Originally Posted by ColinsMum
I was also wondering that, but then this kind of issue:
Originally Posted by AlexsMom
I worry more about conceptual gaps - like the decimal multiplication problem she solved correctly, then asked whether you counted from the right or the left when picking where to put the decimal point. (Upon discussion, it was clear she did not understand why you moved the decimal where.)
does have me worried - unless it's an isolated problem caused by a teacher explaining it wrong, but even then...

I've seen her work exactly one multiplication-with-decimals problem on her own, so am extrapolating from there. The problem was 7.1 x 3.4

After multiplying 7.1 by 0.4, she put what she called a placeholder decimal between the tenths and hundredths columns (so one place in from the right). Then after she finished multiplying and adding, she ignored the placeholder, counted the places to the right of the decimal in the original problem, correctly arrived at two, counted two places from the right in her answer, and correctly placed the decimal point. And then asked me if you counted from the right or from the left, because she remembered her teacher having told her from the right, but she wasn't completely sure.

So she's capable of getting the mechanics right, but she has no understanding of why you do it that way. (We had a similar mechanics-vs-understanding issue when we were working together on factoring, and she was astonished that every item on the list of numbers that were factors of 30 could be constructed from the prime factors of 30. She was capable of accurately generating a list of factors, and of identifying the prime factors, but didn't "get" how those numbers were related.)

The AOPS pretest tests mechanics, not understanding. The course IMHO requires understanding. OTOH, I'm not sure that the standard public school curriculum cares one bit for understanding.

Originally Posted by ColinsMum
How about a combination solution: subject accelerate to 6th, *and* afterschool.

I think it's likely that we'd do at least some afterschooling. 6th graders can do MathCounts, too.

Originally Posted by ColinsMum
The "algebra is hard" mantra always perplexes me

In our house, algebra is fun.