Abstract
Although there is extensive research on attrition in gatekeeper courses and students’ cognition about calculus concepts, there is one population in introductory calculus that remains understudied: those who failed their initial course and chose to repeat it rather than change majors. These students can provide insight into overcoming poor mathematics affect and major persistence. This case study follows eight students repeating calculus from their second try at undergraduate calculus until they graduated or left the university; six graduated with either a mathematics major or mathematics minor. While participants identified several reasons for their success in the repeated course (processing their initial failure, having a better instructor in the repeated course, and participating regularly in the formative assessments), only participation in formative assessment led to the long-term cognitive and behavioral engagement required for long-term success.
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