of functions. Limitations and directions for future research are considered. [The dissertation citations contained here are published with the permission of ProQuest LLC. Further reproduction is prohibited without permission. Copies of dissertations may be obtained by Telephone (800) 1-800-521-0600. Web page:]
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Publication Type: Dissertations/Theses - Doctoral Dissertations
Education Level: Higher Education
Audience: N/A
Language: English
Sponsor: N/A
Authoring Institution: N/A