This investigation evaluated the degree to which creativity training, idea generation instruction, and creative process impacted idea production, creativeness of solutions, and leadership effectiveness. Three sets of hypotheses were tested with a 114 groups of adults. First, groups whose members had some (i.e., one CPS course) or advanced training…

Spurred by Kilpatrick's (1987) "Where do good problems come from?", this study explores problem-posing triggers of experienced problem posers for mathematics competitions. Triggers are conceived as instances of noticing, where an impulse draws a poser's attention and "triggers off" a mathematical re-action, one of the outcomes…

Students often struggle with the concept of dependence of events or random variables. We present a simple coin flipping game that yields surprising results due to the dependencies within the game. The game is simple enough for young children to understand and play, yet complex enough to yield results that are counterintuitive to even most graduate…

The current work builds on research demonstrating the effectiveness of Productive Failure (PF) for learning. While the effectiveness of PF has been demonstrated for STEM learning, it has not yet been investigated whether PF is also beneficial for learning in non-STEM domains. Given this need to test PF for learning in domains other than…

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…