This work is the result of a pre-experiment carried out as part of a master's course, dealing with the study of the parabola through different mathematical views. It aims to recognize possible didactic obstacles in its teaching, based on intuitive manifestations in the resolution of a didactic situation based on GeoGebra software. The methodology…

We present the theoretical argument that the use of mathematics in physics can be productively conceptualized as using a language and that learning to make sense of physics equations and appropriating them into novel scientific inquiry can be understood as a process of learning to read fluently with a high level of reading comprehension and to…

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…

The integration of visual programming in early formal education has been found to promote computational thinking of students. Teachers' intuitive perspectives about optimal learning processes -- "folk psychology" -- impact their perspectives about teaching "folk pedagogy" and play a significant role in integrating educational…

This paper explores how a professional learning community (PLC) redesigns high school mathematics lessons towards a shared commitment. We describe the nature of a PLC's collective curricular vision to illuminate how teachers can come to new understandings as a group in order to shift the ways students experience mathematics. Using the curricular…

Mathematical modeling is a challenging and creative process. If one considers only interim or final solutions to modeling problems or interviews modelers afterward, often only their "explicit" models are accessible -- those expressed in work products or evinced in verbal and written reflections. The inner world of tacit knowledge and its…

Two foundational concepts in biology education are 1) offspring are not identical to their parents, and 2) organisms undergo changes throughout their lives. These concepts are included in both international and U.S. curricular standards. Research in psychology has shown that children often have difficulty understanding these concepts, as they are…

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…

In response to the authors, I demonstrate how threshold concepts offer a means to both contextualise teaching and learning of quantum physics and help transform students into the culture of physics, and as a way to identify particularly troublesome concepts within quantum physics. By drawing parallels from my own doctoral research in another area…

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…

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…

Ah ha moments are often mentioned in education literature. These moments are suggested to be a powerful aspect of learning, yet limited research is present regarding this topic. Ah ha learning moments have also not been defined in the education literature, resulting in the likelihood that each educator and learner may have differing definitions.…

This research examined the decisions that highly experienced outdoor leaders made on backpacking expeditions conducted by a tertiary institution in the Southern Alps of New Zealand. The purpose of the research was to document decision problems and explore them as Recognition-Primed Decisions (RPD) within naturalistic decision making (NDM)…