It is important for Science-Technology-Engineering-Mathematics (STEM) educators to find out about STEM students' success in answering calculus questions, particularly the questions that involve more than one calculus concepts that require to know other calculus concepts. Designing appropriate questions for assignments and exams that involve calculus concepts are critical in measuring student success. Effectiveness analysis of the method used for designing such questions is also important. Efforts have been made in understanding and improving engineering students' ability to respond calculus questions in (STEM) fields that require knowledge of more than one calculus concept [1-11] and more research results are added every year to these results for understanding students' approach to solve these problems. In this work, 26 undergraduate engineering students' written and oral responses to a calculus question that involves multiple calculus concepts are recorded after Institutional Review Board (IRB) approval. Triangulation method [1] and Action-Process-Object-Schema (APOS) theory [10] are used for analysis of the collected data. The students are tested on their capability to use sub-concepts as building blocks to answer the question completely and correctly. APOS classification resulted in most of the participants Intra and Inter level classification. The Triangulation method appeared as a strong method that can be applied for analysis of the participants' calculus knowledge as it was observed in [1].
IntroductionObserving engineering students' success in responding to calculus questions, particularly investigating the details on their conceptual understanding that involve multiple calculus concepts that require knowledge of other calculus concepts has been an interest of engineering educators. Pedagogical efforts have been made in understanding and improving engineering students' ability to respond to calculus questions in Science-Technology-Engineering-Mathematics (STEM) fields