Sound mathematical knowledge is an essential ingredient for student success in many disciplines, and quality mathematics support is crucial to that success. How that support is delivered is often the key to student engagement, satisfaction and positive outcomes. Many students require sound mathematical knowledge to engage in their discipline…

In this paper, we briefly introduce three theoretical frameworks for mathematical identity and why they matter to practitioners teaching undergraduate mathematics courses. These frameworks are narrative identities, communities of practice, and figured worlds. After briefly describing each theory, we provide examples of how each framework can be…

Over the last several centuries, mathematicians have developed sophisticated symbol systems to represent ideas often imperceptible to their five senses. Although conventional definitions exist for these notations, individuals attribute their personalized meanings to these symbols during their mathematical activities. In some instances, students…

Purpose: The purpose of the article is to gain more insight into factors that can explain students' success in business subjects. The focus is on the connection between performance in introductory courses in business mathematics (BM) and business statistics (BS) and success in various business subjects. Design/methodology/approach: Use of a…

Analogical reasoning has played an important role in the development of modern mathematics. However, there has been critique of analogies for the purpose of learning new mathematics. In this article, I counter that students can productively reason by analogy to learn new mathematics and even develop new mathematics themselves. I display examples…

Mathematics is one of the core subjects in engineering education and forms the foundation of all disciplines in engineering. In Hong Kong, a significant number of students are admitted to engineering programmes without sufficient mathematical background. Engineering mathematics is essential for teaching and learning many fundamental and advanced…

Combinatorial proof serves both as an important topic in combinatorics and as a type of proof with certain properties and constraints. We report on a teaching experiment in which undergraduate students (who were novice provers) engaged in combinatorial reasoning as they proved binomial identities. We highlight ways of understanding that were…

Preparing graduates for employment is the goal of postsecondary education. In response to the national quantitative reasoning deficiency, institutions have joined nationwide to align college math content and learning outcomes to meet the needs of common careers and everyday life. The problem addressed in this study is that traditional college math…

Recently, abstracted quantitative structures (AQS), a construct from quantitative reasoning, has been offered as a means to conceptualize and study mathematization during mathematical modeling. Extending this theoretical work, we provide empirical evidence that an intervention targeting participants' AQS can assist in aligning modelers' models…

The value of some university mathematics courses gets characterized within a liberal arts course of study in terms of supporting "critical thinking skills" or some other phrase for generally improved reasoning. This can be seen as an application of the millennia old "Theory of Formal Discipline" that claims that mathematics…

This keynote address explores the history and role of college math requirements with a focus on ensuring math courses serve to expand students' horizons, rather than serve as gatekeepers. It discusses the advent of general education math courses, which brought more students into math departments, which ultimately contributed to broadening the…

Mathematical problem posing, or authoring mathematical tasks, can allow students to integrate their interests and experiences into the classroom. Little research has explored different designs for scaffolding or facets of posed problem quality, particularly when problem posing is based on students' interests. We created an environment that enabled…

The promotion of belonging, purpose, and growth mindset through subtle social psychological interventions has been shown to positively impact student outcomes (Lazowski & Hulleman, 2016; Walton & Cohen, 2007; Yeager & Walton, 2011; Yeager et al., 2016). This study explores how instructor messaging and intentional course design can…

While proof has been studied from different perspectives in the mathematics education literature for decades, students continue to struggle to build proof comprehension. Complicating this, the manner in which proof comprehension is assessed largely remains to be the definition-theorem-proof format in which students are asked to reproduce proofs or…

This study investigates the embodied, symbolic, and formal reasoning of two fourth-year university students while exploring geometric reasoning about the Cauchy-Riemann equations with the aid of "Geometer's Sketchpad (GSP)." These students participated in a teaching activity designed to encourage shifts between embodied, symbolic, and…