This is a case study of a two-semester Extended Calculus course that utilizes standards-based grading. The course integrates Intermediate Algebra, College Algebra, Pre-calculus, and Calculus I, making it possible for students to take the course without any prerequisites. The authors compare the persistence of students in this course and Calculus II with students completing prerequisite course(s) followed by Calculus I. Students in Extended Calculus who were placed into Intermediate Algebra persisted and passed Calculus I and II at significantly higher rates than their peers in prerequisite courses. The authors discuss course logistics and share student learning objectives and analyze survey data about student experiences, self-efficacy, and belonging.

This paper discusses multiple versions of an activity in which participants create, discuss, and analyze possible definitions of the term “sandwich.” This activity has helped us humanize mathematical practices in a low-stakes context, build community in mathematical spaces, model and reflect on effective collaboration for active learning, and peer under the hood of mathematics disciplinary practices around constructing definitions and examples. We have used this activity virtually, both synchronously and asynchronously, and face-to-face, with a wide range of participants, including for secondary, major and non-major undergraduate, and graduate mathematics students and for teaching professional development. This paper will discuss motivation, various implementations, and some outcomes of the activity.

To help students develop a more creative and inquisitive mathematical mindset, we present capstone-style explorations on finding roots of hyperbolic numbers, a generalization of the complex numbers. We include pedagogical reflections, informed by our use of the activities in a capstone course. The explorations are suitable (and challenging!) for undergraduates who are embarking on more abstract mathematics beyond the standard calculus sequence. Students will engage in mathematically enriching tasks such as looking for geometric meaning in algebra, drawing conclusions from equations without solving them, working in hyperbolic coordinates, and making and testing their own conjectures. The explorations may be used in a variety of research-style learning environments, such as a capstone course, an honors project, or an undergraduate research experience.

The teaching and learning of calculus is enhanced by applications to real-world problems. The topic of optimization (finding the maximum or minimum of a function) is a place where many calculus instructors emphasize applications. However, the breadth of applications explored in optimization is usually quite limited. In this paper, we show how the classic statistics problem of fitting a model to data can be incorporated as an application of optimization techniques in single and multivariable calculus classes. In particular, we introduce the reader to the method of maximum likelihood estimation, illustrate its use via a number of examples, and provide a link to a larger collection of worked examples online. We also describe the positive impact that including this material had on student attitudes in a calculus class.

Utilizing active learning, especially game- based learning, within a mathematics classroom can help increase retention, motivation, and overall positive emotions about mathematics. This article presents a case study of using in-class learning activities, based off of popular card games, within an Introduction to Mathematics of Computer Science course. Throughout the paper, games are presented and student feedback is summarized. All games increased students' understanding of course content. These games can be adapted to any undergraduate mathematics course.

This article describes the design and implementation of an upper-level undergraduate geometry course at a Canadian university, employing hands-on pedagogy through interactive online workshops. These workshops were co-designed and facilitated by international experts and the instructor during the COVID-19 pandemic. This collaboration preserved the depth of abstract content while enriching it with tangible activities and interactive engagement, enhancing student motivation and deepening their understanding of geometry's connections to art and culture. Positive student feedback underscored the effectiveness of this approach. Practical strategies are also offered for instructors seeking to incorporate similar hands-on, sustainable, and low-cost activities into online mathematics courses.

In an effort to keep students on track in their degree programs, the Department of Applied Mathematics at the University of Colorado Boulder offers a Winter Break Calculus 1 course for students whose fall semester Calculus 1 course grades are just below the passing threshold. This paper discusses the structure of this course and presents preliminary evidence to judge its successfulness. The 3-week course is taught remotely over winter break and covers the same content as the semester-long course. The vast majority of winter break students complete the course with a passing grade, allowing them to advance to Calculus 2 in the spring semester without needing an extra semester to repeat Calculus 1. Results show that the winter break students are much more likely to pass Calculus 2 within a year than students who declined to enroll. An examination of students from underrepresented groups shows similar positive results. These analyses lead us to believe that this winter break course is successful at keeping more students on a path towards graduation in their desired degree program.

In this lesson analysis, the topic of the lesson is a module on choosing an appropriate differentiation strategy. The course context is a lesson used at two public, 4-year, open-admissions institutions in the southeastern United States. It occurs midway through a Calculus 1 course with a wide variety of STEM majors. The instructional challenge we seek to address is that calculus students are often mainly exposed primarily to procedural ideas and seldom experience ideas that are more conceptual and less procedural. Combining differentiation strategies, including the product, quotient, and chain rule, is one such idea that requires a conceptual understanding of functions, especially composition of functions, as well as a procedural understanding of finding derivatives. Finally, we give a brief overview of the instructional approach: this module uses differentiation strategies implemented conceptually through a Team-Based Inquiry Learning (TBIL) approach, which includes assessing a given function and communicating the properties that lead to choosing the appropriate derivative techniques. At this point in the semester, students have been exposed to the derivative rules, but not many applications or ideas where they are required to build on the procedural knowledge or synthesize large amounts of information. Students work with their teams, engaging with carefully scaffolded inquiry activities that are facilitated by the instructor. Students think critically about what they are doing versus just following a sequence of steps.

This editorial presents the special issue titled Linear Algebra Education: An International Perspective. We highlight the significant role of linear algebra in undergraduate mathematics curricula and provide an overview of each paper included in this issue. The authors offer theoretical and practical insights and effective teaching strategies designed to enhance the instruction and understanding of linear algebra. We hope the innovative approaches highlighted in this special issue will inspire educators and help spark curiosity, excitement, and deeper understanding as students engage with the fascinating world of linear algebra.