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…

When thinking of early childhood STEM, images of active, play-based design challenges, experiences with robotics/coding, or hands-on experiences with open-ended materials (e.g., balls, ramps, loose parts) often come to mind. While these are certainly images that align with developmentally appropriate early childhood STEM practices, some of the…

Since the content of the Theory of Interest course in an actuarial science program is tied to an external exam, instructors may be hesitant to attempt to use inquiry-based learning. In this paper, I outline how and why I did so, including descriptions of the materials that I wrote. I found that student performance on the final exam improved…

Historically, math education at the high school and introductory college levels has focused on computational skills. With the advancement of computational technologies, problemsolving and other higher-order thinking skills should become the focal point. This article discusses ways in which the University of Minnesota has integrated problem-solving…

The COVID-19 pandemic has been one of the greatest challenges faced for a very long time. However, it has also presented educators with novel opportunities for teaching, none more so than in science. There are the obvious links between COVID-19 and the body of scientific knowledge that curriculum designers think educators should help students to…

In calculus, related rates problems are some of the most difficult for students to master. This is due, in part, to the nature of the problems, which require constructing a nuanced mental model and a solid understanding of the function. Many textbooks present a procedure for their solution that is unlike how experts approach the problem and elide…

Students' negative affective performance in mathematics learning is a global problem, and the situation is especially challenging in high-achieving East Asian countries. Taiwan's Just Do Math (JDM) program was launched to resolve this problem and to serve as an example of successful scaling up with regard to implementation of innovation. We…

Despite the call for instructional designers to employ design thinking as a means to foster creativity in problem-solving, many students struggle with enacting creative risk. While several studies have been conducted studying how instructional designers engage in problem-solving to contend with project constraints, few have addressed whether this…

Comparison is a powerful and important way that we learn. To support teachers in the use of comparison in their instruction, the authors developed an instructional routine called compare and discuss multiple strategies (CDMS). Similar to other instructional routines, CDMS is a structured, specific, repeatable minilesson that teachers can use to…

The author focused on solving problems of third-degree price discrimination under a monopoly by integrating microeconomic theory and spreadsheet modeling. Price discrimination refers to a firm situation in which the same good is sold to different groups of consumers at different prices. First, the author included an introductory math background…

Research shows that when students engage with mathematical inquiry their problem-solving skills are strengthened. Demands in the revised Australian curriculum raised problem-solving of new senior secondary mathematics assessment, specifically in Queensland Problem-solving and Modelling Tasks (PSMTs). The challenge for Queensland was to scale…

Bringing peace to the world is a profound aspiration, and it can be achieved by instilling the values of empathy, compassion, and respect in young children through humane education. Humane education sows the seeds of hope for a future that can heal our planet and usher in positive societal change. Humane education fosters empathy and ethical…

Design thinking--a human-centered approach to problem solving--is a process by which K-12 teachers engage students in solving relevant issues that occur in their schools. In this article, the authors describe a project in which fourth-graders used design thinking to solve an unexpected issue related to a much-anticipated class project. The project…

Transforming an observable phenomenon into a tractable model is a challenging process, from determining the appropriate modeling scale to making realistic simplifying assumptions. However, many modeling texts are anchored around problems that have already been synthesized into a digestible format, which inhibits an opportunity to engage students…

Analogical reasoning is a core facet of higher cognition in humans. Creating analogies as we navigate the environment helps us learn. Analogies involve reframing novel encounters using knowledge of familiar, relationally similar contexts stored in memory. When an analogy links a novel encounter with a familiar context, it can aid in problem…