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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…
The Weihrauch degrees are a tool to gauge the computational difficulty of mathematical problems. Often, what makes these problems hard is their discontinuity. We look at discontinuity in its purest form, that is, at otherwise constant…
We survey the history and recent developments around two decades-old problems that continue to attract a great deal of interest: the slicing $\times 2$, $\times 3$ conjecture of H. Furstenberg in ergodic theory, and the distance set problem…
Undergraduate students of mathematics continue to solve equations in virtually any course they attend, just as they did in secondary school -- yet what do they learn about equations and their solutions at university? Are they capable to…
The rate vs. distance problem is a long-standing open problem in coding theory. Recent papers have suggested a new way to tackle this problem by appealing to a new hierarchy of linear programs. If one can find good dual solutions to these…
In a companion paper, we discuss students' ability to take advantage of what they learn from a solved problem and transfer their learning to solve a quiz problem that has different surface features but the same underlying physics…
We describe a study focusing on students' and faculty members' reasoning about problems of differing cognitive complexity related to the double-slit experiment (DSE) with single particles. In the first phase of the study, students in…
Linear algebra represents, with calculus, the two main mathematical subjects taught in science universities. However this teaching has always been difficult. In the last two decades, it became an active area for research works in…
Research-validated multiple-choice questions comprise an easy-to-implement instructional tool that serves to scaffold student learning and formatively assess students knowledge. We present findings from the implementation, in consecutive…
This paper frames calculus as a global, centuries-long development rather than a subject that began only with Newton and Leibniz. Drawing on ideas from Greek, Indian, Islamic, and later European mathematics, it highlights how concepts like…
This article has been written for an educational magazine whose target audience consists of students and teachers of mathematics in universities, colleges and schools. It concerns a notion of duality between rectangles. A proof is given…
A bilateralist take on proof-theoretic semantics can be understood as demanding of a proof system to display not only rules giving the connectives' provability conditions but also their refutability conditions. On such a view, then, a…
The unbounded knapsack problem can be considered as a particular case of the double partition problem that asks for a number of nonnegative integer solutions to a system of two linear Diophantine equations with integer coefficients. In the…
This paper outlines a deceptively complex problem in classical mechanics which the paper names the "Falling Astronaut Problem," and it explores a method for teachers to implement this problem in an undergraduate classroom. The paper…
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…
We study the unit distance and distinct distances problems over the planar hypercomplex numbers: the dual numbers $\mathbb{D}$ and the double numbers $\mathbb{S}$. We show that the distinct distances problem in $\mathbb{S}^2$ behaves…
High school science classrooms across the United States are answering calls to make computation a part of science learning. The problem is that there is little known about the barriers to learning that computation might bring to a science…
There has been an increasing trend of females performing better than males academically across the mathematical engineering courses. To confirm this assumption, final marks of two independent samples of students from Calculus courses across…
For more than half a century, dualities have been at the heart of modern physics. From quantum mechanics to statistical mechanics, condensed matter physics, quantum field theory and quantum gravity, dualities have proven useful in solving…
Creating a study program for optimal academic completion is a complex assignment. Especially programs in the science, technology, engineering, and mathematics field are known for extended completion time as well as high drop-out rates…