Undergraduate STEM Students’ Comprehension of Function Series and Related Calculus Concepts

Action-Process-Object-Schema (APOS) is a constructivist methodology that relies on learners' ability to construct and reconstruct certain mental structures and organize them in schemas [1].Taylor series expansion of functions have important applications in STEM including image processing and algorithm design; therefore, understanding and improving Taylor series mental construction of undergraduate engineering students are important in engineering and mathematics education.In this work, 20 undergraduate engineering students' responses to a set of power series questions are analyzed by using APOS theory.The research question used in [19] is used in this work for data collection from a different group of participants.Qualitative and quantitative analysis of the participants' video recorded oral interviews and written responses are executed.Similar to the results attained in [19], the analysis of the collected empirical data indicated a well-established knowledge of approximation, a poor center of Taylor series expansion of function conceptual knowledge, and a well-established knowledge of the meaning of infinity within infinite series concept.The results of this work can help mathematics and engineering educators to improve students' series knowledge and develop a successful teaching methodology.