What I'm learning by re-learning calculus

I'm re-learning calculus this summer using Khan Academy, and I've already had some great reminders of what it's like to be a learner.

I've taken this on as a summer project for a few reasons:
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• I want to be able to help my students through their senior years, rather than having to refer them to (admittedly very capable) colleagues after precalculus.
• It's exciting to increase my knowledge base beyond the topics I've tutored consistently over the last 15 years.
• I'm planning ahead in case the SAT and ACT continue to fall out of favor and test prep is a less viable business in a few years.

I've learned calculus before. It was 22 years ago, though! I'm early in my studies, but here are three great reminders I've already experienced:

1. Khan Academy's design is really intelligent. In particular, those little chimes and sounds that come with correct answers—they have HUGE reinforcement value. It's crazy. Think of how immediately you react to your text message tone, or to the "tssSSS kr-POP" of a can being opened (I googled that spelling). Sound is a wildly strong reinforcer. It's something I was already planning to incorporate more in my work, and even more so now.
2. Learning from wrong answers is awesome. On one early question, I was unsure if a function was differentiable at a corner. I could have watched the lengthy instructional video. Instead, I just picked an answer. I was wrong—but by knowing which one was wrong, I learned the rule just as effectively as if I'd answered it right! I realized that no matter which answer I had picked, I would learn instantly that functions were not differentiable at corners. With that in mind, who cares that I got it wrong? Sometimes it's the fastest way to figure something out.
3. Spreading out learning is so important. I understand that my brain can handle only so many new concepts at once, so even if I have time to continue, I stop working if I feel my short-term memory getting full. I talk to my students constantly about spreading out their study time, and yes, this is a reminder about that message being important. But it also reminds me that students only have the luxury of spacing out work if they plan ahead. If they don't start studying for that History test until the night before, spreading out their work is not an option. It's not an overstatement to say that planning is the foundation of learning.

I'll update from time to time as I (hopefully!) progress in my studies and have more interesting experiences to share. Thanks everyone!

-Matt