Abstract
Calculus I is a mathematics course that is offered in both high school and college. It can be a final high school mathematics course for some students, and it is an introductory course for undergraduate students that plan to major in one of the science, technology, engineering, or mathematics (STEM) fields. Some students retake calculus in college even if they have successfully completed the course in high school. A nationwide survey has shown that 67% of Calculus I students in private and larger state universities have already completed a calculus course in high school with a mean grade of 3.8 out of 4.0. However, only 50% of these students receive an A or a B in college. Research has shown that students are switching out of the STEM fields, citing a lack of success in Calculus I as one of the reason for leaving these fields. The Mathematical Association of America surveyed Calculus I students across the nation and has found that professors’ pedagogical strategies in the classroom have been one of the deciding factors of student success. Good teaching strategies, such as group work and class discussion, that utilize professor and peer-feedback, include formative assessment strategies. Formative assessment is an ongoing process of evaluating teaching and learning that can make the students’ problem solving explicit for both the professor and the students themselves. This information can then be used by the professor to modify teaching or by the students to modify their learning strategies. Most of the literature investigating formative assessment in a classroom documents learning gains on the K – 12 grade levels. There are few studies that investigate the use of formative assessment in undergraduate mathematics classrooms. Therefore, the purpose of my study was to provide an in-depth look at an undergraduate Calculus I classroom where formative assessment techniques are part of the routine practice in the course. This study was analyzed with an interpretivist lens and guided by case study methodology. I utilized observations, interviews, and artifacts to investigate the use of formative assessment by analyzing the interactions among and between the professor, peer tutor and students within a college Calculus I classroom while they were studying the Chain Rule. It was found that the use of formative assessment tools provided opportunities for community interaction, these interactions were mediated by the perceived calculus ability of the student and centered on the students’ problem solution processes.