[csa]

Sure. The way I presented it was not an accident (abstract with little scaffolding).

The question with the software that I have is how much is actually understood. Specially, how much of what was done can be applied in a different context. Ideally consistently, accurately, and without any scaffolding. I’m guessing the answer might be “a lot” for a typical HNer’s child (or maybe not), but it rounds to zero for the average or lower 5yo.

I would also be curious about how much success can be had with just rapid trial and error rather than learning and applying. 5 year olds can be great at the trial and error part while not actually developing and retaining much understanding. I could be very off the mark with this speculation, but a lot of my experience in this area makes me think I’m not.

[mturmon]

This sounds like the difference between basic understanding of the idea, and mastery. Mastery would always take a lot of repetition and diverse problem-solving -- true even for algebra.

Basic understanding is a lower bar, and I'd suggest that most students leave Algebra 1 with just basic understanding. Hopefully a little better than Dragon Box.