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.

This study explored instructional strategies that teachers in multilingual mathematics classrooms use to support the development of mathematical proficiency in algebra. The need for improvement of mathematics matriculation results in many multilingual schools is a well accepted concern in South Africa. The research method used was two case studies. In one case, the teacher shared a home language with all the learners. In the other case, the teacher did not share a home language with most of the learners. Data collected revealed that the teachers used language strategies as well as other strategies that would be used in any other mathematics classroom. These strategies were: Interactive Instruction; Scaffolding; Multiple Representations; Code-Switching and Language Modes. The data further revealed that the strategies were not used in isolation but in different combinations as needed, to support the learners.

This study examined the effectiveness of a researcher-designed, computer-based, interactive listening guide system for use by instructors of music appreciation courses. The system was designed to control audio compact discs and present coordinated graphic displays describing musical events as they were heard. Its effectiveness was examined by comparing student outcomes of two subject groups, one exposed to the interactive system in one section of a music appreciation course and another exposed to traditional materials (audio compact disc player, textbook, and writing on the board) in another section of the course. In the first part of the study (“instructional effectiveness”), outcomes were quiz scores and attitudes toward instruction; in a second part of the study; in a second part of the study (“transfer of learning”), outcomes were the quality of student-generated listening guides based on music of their own choice and attitude toward this activity. Results indicated that although there was a marked difference in the reporting of enjoyment of the instructional experience between treatment and control groups, there was no significant difference in any of the product outcomes, such as quizzes or student-generated listening guides. Additional opportunities to examine and compare the effects of the two different modes of instruction over longer periods of exposure is one of nine recommendations for further research reached as a result of this study.

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