The objective of this article is to determine which are the international standards and norms of usability that are used in educational technology applied to the teaching of mathematics at secondary and higher education levels, focused on two scenarios: (1) digital educational resources and virtual learning environments (VLEs), and (2) game-based…

In Australian universities, mathematics is often an essential core subject for disciplines such as engineering, information technology and science. These first-year mathematics subjects may have large enrolments of which a significant number fail the subject and repeat. While interventions to retain students are common, those who have failed…

In a recent article, Crider recommends ending a course with a memorable learning experience, called an epic finale, instead of a final exam. Here, we give the details of epic finales given in four mathematics courses: Discrete Mathematics, Information and Coding Theory, Real Analysis, and Complex Analysis. We describe how to reconfigure a course…

Students' proof abilities were explored in the context of an inquiry-based learning (IBL) approach to teaching an introductory proofs course. IBL is a teaching method that puts the responsibility for proof on students and focuses on student discussion and exploration. Data collected from each of the 70 participants included a portfolio consisting…

Virtual learning environments give students more autonomy over their learning than traditional face-to-face classes and require that students adapt the ways they consume and assimilate new information. One theory of this process is self-regulated learning, which is illustrated in Efklides' Metacognitive and Affective model of Self-Regulated…

This study was designed to examine the use of mistakes to promote students' performance in undergraduate Algebra classes by developing a growth mindset. Participants were seventy-four students from three Algebra classes and received one of the three interventions along with regular instruction: (a) growth mindset feedback on mistakes…

Mathematics is used in the physical sciences to describe and model phenomena, resulting in a unique interface between mathematics and disciplines such as chemistry and physics. This paper focuses on themes emerging from a larger project that investigated how students understand and use mathematics in chemical kinetics, a field of study concerned…

Computer programming and mathematical algorithms are natural partners in the development of programming skills, logical thought, and a deeper understanding of mathematical concepts. We present the details of a course which blends the two at the sophomore level. This course is required of our mathematics majors, but attracts mathematics minors from…

In our modern world, we are inundated and grapple with data daily. As mathematicians, we are often more comfortable discussing the behavior of functions presented analytically, in contrast with the data-driven or tabular presentations of functions ubiquitous in our culture. This paper introduces an entry-level course, Mathematical Modeling and…

The activity described in this paper is based on the idea that reading an introductory undergraduate mathematics text is similar to reading instructions. I want my students to think about how to read when the goal is to learn to complete a task. I give them written instructions for doing a card trick and ask them to complete the trick. The…

In this paper we analyze common solutions that students often produce to isomorphic tasks involving proportional situations. We highlight some key distinctions across the tasks and between the different equations students write within each task to help elaborate the different interpretations of equivalence at play: numerical, transformational, and…

Flipped classroom (FC) pedagogical frameworks have recently gained considerable popularity, especially at secondary school levels. However, there are rich opportunities to explore FC at tertiary levels, but progress on the area requires instructors' attention to well-designed tasks for students' collaborative learning. Realistic Mathematics…

Nationwide, many students fail to complete the key mathematics courses that are required for most STEM majors, including Precalculus. This paper describes the rationale, implementation, and impact of the redesign of Precalculus at one regional west coast institution. Prior to the redesign, pass rates in Precalculus were modest (75.8% of all…

This article looks at an interdisciplinary college movement and mathematics course from the perspectives of one of its co-creators and a mathematics education researcher. It suggests deep, embodied use of choreographic problem solving can form an effective path to mathematics learning through (a) conceptual overlap between mathematics and dance,…

This paper deals with a set of geometrical problems for mathematical problem-solving at different difficulty levels. All of these are presented as national flags and one has to investigate invariant area proportions when changing the locus of any corner of the flag. This dynamic element suggests the usage of dynamical geometry environments.…