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

Autor/in	Thomas, Matthew
Titel	Analyzing Conceptual Gains in Introductory Calculus with Interactively-Engaged Teaching Styles
Quelle	(2013), (189 Seiten) PDF als Volltext Verfügbarkeit Ph.D. Dissertation, The University of Arizona
Sprache	englisch
Dokumenttyp	gedruckt; online; Monographie
ISBN	978-1-3032-9298-9
Schlagwörter	Hochschulschrift; Dissertation; Introductory Courses; Calculus; Mathematics Instruction; Teaching Styles; Video Technology; Achievement Gains; Teaching Methods; Hierarchical Linear Modeling; Learner Engagement; Undergraduate Students; Item Response Theory; Student Characteristics; Classroom Communication; Guidelines; Mathematics Teachers; Correlation; Prior Learning; Models; Scores; Mathematics Achievement; Predictor Variables; Mathematics Tests; Mathematical Concepts; Concept Formation; Measures (Individuals) + Suchen Sie Ihr Suchwort? Thesis; Dissertations; Academic thesis; Einführungskurs; Analysis; Differenzialrechnung; Infinitesimalrechnung; Integralrechnung; Mathematics lessons; Mathematikunterricht; Lehrstil; Unterrichtsstil; Achievement gain; Leistungssteigerung; Teaching method; Lehrmethode; Unterrichtsmethode; Item-Response-Theorie; Klassengespräch; Richtlinien; Mathematics; Teacher; Teachers; Mathematik; Lehrer; Lehrerin; Lehrende; Korrelation; Vorkenntnisse; Analogiemodell; Mathmatics sikills; Mathmatics achievement; Mathematical ability; Mathematische Kompetenz; Prädiktor; Concept learning; Begriffsbildung; Messdaten
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. [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: http://www.proquest.com/en-US/products/dissertations/individuals.shtml.] (As Provided).
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Update	2020/1/01