University of Oklahoma. His pedagogical research interest includes technology and calculus education of STEM majors. He worked on an IRB approved pedagogical study to observe undergraduate and graduate mathematics and engineering students' calculus and technology knowledge in 2011. His other research interests include nonlinear optimization, financial engineering, facility allocation problem, vehicle routing problem, solar energy systems, machine learning, system design, network analysis, inventory systems, and Riemannian geometry. Gabriela C Gualpa, Quinnipiac UniversityGabriela is currently a second semester junior attending Quinnipiac University. Engineering and mathematics undergraduate and graduate students' conceptual function knowledge can have an important impact on their success in conceptually advanced courses. In building blocks of STEM concepts, function concept requires knowledge of sub-concepts such as limit, first derivative, second derivative, and asymptote. In this study, calculus concept knowledge of seventeen undergraduate and graduate engineering and mathematics students enrolled in a Numerical Methods-Analysis course at a large Midwest Research Institution are analyzed based on their responses to a calculus graphing question similar to the research question of Baker, Cooley, and Trigueros (2000). This question is analyzed qualitatively and quantitatively by using the triad classification in Action-Process-ObjectSchema (APOS) theory. Mathematics graduate and undergraduate students succeeded the most among all the participants.

Quinnipiac University. He completed a Ph.D. in Mathematics and another Ph.D. in Industrial and Systems Engineering at the University of Oklahoma. His pedagogical research interest includes technology and calculus education of STEM majors. He worked on several IRB approved pedagogical studies to observe undergraduate and graduate mathematics and engineering students' calculus and technology knowledge since 2011. His other research interests include nonlinear optimization, financial engineering, facility allocation problem, vehicle routing problem, solar energy systems, machine learning, system design, network analysis, inventory systems, and Riemannian geometry. Hasan Alp Tekalp Mrs. elif naz tekalp My name is Elif Naz Tekalp. I am a junior industrial engineering student at Quinnipiac University. I also have mathematics and general business minor. I am interested in the role of mathematics in engineering education and professional life. I was very passionate about the research that I participated with my Dr.

Success in many engineering and mathematics courses is tied to well-developed calculus knowledge. Several important calculus concepts used in STEM courses include limit, first derivative, second derivative, and asymptote. In this article, undergraduate and graduate engineering and mathematics students' ability to transform an algebraic function to its geometric representation is analyzed. Participants were either enrolled or recently (two week period) completed a Numerical Methods/Analysis course during the data collection period. Video recorded and written responses to graphing a quotient function are analyzed by using Action-ProcessObject-Schema (APOS) theory. Participants are asked to sketch the graph of the given quotient function after calculating its limiting values, first derivative, second derivative and asymptotes. Qualitative and quantitative results indicated Mathematics majors' higher success rate among all the participants.

No abstract

University of Oklahoma. His pedagogical research interest includes technology and calculus education of STEM majors. He worked on an IRB approved pedagogical study to observe undergraduate and graduate mathematics and engineering students' calculus and technology knowledge in 2011. His other research interests include nonlinear optimization, financial engineering, facility allocation problem, vehicle routing problem, solar energy systems, machine learning, system design, network analysis, inventory systems, and Riemannian geometry.c American Society for Engineering Education, 2016 Evaluation of Engineering & Mathematics Majors' Riemann Integral Definition Knowledge by Using APOS TheoryIn this study senior undergraduate and graduate mathematics and engineering students' conceptual knowledge of Riemann's definite integral definition is observed by using APOS (Action-ProcessObject-Schema) theory. Seventeen participants of this study were either enrolled or recently completed (i.e. 1 week after the course completion) a Numerical Methods or Analysis course at a large Midwest university during a particular semester in the United States. Each participant was asked to complete a questionnaire consisting of calculus concept questions and interviewed for further investigation of the written responses to the questionnaire. The research question is designed to understand students' ability to apply Riemann's limit-sum definition to calculate the definite integral of a specific function. Qualitative (participants' interview responses) and quantitative (statistics used after applying APOS theory) results are presented in this work by using the written questionnaire and video recorded interview responses. Participants are asked to calculate the definite integral of the function f(x) = x 2 on the interval [1, 2] by using the limit definition of Riemann integral. Missing conceptual knowledge of the participants in calculus are observed when they were incapable of determining the solution to the problem.