Understanding STEM Students’ Conceptual Derivative Knowledge Through Analysis of Sub-concept Cognition

One of the most frequently used concepts by STEM majors during their undergraduate education is differentiation of mathematical functions.Investigating undergraduate students' differentiation knowledge through collected empirical data and determining weaknesses to improve pedagogical approaches to teach differentiation to STEM students are the main goals of this work.The conducted research's data collection procedure received Institutional Review Board (IRB) approval.Quantitative and qualitative data is collected from 20 STEM students at a university located at the Northeastern side of the United States.Written and video recorded information is collected and analyzed qualitatively and quantitatively to understand STEM students' ability to solve a research question related to derivative, absolute value, and trigonometric function concepts.The pedagogical techniques used in this work to analyze the collected data are Action, Process, Object and Schema (APOS) theory introduced in [1], and concept image and concept definition introduced in [16].The written results indicated participants' elementary level ability to form a bridge between the derivative of the absolute value function and its image.The participants also had hard time to progress the solution step-by-step by using the building blocks of derivative of a composition function.These results indicated a need for a better concept image and concept definition coverage of the composition functions' differentiability in calculus education for improving their conceptual understanding of STEM majors.