Precalculus in Tucson

Precalculus, as its name suggests is largely to prepare students for Calculus. However, in its modern adaptation, or at least its adaptation in the Arizona Math Standards, it’s more than just that. Per the documentation provided by the Arizona Department of Education, while traditionally Precalculus courses have “served to prepare students for entrance into Calculus,” the Arizona standards have been written for students to “experience extended mathematical concepts regardless of their future pathway.”

What explains this shift in emphasis? This shift from strictly preparing students for Calculus to more broadly giving an “experience” of topics applicable to some nebulous array of potential “future pathways” (which presumably still includes Calculus)?

While I’m not aware of any official documentation accounting for the shift, it seems we can piece together a plausible picture in light of the evolving nature of the STEM field through the 20th and 21st centuries.

It’s not a novel idea that 20th century math education was grounded in Cold War era, Space-Race fueled, physics-readiness fever. The idea here is that math education was centered around producing the physicists and mechanical engineers ‘necessary’ to compete in a global posturing conflict, and that meant sending as many students as possible through the Precalculus-to-Calculus pipeline.

However, at the turn of the 21st century, with global conflicts having fallen into the background and the rise of computers, Calculus began to lose its ‘peerless’ status. Math was no longer solely about modeling a physical world that moves in continuous curves – vehicle motion, rocket trajectories, pricing trends – but started to become more and more about dealing with discrete phenomena and binary states; (e.g., with computers, but also with advances into the subatomic realm).

Hence, in the modern day, a well-rounded approach to a student’s math education, not only prepares them to apply math in the “continuous” sciences with Calculus (e.g., engineering), but to the “discrete” sciences with other high-level math courses (e.g., computer science and logistics), and to fields that combine both (e.g., modern physical & biological sciences that rely on computational methods or increasingly deal with small particles, such as geology, molecular chemistry, and computational biology). Below is a graphic showing some broadly categorized fields.

While this may all sound rather complicated, per the Arizona Precalculus standards, preparing students for these realms beyond Calculus apparently only requires one addition; and that is matrices. Below is a mapping of the topics in a “modern” Precalculus course – namely, in this case, one defined by the Arizona standards.

As the diagram shows, every topic in Precalculus maps to a Calculus courses except matrices. This illustrates how, generally speaking, a “traditional,” 20th-century style Precalculus course would stop at vectors, while modern Precalculus – to adapt to the evolving STEM landscape – adds them on. Matrices are the building block and universal language of the discrete sciences (e.g., as functions are the language of the continuous sciences).

And so, the idea is, equipped from Precalculus with not only the tools needed to succeed in Calculus, but also those required in fields related to sciences emerging from 21st century technological & theoretical advances, a student is prepared to continued onward into the modern landscape, academically or otherwise.

The following additional services are offered for those in ESA learning contexts. (ESA-Approved Vendor – $0 out-of-pocket with ClassWallet).