Contrasting cases of college calculus instructors: their preferences and potential pedagogy in teaching derivative graphs

This study examined college calculus instructors’ preferences in solving two calculus tasks to examine college calculus instructors’ use of important cognitive roots in understanding derivatives of function. Our results showed that only one instructor consistently uses cognitive roots while other instructors either focus on algebraic methods or expressing the constraints of students’ knowledge, demonstrating their orientations and conflicts. These results potentially show what students experience when differentiation of function is taught.