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Re:California moves to recommend delaying algebra to 9th gra... by mturmon on Tuesday November 23, 2021 @07:43PM (#29325625)
You can't quite do it the way you have shown, but take a look at:

https://dragonbox.com/products/algebra-5

My kid tore through almost the whole set of problems in the app at about the recommended age (5yo).

Re:California moves to recommend delaying algebra to 9th gra... by csa on Tuesday November 23, 2021 @08:35PM (#29326027)
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.

Re:California moves to recommend delaying algebra to 9th gra... by mturmon on Wednesday November 24, 2021 @11:43AM (#29331909)
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.