If students can perform above grade level give them opportunities to do so.
When I had to home school my oldest for 4 months--he was almost 13 at that time--I used a discarded college algebra text I'd found in a donated book box to pull ideas about what to teach him. I remember thinking that by the time I was 12, I'd already been introduced to algebra/geometry, but when I asked my son, he told me he'd never been taught either before, so...
I sat for two nights and put together two consecutive days worth of what I intended to be *math assessment*--I felt I first needed to discover for myself what level my son was at 'in all of the basics', and without doubt, I needed to first know what his *arithmetic skills* were, so anyway, my son demonstrated to me that he was actually well grounded in arithmetic to the point of confidence (ease, speed, correct). No struggle or questions, so....
From there, I started his algebra intro by introducing him to a scientific notation 'review' (it was what he was being taught at the time he got ill), and after that, I went straight to a *talk* about what algebra was, how it involved equations, how learning algebra relied on his arithmetic skills, yet was different. I then immediately went to *What is the value of X* stuff, and he straight turned on to it.
That boy PUSHED ME! At the time I tackled teaching him college algebra, I was well aware that I'd never finished my own algebra in college beyond intermediate! In the end, because I eventually hit a point when I couldn't teach him what I didn't know how to do consistently, myself, I had to stop with math altogether as part of his home school coursework.
Though I'd kept him in home school with me for 4 months, he'd actually recovered enough to return to regular school after maybe 9-10 weeks. Because he needed to be prepped for late spring state testing, I sent him back to his school for the remainder of that school year.
Thing is, one day maybe a month later, I came across my son reorganizing his backpack. As it happened, I spotted some math work he'd been assigned. It was arithmetic. 323 x 44. A problem like that was the HARDEST single problem that he had to solve! Not 7-8 weeks before--in my home school--my kid was working on *application problems* at COLLEGE LEVEL! Doing them correctly! Using my TI-83! He was comfortable with using a protractor and compass. He was doing Radicals! IMAGINARY NUMBERS! I can't say this loudly enough: He was doing radicals, imaginary numbers, intro physics too, including APPLICATION PROBLEMS.
Anyhow, when I picked up that paper and just looked at it, and then I glanced up at my kid, HE SHRUGGED! At his parent/teacher conference, I mentioned this to his teacher. In hindsight, I actually don't think she believed me--that I knew anything about algebra, and that my kid as good as *sopped up* all I could put in front of him! In any case, she informed me that it was ok--my son was an A student in her class--and besides, it wasn't necessary for students in the 6th grade to know algebra yet, and CERTAINLY not college algebra! I remember wondering why not? I had to learn it (introductory) by then (age 12, late 60's)! Why not 12 year old kids in the early 90's???
If *elementary schooling* doesn't UPGRADE the curriculum--make the coursework more challenging or *routinely accessible* to students earlier in their educations, then their longterm academic outlooks will be NOTHING like they used to be.
One Love, and PEACE