Examining the least preferred topics among advanced placement calculus students

This mixed-methods study investigates the perceptions of Grade 12 students enrolled in Advanced Placement (AP) Calculus regarding their least preferred topics, to identify instructional and cognitive challenges that hinder their engagement. Data were collected from 53 students across five schools in the United States and Iraq using a survey that included both quantitative and qualitative items. Quantitative analysis revealed that topics related to integration, particularly Applications of Integration and Accumulation of Change, were most frequently identified as difficult. Latent class analysis further distinguished two distinct student groups based on topic preferences. Thematic analysis of open-ended responses highlighted key challenges such as cognitive overload, lack of engagement, struggles early in the semester, and anxiety related to assessments. Students also expressed negative emotional responses, emphasizing the affective dimensions of learning advanced mathematics. Despite these difficulties, participants identified effective instructional methods, including concise teacher explanations, visual aids, guided practice, and the use of multimedia resources. The findings suggest that student-centered, scaffolded instruction can help alleviate conceptual barriers and improve learning outcomes in AP Calculus. This study adds to the growing body of literature advocating for responsive and differentiated teaching practices in high-stakes mathematics courses. Implications for instruction, curriculum design, and teacher training are also discussed.