I don't agree with OP's teacher. Gifted kids are all over the place, and as the comments on this page show, not all gifted kids even walk the same path, let alone with NT kids. I would try to informally assess him at home and if the results are good, letting the teacher in on them to convince her. Collinsmum posted an excellent readiness test from the art of problem solving website. Her post, along with the readiness test website is here:

http://giftedissues.davidsongifted....ion_on_demonstrating_gift.html#Post87936


Here's our experience:
DS7 is much better at problem solving than at arithmatic. In his case, he needs practice and drill for arithmatic skills, but he hates it to the core. So that's why he finshed the entire Primary Grade Challenge book by Ed Zacarro last year when he was 6 - every question provides a different take (luckily he has zero problems with the basics, like multiplication tables). He started on EZ's Real World Algebra before the questions on percentages floored him (yes that's his bugbear too). I'm not a teacher so I never realized children could have problems with the abstract "X".

According to the Gifted Math Specialist from the Ministry, math should be lock step and he should work with number puzzles first. But my son has vision issues and (I now realize) can't see straight lines, so try telling him to do a Magic Square. Apparently, kids who are 6/7yo should not understand probablity, but my son loves!

What he finds challenging at this stage - Singapore Math word problems for Primary 5 and above, so we are leaving them off till he's more develpmentally ready. Instead, he seems to really love the Math Olympiad style questions because they are short, sharp, and usually bring some imagery to him. These are not algebra per se, but they are bursting with abstraction.

So I don't think all young kids are not developmentally ready for abstraction. It's finding the appropriate level to offer them that's the key. Your son's scores are terrific - beginning algebra may not require such a great leap at all for him.

Good luck!