Although complex analysis is part of the study programs of many mathematics undergraduates, little research has been done on how individuals interpret basic concepts from complex analysis. To address this gap, this paper investigates how experts individually think about complex path integrals. For this purpose, the commognitive framework is used…

We discuss how research on student difficulties was used as a guide to develop, validate, and evaluate a Quantum Interactive Learning Tutorial (QuILT) to help students learn how to determine the completely symmetric bosonic or completely antisymmetric fermionic wave function and be able to compare and contrast them from the case when the particles…

This paper describes our work to determine the naturalistic images that first-time second-semester university calculus students possess for series convergence. We found that the students we interviewed most frequently determined whether a series converged by imagining a process of appending summands into a running total and examining whether this…

How should our students think about external forcing in differential equations setting, and how can we help them gain intuition? To address this question, we share a variety of problems and projects that explore the dynamics of the undamped forced spring-mass system. We provide a sequence of discovery-based exercises that foster physical and…

A textbook model of a contagious disease, the dynamics of which are represented by the SIS epidemic model with saturating treatment, is considered. I show that this model, as originally formulated, is not dimensionally consistent. The model can be fixed by including a dimensional constant [alpha] of value one (with units individuals[superscript…

Students in a course on the psychology of language and thought first wrote flash fiction stories and analyzed them using course concepts. As an experiential learning exercise, they subsequently analyzed those stories for a number of psycholinguistic variables using the discourse technology Coh-Metrix. Their assignment was to change a number of…

Structural concepts are fundamentals of civil engineering for students to learn, for lecturers to teach and for engineers to use. Many students however find it difficult to understand structural concepts due to their abstract nature. "Seeing and Touching Structural Concepts" has been developed as an approach to help civil engineering…

Reasoning about visual representations in science requires the ability to control one's attention, inhibit attention to irrelevant or incorrect information, and hold information in mind while manipulating it actively--all aspects of the limited-capacity cognitive system described as humans' executive functions. This article describes pedagogical…

Reasoning about visual representations in science requires the ability to control one's attention, inhibit attention to irrelevant or incorrect information, and hold information in mind while manipulating it actively--all aspects of the limited capacity cognitive system described as humans' Executive Functions (EFs) (see Diamond, 2002). This…

Connection-making among multiple representations is a crucial but difficult competence in STEM learning. Prior research has focused on one type of learning process involved in connection-making: sense-making processes leading to conceptual understanding of connections. Yet, other research suggests that a second type of learning process is…

To advance the pedagogical discussion on adopting third-party certifications in marketing courses, this article examines responses of undergraduate students with different learning styles to the online certification program incorporated into marketing classes. While the overall student opinions were positive especially as a valuable addition for…

Connection-making among multiple representations is a crucial but difficult competence in STEM learning. Prior research has focused on one type of learning process involved in connection-making: sense-making processes leading to conceptual understanding of connections. Yet, other research suggests that a second type of learning process is…

[This paper is part of the Focused Collection on Curriculum Development: Theory into Design.] Research in physics education has contributed substantively to improvements in the learning and teaching of university physics by informing the development of research-based instructional materials for physics courses. Reports on the design of these…

Open-ended questions that can be solved using different strategies help students learn and integrate content, and provide teachers with greater insights into students' unique capabilities and levels of understanding. This article provides a problem that was modified to allow for multiple approaches. Students tended to employ high-powered, complex,…

Learning physics often requires overcoming common misconceptions based on naïve interpretations of observations in the everyday world. One proposed way to help learners build appropriate physics intuitions is to expose them to computer simulations in which motion is based on Newtonian principles. In addition, playing video games that require…