A typical mathematics assignment consists of a block of problems devoted to the same topic, yet several classroom-based randomized controlled trials have found that students obtain higher test scores when most practice problems are mixed with different kinds of problems--a format known as interleaved practice. Interleaving prevents students from…

We propose some generalizations of the classical Division Algorithm for polynomials over coefficient rings (possibly non-commutative). These results provide a generalization of the Remainder Theorem that allows calculating the remainder without using the long division method, even if the divisor has degree greater than one. As a consequence we…

Although we move and live in three-dimensional space, many prefer "two-dimensional" thinking in mathematics lessons. As a result, the transition between physical objects and their graphical representations can be considered one of the most common difficulties in learning and teaching solid geometry. This paper describes results of our…

Despite the increasing amount of research on students' quantitative reasoning at the secondary level, research on students' quantitative reasoning at the undergraduate level is scarce. The present study used task-based interviews to examine 16 high-performing undergraduate calculus students' quantitative reasoning in the context of solving three…

In this study, we investigated two students', ages ten and eleven, emotions while they engaged in mathematical problem solving. During three task-based interviews, the students explored parts of the unsolved problem the Graceful Tree Conjecture. While they were engaged in the interviews, they self-identified the emotions of frustration and joy…

A typical mathematics assignment consists of a block of problems devoted to the same topic, yet several classroom-based randomized controlled trials have found that students obtain higher test scores when most practice problems are mixed with different kinds of problems -- a format known as interleaved practice. Interleaving prevents students from…

In the first main section of this thesis, I investigate superirreducible polynomials over fields of positive characteristic and also over [set of rational numbers] and [set of integers]. An n-superirreducible polynomial f(x) is an irreducible polynomial that remains irreducible under substitutions f(g(x)) for g of degree at most n. I find…

The notion or expectation of simplifying final mathematical results remains problematic in that it is ill-defined, tied more closely to algorithmic versus conceptual understanding, and decontextualized from the content, purpose, and application of the mathematics in question. In this article, the authors advocate for a tool-focused view of…

In higher education, diversity, equity, and inclusion (DEI) statements are texts written by faculty members which explain their commitments to improving education for marginalized students. Requesting, reviewing, and acting upon DEI statements is just one practice, among others, which higher education institutions can use to transform individual…

The COVID-19 pandemic posed significant challenges for practical teaching within the sciences. While many instructors adopted innovative alternatives to conventional practicals, many relied on digital approaches that did not give students hands-on experience. In this study we evaluate the use of 'at home' practical kits used in first year physics…

Escape rooms are collaborative puzzle solving activities that require the participants to utilize logical reasoning and teamwork. With a slight refocusing on previously acquired knowledge, escape rooms can also be used to test and promote learning of certain topics. This paper describes the development of a one-hour in-person STEM focused escape…

Teachers' conceptions of teaching play a key role in the pedagogical practices they apply in their teaching. Previous studies of conceptions of teaching generic skills have been mainly qualitative with small samples, and thus there is a need for a more extensive quantitative study. This study investigates the associations between higher education…

Problem-solving competency is crucial for social development, especially in complex environments. In mathematics education, problem-solving enhances logic, creativity, and analytical skills, contributing to societal progress. This article identified quantitative information about important publications, authors, resources, and research trends on…

Case-based learning (CBL) is a learner-centric educational approach that fosters independent learning and exploration through case analysis, guided by teachers' heuristic instruction. The study aimed to evaluate the efficacy of CBL versus traditional teaching methods in advanced breast cancer education for residents. In this randomized controlled…

The development of geocapabilities has been a concern in geographical education, and the application of geospatial technologies such as geographical information systems (GIS) has been popularized in both geography and non-geography courses. However, there are still gaps in how GIS courses could be designed to promote students' geocapabilities. In…