This research centers on implementing Quantitative Reasoning (QR) within a differential equations course at an urban public community college. As a participant in the Numeracy Infusion for College Educators (NICE) faculty development program, I sought to integrate QR skills into my curriculum. Students in the course were introduced to QR goals…

The purpose of this paper is to describe the use of a problem involving superfactorials (a specific product of factorials) that provides an in-depth and comprehensive mathematical experience, encompassing skills that mathematicians view as tantamount to exploration. The problem is easily accessible and fosters creativity and perseverance, thereby…

Creativity plays an important role in mathematics, but it can be overlooked in undergraduate courses. This article describes three ways an existing first-year math seminar was modified to increase its focus on creativity: introducing readings and discussions related to creativity, drawing connections to creativity in other disciplines, and adding…

Of the many disciplines that rely on calculus, physics is among those with the strongest connections to this branch of mathematics. For instance, the derivative--one of the key notions of calculus--is used to describe velocity and acceleration, which play a central role in mechanics. In post-secondary education, in particular at the college level,…

LEGO® stop-motion animations were developed to engage first-year university students in the topics of matrices, vectors, linear geometry and linear transformations. LEGO® provided a versatile medium through which a wide range of concrete and abstract concepts could be physically demonstrated in both two and three dimensions. It was also familiar…

Nonlinear equations are usually solved numerically. However, approximated analytical solutions of nonlinear equations are useful as an initial iteration point for numerical methods. Furthermore, these analytical approximations are sometimes quite close to the actual root. In order to teach at undergraduate level how to perform this kind of…

Based on our work teaching undergraduate Calculus courses, we offer insight into teaching the chain rule to reduce cognitive load for students. A particularly difficult topic for students to grasp, problems likely arise due to student struggles with the concept of function and, particularly, function composition relative to when they first…

Students determined to be underprepared for college-level mathematics would be enrolled in a sequence of developmental mathematics courses before taking their college-level mathematics course. Students who started in the lowest level of developmental mathematics had a twenty percent chance of completing their college-level mathematics credits…

Critical thinking (CT) is an essential competency for global citizens in the 21st century. Few systematic reviews have evaluated and analyzed instructional interventions to enhance CT in mathematics at the university. This study includes 15 studies on cultivating CT among undergraduate students through instructional interventions within the…

This book provides a critical review of research in mathematics education published in or about the Australasian region in the four years from 2020 to 2023. Research in Mathematics Education in Australasia 2020-2023 (RiMEA 2020-2023) is the eleventh edition of the four-yearly review of mathematics education research in Australasia. It is compiled…

Research on developmental education reform has given surprisingly limited attention to what happens inside the classroom between faculty and students. Our qualitative study used interview data from 20 faculty and 20 students in corequisite math and English courses at one of the nation's largest and most racially diverse community college systems.…

Within the last decade, the National Council of Teachers of Mathematics (NCTM) has made a call to action, asking educators to engage in effective teaching of mathematics which includes having classrooms rich in mathematical discourse (NCTM, 2014). In this nine-week dissertation study, three mathematics graduate student instructors (GSIs) teaching…

The ubiquitous acquisition and generation of data require a reworking of curricula in introductory statistics in tertiary education. We present a renewed curriculum that focuses on scientific thinking, modeling, and simulation-based inference, utilizing R and various R tools such as shiny and learnr apps. We teach statistics from a data-centric…

In this paper we explore the difficulties engineering undergraduates encounter with tertiary mathematics. Results from our survey (N = 71) show that students in our sample face issues mostly related to the challenging nature of university mathematics, the absence of worked examples during lectures and the discontinuity of school and university…

Ciphers based on rotor machines were the state-of-the-art in the mid-1900s, with arguably the most famous being the German Enigma. We have found that students have great interest in the Enigma and its cryptanalysis, so we created our own rotor cipher that is simulated with shifting tables and can be cryptanalyzed. Ours and the historic rotor…