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Starting from the well-known and elementary problem of inscribing the rectangle of the greatest area in an ellipse, we look at possible, gradually more and more complicated variants of this problem. Our goal is to demonstrate to an average…
While proof is a central component of postsecondary mathematical study, proof construction has historically posed significant difficulties for students who intend to earn mathematics degrees at the undergraduate level. This work is…
Introductory programming courses often emphasize mastering syntax and basic constructs before progressing to more complex and interesting programs. This bottom-up approach can be frustrating for novices, shifting the focus away from problem…
Quantum mechanics is a field often considered very mathematical, abstract, and unintuitive. One way some instructors are hoping to help familiarize their students with these complex topics is to have the students see quantum effects in…
The importance of innovation in the world's economy, now undeniable, draws great attention to the need to improve organizations' creative potential. In the last 60 years, hundreds of books have been written on the subject and hundreds of…
Very little is known about how the nature of expertise in introductory and advanced courses compares in knowledge-rich domains such as physics. We develop a framework to compare the similarities and differences between learning and patterns…
Many have argued that statistics students need additional facility to express statistical computations. By introducing students to commonplace tools for data management, visualization, and reproducible analysis in data science and applying…
In the U.S., introductory calculus-based courses often acts as a gatekeeper to STEM degrees. But access to the prerequisite math is far from equal--students from low-income and racially marginalized communities are far less likely to have…
There is a growing consensus that physics majors need to learn computational skills, but many departments are still devoid of computation in their physics curriculum. Some departments may lack the resources or commitment to create a…
Computation is becoming an increasingly important part of physics education. However, there are currently few theories of learning that can be used to help explain and predict the unique challenges and affordances associated with…
Much effort and research has been invested into understanding and bridging the gaps which many students experience in terms of contents and expectations as they begin university studies with a heavy component of mathematics, typically in…
In their study of physics beyond the first year of University -- termed upper-division in the US, many of students' primary learning opportunities come from working long, complex back-of-the-book style problems, and from trying to develop…
New technologies, such as MOOCs, provide innovative methods to tackle new challenges in teaching and learning, such as globalization and changing contemporary culture and to remove the limits of conventional classrooms. However, they also…
The evolution of science education is a dynamic process driven by advances in pedagogy, technology, and especially, our understanding of how students learn. Educators are exploring innovative teaching and learning methodologies such as…
This paper is one of a series in which elementary-education practice is analyzed by comparison with the history of mathematics, mathematical structure, modern practice, and (occasionally) cognitive neuroscience. The primary concerns are:…
The widespread establishment of computational thinking in school curricula requires teachers to introduce children to programming already at primary school level. As this is a recent development, primary school teachers may neither be…
"Math is not a spectator sport." "Lecturing is educational malpractice." Slogans like these rally some mathematicians to teach classes that feature "active learning", where lecturing is eschewed for student participation. Yet as much as I…
Shaping first year students' mind to help them master abstraction skills is as crucial as it is challenging. Although abstraction is a key competence in problem-solving (in particular in STEM disciplines), students are often found to rush…
With an investigation into how students in a physics Master of science program make sense of their whole first year study experience in one of the years following a programme reform, we try to offer insights and advice to consider when…
We describe the development of a junior-senior level course for Physics majors designed to teach Mathematica skills in support of their undergraduate coursework, but also to introduce students to modern research level results. Standard…