Many students who take calculus in high school opt to retake the course in college. This study investigated the impact of that prior exposure. Students were invited to complete a survey about their experiences with calculus, with eight being interviewed afterwards. While students nearly unanimously agreed that prior experience with calculus was a benefit, none felt that it was a necessity to succeed in a college calculus course. Also, a few students identified some detriments to having taken calculus in high school, mostly stemming from an inadequate high school class. Despite the students' perceptions, Pearson's Chi Square Tests identified a significant difference in both the students' success (pass/fail) and letter grades based on the method of placement into Calculus I (testing in via a placement test did better than taking the prerequisite courses), but not based on either prior exposure to calculus or type of calculus taken during high school (AP and taking the test, AP and not taking the test, non-AP, or no calculus). A survey on student perceptions identified calculus as the most beneficial class to take before Calculus I, but interviews indicated algebra and trigonometry as the most beneficial.

The enrollment in lower-level mathematics courses has been on the increase in the last decade. It has been estimated that the DFW rate may rise to the level of 50% in courses that can be classified as college algebra. Numerous interventions have been utilized for college algebra and other mathematics classes to help students, including supplemental instruction, peer-led team learning, group learning, flipped classrooms, and integrating technology. In this study, we offered a half-semester course that implemented worked example worksheets, which were used in a previous full-semester intervention, to help students with the college algebra material. Results showed that the thirty students who participated in the worked example pass/fail mid-semester class significantly outperformed the college algebra students who did not participate in the intervention on total points in the course, quizzes, and tests 3 and 4. In addition, participants earned a significantly higher course GPA, attended significantly more regular class lectures, and earned a higher final exam score. Finally, we analysed the qualitative data to develop five themes about the worked examples and intervention. We conclude that the mid-semester intervention is a good just-in-time mechanism to implement after the semester has started to help students succeed in the class.

Lecturing is a common way to teach large classes, especially in mathematics. Other styles of instruction have been proven to be more effective in small classroom settings, but those styles are not always practical (or even feasible) in classes with 200+ students. The lecturing dialogue primarily exists at the intersection of Spectrum Theory and the Socratic Method, utilizing inquiry-based learning within the realm of active learning, experiential learning, and constructivism to appeal to learners with various learning styles, which helps students to discover new information (specifically, why things occur in the way that they do) and make connections between old and new material. Spectrum Theory outlines different teaching styles, based on how much a specific style is teacher-centered versus student-centered. The lecturing dialogue combines several of the different approaches from the Spectrum of Teaching Styles, specifically lecture, tutoring, instructional conversation, inquiry-based learning, and guided discovery. It utilizes the Socratic Method to turn students into active learners through constructivism and experiential learning. A high-enrollment, college algebra class using a standard lecture significantly outperformed a class using the lecturing dialogue on labs, surveys/questionnaires, and final grade, but not on final grades without the labs. The labs could be worked on outside of the class, so factors beyond the teaching style may have influenced the results. There was not significant difference between the classes in regards to attitude (enjoyment, motivation, value, and self-confidence). Overall, it appears as though the teaching style has no real impact on either student performance or student attitude in large college algebra classes. I would like to acknowledge the contributions of the several people who helped me along the journey of completing my dissertation. Dr. Sam Stack, my advisor, was a tremendous help throughout the process, mainly in getting everything done that needed to be done (taking the correct classes, filling out the necessary forms, doing things on time). Connie Miranov and Char Allen also helped with these tasks (even when I needed things done at the last minute because I lost track of due dates).