I teach Calculus to middle school students during the summer. I cover the conceptual entirety of a College Calculus I course adapted for Algebra I backgrounds. Calculus is something most people (never mind middle school students!), regardless of socioeconomic background, are typically intimidated by. serve my community by teaching calculus and showing young people they can thrive.
One of my students, Z, was going to be absent from Summerbridge for the first week of the program. When he started, I met with him for his pre-test on Algebra I concepts. Then we went straight into Finite Limits, Infinite Limits, the Derivative and the Limit Definition of the Derivative. This represents about three weeks worth of college work, and about our first week of math at Summerbridge. Z completed this in working with me in one and a half hours.
But did he really understand it? Was he just regurgitating what I told him? Well, maybe if he was telepathic. He would spontaneously describe Algebra II concepts (the asymptote for example, simply after looking at a graph of 1/x and solving the infinite limits of 1/x), without any prior exposure to it (I simply drew the graph, drew the dotted lines, “what do these mean?”). He did similar things with Calculus concepts, such as the numbers to pick for evaluating limits. His thoughts wandered fast enough even in this intensive setting to uncover these insights.
Incredible, right? So anyone could spot him from a mile away, right? I talked with his mom, asked if he’d been identified or evaluated as gifted, “Yes, I’ve identified him, and a few teachers have said so.” Unfortunately, Z had not been challenged in any formal ways at school. I was pleased that his mom was so attentive to him, but disappointed that this potential had not been met by an opportunity to fully develop in a deeply academic way.
For me, Calculus is academic rigor, independent of background. Z got 2 of the 10 questions right on the pre-test. He would unlikely make it past a selective high school entrance exam. But Calculus is different. It doesn’t test where you come from, it shows where you can go. There is no advantage coming in, other than the motivation and ability that you bring with you. Calculus allows those possessing these outstanding qualities to truly shine. That is why I do this work at Summerbridge.