We describe a lecture-free problem-solving Mathematical Communication and Reasoning (MCR) course that helps students succeed in the Introduction to Advanced Mathematics course. The MCR course integrates elements from Uri Treisman's Emerging Scholars workshop model and Math Circles. In it students solve challenging problems and form a supportive…

We automate and randomize the building of linear systems with a parameter, appropriate for assigning to students. When the parameter takes on a specific value, the system has no solutions. When the parameter takes on a different value, the system has an infinite number of solutions.

Students need a robust understanding of the derivative for upper-division mathematics and science courses, including thinking about derivatives as ratios of small changes in multivariable and vector contexts. In "Raising Calculus to the Surface" activities, multivariable calculus students collaboratively discover properties of…

Perusall, a collaborative reading tool, was introduced in an advanced reading and writing skills course in Hong Kong to increase engagement with texts and encourage critical discussion during the COVID-19 face-to-face class suspension. Students were asked to use the Perusall platform to complete pre-class readings, highlight and annotate text and…

Generative large language models (LLMs) like ChatGPT can quickly produce informative essays on various topics. However, the information generated cannot be fully trusted, as artificial intelligence (AI) can make factual mistakes. This poses challenges for using such tools in college classrooms. To address this, an adaptable assignment called the…

General Chemistry I is known as a STEM (Science, Technology, Engineering, Mathematics) gatekeeper, often playing a role in determining students' STEM college pathways and their career prospects. However, there have been recent efforts to transform General Chemistry I from a gatekeeper course into a gateway course by implementing equity approaches.…

This design case documents the development of a new online training program to teach circuit court interns in Wise County, Virginia, how to create smart land records, or land record abstracts stored on a blockchain. The authors first describe the instructional context behind land record abstraction and the clients' original specifications for the…

It has become increasingly important for future business professionals to understand statistical computing methods as data science has gained widespread use in contemporary organizational decision processes in recent years. Used by scores of academics and practitioners in a variety of fields, Monte Carlo simulation is one of the most broadly…

In this note we demonstrate two instances where matrix multiplication can be easily verified. In the first setting, the matrix product appears as matrix element concatenation, and in the second, the product coincides with matrix addition. General proofs for some results are provided with a more complete description for 2×2 matrices. Suggested for…

A literature review is an important part of conducting academic research. Knowing how to conduct a literature search and write a high-quality literature review is a valuable skill. Herein, the authors describe the method of introducing a literature review writing exercise in an upper-level biochemistry course. Since 2020, authors have collaborated…

This paper is written to provide ideas and guide faculty who want to design a mathematical modeling course for undergraduate mathematics majors and minors. We discuss course goals, assignments, and projects that can be used to help students gain experience relevant for careers and mathematical modeling opportunities. The authors designed this…

An instructional approach is presented for teaching the mole concept to high school introductory-level chemistry classes. Extensions to the strategy are presented for more advanced classes. The strength of the approach is based upon discovery. Students discover the Avogadro number and the mole concept. The discovery is based upon calculations that…

In this paper, a problem set activity focused on understanding and applying unsupervised and supervised chemometric methods for the analysis of biodiesel-diesel blended fuels is described. This problem set was utilized in two upper-level analytical elective courses aimed for junior and senior level students. The data set consists of peak areas…

Quantum computing is a growing field at the intersection of physics and computer science. The goal of this article is to highlight a successfully trialled quantum computing course for high school students between the ages of 15 and 18 years old. This course was designed to bridge the gap between popular science articles and advanced undergraduate…

We present an instructional approach to teaching causal inference using Bayesian networks and "do"-Calculus, which requires less prerequisite knowledge of statistics than existing approaches and can be consistently implemented in beginner to advanced levels courses. Moreover, this approach aims to address the central question in causal…