Can you Use AoPS to Cement Math, rather than to teach it?

[mom2bee]

Would it defeat the purpose if students had already covered the material from the course prior to studying from the AoPS textbooks?

 

For example, if you have a student who has taken and passed with a fairly decent grade PreAlgebra all the way through Pre-Calculus using generix textbooks.

 

Could this student benefit from the Art of Problem Solving texts? I know that AoPS is supposed to be discovery based, but would it defeat the purpose if used as a course to cement and expand the ideas that a students has already been exposed to?

[Arcadia]

I'll go for the two AoPS problem solving books instead for your case.

Volume 1: the Basics

Volume 2: and Beyond

 

Each AoPS book covers more than the standard public school textbook though. So for expanding a child's scope and if you already have the books (or can borrow them), why not use it. If you have to buy all the books from prealgebra to precalculus, I'll rather go for the two books I link above.

My older has learnt some of the stuff in his prealgebra elsewhere. He still benefit from having to think harder when using the AoPS prealg book.

 

ETA:

I borrowed the McGraw-Hill California Geometry textbook from the library and my older has learnt some of the stuff from the AoPS videos. I would want him to go over the AoPS Introduction to Geometry book much later to cement the concepts.

[dereksurfs]

I would say yes. There are quite a few students who afterschool with AoPS using other math texts in their regular classroom. I think there are many benefits to AoPS beyond just its discovery approach. In addition it is very likely a student will still 'discover' new methods of problem solving beyond where their basic texts took them. Many parents who have taken advanced math courses in college still find parts of AoPS challenging in a good way of course. :p

 

The only question I would ask is how far back you need to go. Starting with 'Intro to Algebra' would probably be a safe bet as it covers both Algebra 1 & II.

[kiana]

I think it would depend on the quality of prior instruction and on understanding of what's been taught.

 

If they've had a solid and challenging course through precalculus, I would be more inclined to use the discrete math texts and the problem-solving texts.

 

If they've hurried through a weak curriculum I'd go back further.

[crazyforlatin]

I've learned new things in AOPS Pre-A and I did have a decent math education, but I would rather have a child go through Algebra twice, using something like Jacobs and then AOPS, than Pre-A another time, if he already has a decent grade. But it depends on what the foundation is, giving that a grade may not reflect his conceptual understanding.

 

 

[Mom0012]

My current plan is to have my dd use Saxon for algebra and then take a semester and do alg again w/ AOPS. If that goes well, I'll have her do the same thing after Saxon 2.