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.

Beginning in the first semester, it is important to affirm students' gender identities and also provide level-appropriate information about pronouns and gender-inclusive language, including the current cultural contexts. As students take advanced courses, incorporating topics that address gender diversity provides opportunities for them to develop…

This article's author describes an upper-level economics course that introduces students to experimental economics. The course, built around a term-long project requiring students to develop experiments in small groups, has two main objectives: (1) solidify students' learning of key economic concepts, and (2) introduce students to experimental…

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…

An advanced graduate-level financial accounting theory course should provide integral content for all accounting programs. However, we are aware that such courses are not always required at either the undergraduate or graduate level. We taught the accounting theory class at three institutions for many years, and as a result, we provide our views…

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…

Discussions of the primary literature are an important part of undergraduate education, and much work has been done to develop methods of integrating the literature into the curriculum. Examples include individual single-article discussion activities, literature-based courses, and regular journal club events. While many published examples focus on…

We describe a three-day advanced organic laboratory experience that includes the solid-phase synthesis of an unknown three amino acid polypeptide for junior/senior undergraduate chemistry majors. Students conduct a series of 1D and 2D NMR experiments (HSQC, HMBC, TOCSY) and analyze the data to identify the side chain residues of the peptide and…

Creating equity for Black science students requires deep listening and can be achieved with phenomenological qualitative research and a community of inquiry. The phenomenological study examines the lived experience of a phenomenon by a student. This article investigates how Black students perceive advanced science classes and what prevents them…

In this article we consider two triangles: one inscribed in another. We prove that the area of the central triangle is at least the harmonic mean of the areas of corner triangles. We give two proofs of this theorem. One is based on Rigby inequality and the other is based on the known algebraic inequality, to which we bring a new, geometric, proof.…

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…

To explore and identify gaps in students' opportunities to take and prepare for advanced math since the coronavirus disease 2019 (COVID-19) pandemic, RAND Corporation researchers conducted a nationally representative survey of teachers and principals in spring 2022. The researchers focused on two key ingredients that enable equitable student…

Are you frustrated when students focus on "getting the right answer" without understanding why the physics works that way, or even why their own brains came to that conclusion? If so, this might be less about the student and more about the pedagogy--you might be stuck on the "One True Path," a way of thinking "that assumes…

TNT is both toxic and explosive, and therefore, the detection of TNT represents an environmental concern and a security concern. Dogs are often used for detection, but other methods are needed. This laboratory investigates a ruthenium bipyridine ([Ru(bpy)[subscript 3]][superscript 2+]) luminescence-based trinitrotoluene (TNT) sensor. Students will…