To my mind, acceleration vs enrichment isn't the most important distinction to draw in mathematics. For purposes of developing as a mathematician, what's needed is a balance between solving hard problems using techniques you already know, and learning new techniques. Taking a course on new material - whether it's the one that would typically be taken next (acceleration) or one that wouldn't (enrichment) is certainly going to involve learning new techniques, and that's great. I don't have strong views on which of cryptography and intro to algebra would be best; in your position, I'd ask my son what he wanted to do and go with that. AoPS is as the name suggests pretty good at being problem-focused. We have the intro to algebra book, which is mostly routine but has some good challenge problems. I don't know how the online course plays out, but it might tick both boxes or it might only tick the "new material" box depending on the approach. I know nothing about that cryptography course (really interesting field though).

There's lots of problem-solving material out there, though: think Olympiads. My point would just be that it's vital to have plenty of problem solving, one way or the other. Rule of thumb: your DS should not be able to solve more than about 3 out of 4 problems without going away and mulling them over over more than one session, otherwise they're too easy. The number one problem in school mathematics education, IMNSHO, is that people who are good at maths don't get enough practice at persevering in the face of apparently insoluble problems, something which is absolutely vital to professional mathematics :-)

If it's of any interest I recently posted an update about my DS's experience doing maths on his own in class
here.


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