Calculus students with different curricular histories: a look at past mathematics experiences, learning preferences, and understanding of various representations of derivatives

When a school offers two mathematics sequences, Traditional and Integrated, and has the students take a course together, it is important to look at the students\u27 perspective on their past mathematics experience. The overarching goal of this study is to examine the nature of the similarities and differences between students who are currently taking calculus who come from two different past curriculum materials. This study also investigates how the students solve problems with different representations of derivatives. A group of twelve students, six from each mathematics sequence, was interviewed and answered tasks worksheets on different representations of derivatives. The students\u27 past mathematics experiences did impact their current experiences in calculus. The students performed equally well on three of the four representations of derivatives. The Integrated students performed better on the application representation. This study highlights students\u27 perspectives; students\u27 perspectives should be a key factor in planning and discussing issues in mathematics education