Sencindiver, Benjamin D., authorHagman, Jess E., advisorPilgrim, Mary E., advisorAdams, Henry, committee memberGloeckner, Gene, committee memberZarestky, Jill, committee member2020-08-312020-08-312020https://hdl.handle.net/10217/211793High failure rates in Calculus I contribute to the course acting a filter, rather than a pump, for STEM disciplines. One often cited source of difficulty for students in Calculus I is their weak precalculus content knowledge. In this three-paper dissertation, I investigate Calculus I students' precalculus content knowledge and their awareness of that knowledge. In the first paper, I describe a methodology for collecting data about Calculus I students' tendency to regulate their precalculus content knowledge and analyze the utility of quantifying self-regulated learning as a means for identifying at-risk students. In the second paper, I focus on two factors (calibration and help-seeking) to investigate the how they correlate with Calculus I students' first exam performance. Results highlight the importance of calibration of precalculus content knowledge both directly on student success and how calibration accuracy mediates the benefits of help-seeking. Quantitative analyses of students' precalculus content knowledge highlight Calculus I students' difficulty with the concept of graph, despite students' high confidence in questions related to graph. In the third paper, I conduct interviews with Calculus I students to examine their conceptions of outputs and differences of outputs of a function in the graphical context to understand nuance in how students understand and reason with graphs. Results highlight that students' understandings of quantities and frames of references in graphs of functions can be varied and stable. Students' understanding of quantities also impacts their understanding of other concepts such as differences of outputs and difference quotient. Results of this dissertation have implications for educators, tutor center leaders, and researchers interested in students' understanding of graph, calibration, and help-seeking.born digitaldoctoral dissertationsengCopyright and other restrictions may apply. User is responsible for compliance with all applicable laws. For information about copyright law, please see https://libguides.colostate.edu/copyright.Text