Analyzing Conceptual Gains in Introductory Calculus with Interactively-Engaged Teaching Styles

Persistent Link:
http://hdl.handle.net/10150/299075
Title:
Analyzing Conceptual Gains in Introductory Calculus with Interactively-Engaged Teaching Styles
Author:
Thomas, Matthew
Issue Date:
2013
Publisher:
The University of Arizona.
Rights:
Copyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author.
Abstract:
This dissertation examines the relationship between an instructional style called Interactive-Engagement (IE) and gains on a measure of conceptual knowledge called the Calculus Concept Inventory (CCI). The data comes from two semesters of introductory calculus courses (Fall 2010 and Spring 2011), consisting of a total of 482 students from the first semester and 5 instructors from the second semester. The study involved the construction and development of a videocoding protocol to analyze the type of IE episodes which occurred during classes. The counts of these episodes were then studied along with student gains, measured in a number of different ways. These methods included a traditionally used measure of gain, called normalized gain, which is computed at the instructor level. Additionally, gains were further investigated by constructing hierarchical linear models (HLMs) which allowed us to consider individual student characteristics along with the measures of classroom interactivity. Another framework for computing ability estimates, called Item Response Theory (IRT), was used to compute gains, allowing us to determine whether the method of computing gains affected our conclusions. The initial investigation using instructor-level gain scores indicated that the total number of interactions in a classroom and a particular type of interaction called "encouraging revisions" were significantly associated with normalized gain scores. When individual-level gain scores were considered, however, these instructor-level variables were no longer significantly associated with gains unless a variable indicating whether a student had taken calculus or precalculus in high school or in college was included in the model. When IRT was used to create an alternative measure of gain, the IE variables were not significant predictors of gains, regardless of whether prior mathematics courses were included, suggesting that the method of calculating gain scores is relevant to our findings.
Type:
text; Electronic Dissertation
Keywords:
conceptual knowledge; interactive instruction; undergraduate mathematics education; Mathematics; calculus instruction
Degree Name:
Ph.D.
Degree Level:
doctoral
Degree Program:
Graduate College; Mathematics
Degree Grantor:
University of Arizona
Advisor:
Lozano, Guadalupe I.

Full metadata record

DC FieldValue Language
dc.language.isoenen_US
dc.titleAnalyzing Conceptual Gains in Introductory Calculus with Interactively-Engaged Teaching Stylesen_US
dc.creatorThomas, Matthewen_US
dc.contributor.authorThomas, Matthewen_US
dc.date.issued2013-
dc.publisherThe University of Arizona.en_US
dc.rightsCopyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author.en_US
dc.description.abstractThis dissertation examines the relationship between an instructional style called Interactive-Engagement (IE) and gains on a measure of conceptual knowledge called the Calculus Concept Inventory (CCI). The data comes from two semesters of introductory calculus courses (Fall 2010 and Spring 2011), consisting of a total of 482 students from the first semester and 5 instructors from the second semester. The study involved the construction and development of a videocoding protocol to analyze the type of IE episodes which occurred during classes. The counts of these episodes were then studied along with student gains, measured in a number of different ways. These methods included a traditionally used measure of gain, called normalized gain, which is computed at the instructor level. Additionally, gains were further investigated by constructing hierarchical linear models (HLMs) which allowed us to consider individual student characteristics along with the measures of classroom interactivity. Another framework for computing ability estimates, called Item Response Theory (IRT), was used to compute gains, allowing us to determine whether the method of computing gains affected our conclusions. The initial investigation using instructor-level gain scores indicated that the total number of interactions in a classroom and a particular type of interaction called "encouraging revisions" were significantly associated with normalized gain scores. When individual-level gain scores were considered, however, these instructor-level variables were no longer significantly associated with gains unless a variable indicating whether a student had taken calculus or precalculus in high school or in college was included in the model. When IRT was used to create an alternative measure of gain, the IE variables were not significant predictors of gains, regardless of whether prior mathematics courses were included, suggesting that the method of calculating gain scores is relevant to our findings.en_US
dc.typetexten_US
dc.typeElectronic Dissertationen_US
dc.subjectconceptual knowledgeen_US
dc.subjectinteractive instructionen_US
dc.subjectundergraduate mathematics educationen_US
dc.subjectMathematicsen_US
dc.subjectcalculus instructionen_US
thesis.degree.namePh.D.en_US
thesis.degree.leveldoctoralen_US
thesis.degree.disciplineGraduate Collegeen_US
thesis.degree.disciplineMathematicsen_US
thesis.degree.grantorUniversity of Arizonaen_US
dc.contributor.advisorLozano, Guadalupe I.en_US
dc.contributor.committeememberHughes Hallett, Deborah J.en_US
dc.contributor.committeememberKersting, Nicole B.en_US
dc.contributor.committeememberEli, Jennifer A.en_US
dc.contributor.committeememberLozano, Guadalupe I.en_US
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