Dissertation Proposal Announcement Ph.D. Program: Rasha Abadir “Maximizing Students’ Potential: A Cognitive Science Framework for Calculus Optimization Problems”
Proficiency in first-year calculus courses is critical not only as a measure of students’ mathematical ability but also as a predictor of future success in advanced STEM courses, making calculus a gateway to STEM majors. However, students often struggle with specific calculus topics, particularly those requiring reasoning, modeling, and problem-solving skills. Bressoud (1992) emphasized that calculus is foundational to scientific thought and should be taught with enthusiasm, highlighting its interconnectedness with the world. Despite its importance, many students find calculus abstract and difficult, often due to traditional learning style coupled with fast curricula that limit the opportunities for active learning. This disengagement leads to confusion and a loss of interest. Baisley and Adams (2019) contented that the retention rate among engineering students is only 50% where poor performance in Calculus I contributing to students leaving the major or dropping out of college altogether. Moreover, Bressoud et al. (2013) reported a 28% dropout or failure rate in Calculus I courses in the United States. A key topic in these courses is solving applied optimization problems, which is historically documents as a challenging topic for many students (Borgen & Manu, 2002; Brijlall & Ndlovu, 2013; Dominguez, 2013; LaRue, 2016; Mkhatshwa, 2016; Swanagan, 2012; White & Mitchelmore,1996). Given the documented difficulties students face when solving optimization problems, there is a need for further research to better understand students’ learning experiences, identify obstacles, and develop strategies to enhance success in calculus courses. Drawing on the “cognitive science approach to mathematics education” (Davis, 1984), this study aims to enhance students’ learning of the optimization topic by promoting the construction of a knowledge representation structure, while addressing the needs of a diverse student body, and ensuring equitable learning experience by providing ample opportunities and sufficient time for students to process and acquire the main ideas required for effective learning of this topic.
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