One of the concepts in education that I've sometimes had a hard time relating is the idea that the fastest progress is made when a foundation is built at the necessary pace, regardless of the time that takes. This means stopping to have conversations about whatever is necessary. In our fourth lesson, I spent some time talking with Antonio about the notation of set theory. It wasn't the first time, but it was clear that we needed to walk through it before and during a lesson on a topic that involved thinking in terms of sets. Seeing, reading, writing, and using notation is part of math. It's part of the symbol dancing game. It needs time for absorption before plowing ahead. The Daniel Kahneman fans understand this as training System 1 and System 2 thinking both together.

To Antonio's credit, he patiently worked through our first few lessons completely. Though we do not have video of the first two lessons, many viewers might have watched them and thought we worked slowly. Given that Antonio is more than a decade removed from a classroom, I knew this would be necessary. I suspected the results would be good, and judging by our recent lessons, they have been.

Earn the foundation slowly and completely, then practice working through problems, and the results will be highly complete.

Not only did we work through the Principle of Inclusion-Exclusion in this lesson, but we also talked about combinations for the first time.