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…

In this personal essay, I explain how my use of visual modelling has the capacity to broaden constructionism in five important ways. (1) It introduces new techniques for students to describe and document, in a personal way, what they are actually doing in modelling. (2) It introduces the big ideas of mathematical modelling and computational…

Generating, collecting, and analyzing data is an essential practice in the science classroom (NRC 2012). Taking this data and using it to craft an explanation that demonstrates understanding of content is another essential practice. But both practices can be challenging, and students often require teacher support to succeed. Accordingly, the…

How do teachers teach students to count rhythms? Teachers can choose from various techniques. Younger students may learn themed words (such as "pea," "carrot," or "avocado"), specific rhythm syllables (such as "ta" and "ti-ti"), or some other counting method to learn notation and internalize rhythms. As students grow musically, and especially when…

Three undergraduate students functioned as teaching assistants in unit ops lab for their senior project, which included developing a purchased size exclusion chromatography experiment, supervising the running of this experiment, and assisting the junior students with their calculations. They also read the reports, graded them, and commented on…

Metal oxalate synthesis and pyrolysis provides an opportunity for students to (i) learn stoichiometry, (ii) experience the consequences of proper stoichiometric calculations and experimental techniques, and (iii) be introduced to the relevance of chemistry by highlighting oxalates in context, for example, usages and health effects. At our…

A concise roadmap for using computational chemistry programs (i.e., Gaussian 03W) to predict the color of a molecular species is presented. A color-predicting spreadsheet is available with the online material that uses transition wavelengths and peak-shape parameters to predict the visible absorbance spectrum, transmittance spectrum, chromaticity…

Meaningful visual experience requires computations that identify objects as the same persisting individuals over time, motion, occlusion, and featural change. This article explores these computations in the tunnel effect: When an object moves behind an occluder, and then an object later emerges following a consistent trajectory, observers…

Many counting problems can be modeled as "colorings" and solved by considering symmetries and Polya's cycle index polynomial. This paper presents a "Maple 7" program link http://users.tamuk.edu/kfdrc00/ that, given Polya's cycle index polynomial, determines all possible associated colorings and their partitioning into equivalence classes. These…