Some self-paced kids move fast.

C is starting third grade now, and she has finished Oakland LEARN's self-paced elementary math curriculum (Beast Academy), raced through pre-algebra over the summer, and is ready to do algebra this fall. 

I've spoken to other parents whose kids tested ready for pre-algebra and then algebra in second, third or fourth grade. It's rare, but it doesn't require once-in-a-generation prodigy. Elementary school math is mostly about attaining mastery of basic arithmetic, and some kids only need a few years to attain that mastery. Once they have fluency with arithmetic, they're ready for pre-algebra, and once they finish pre-algebra they're ready for algebra. The problem is that very few elementary schools offer algebra. When I was a kid, I was also one who found math came very, very easily. But no one even contemplated offering me algebra. My elementary school sent advanced fifth graders to the local middle school for pre-algebra; that was the best accommodation I've heard of any public school offering, and it would still represent making C tread water for three years before taking the math course that she is ready for.

The world of education theory is full of justifications for why making students like C wait three years to take algebra is actually good. 

Won't rushing ahead destroy their childhood? 

I don't think you should make an 8 year old do hours of math every day, but C is ready for algebra while having attended a chill, hippie school where classes are optional and you proceed entirely at your own pace. Some kids just pick things up pretty fast. If you don't think that all education is an affront to childhood, offering these kids algebra in third grade isn't.

Isn't it better to encourage 'solid foundations'?

It is a good idea, especially in math, to make sure that kids have rock-solid foundations. Kids moving on to advanced material without good number sense and fast, accurate mental arithmetic skills are likely to learn it badly, memorizing blindly without intuiting why the processes they're using work. But how solid a kid's foundations are is something you have to actually measure by studying their math skills - you can't just infer it from how many years they've been in a classroom. C does well on novel word problems and on transferring skills she learned to new domains. She can do complex mental arithmetic. She never randomly does operations to numbers hoping to stumble on the answer; she often catches her own mistakes by noticing 'wait, that doesn't make any sense'. So, yes, it's important to encourage solid foundations. But once a kid has solid foundations, they should get to move on to new material.

With C, in fact, we found that she has limited patience for drilling her arithmetic; she'll do it, but it's mastering new material that gives her a passion for math. The thing that got her to finally commit her multiplication tables to memory was solving lots of pre-algebra problems that incidentally required multiplication-tables fluency.  A mathematician friend advised us to separate out drill math and new math and do both, so she could work on shoring up her fluency with arithmetic while also encountering challenging new material. 

Honestly, I don't buy that elementary schools refuse to offer third graders algebra to give them 'solid foundations'. I think elementary schools refuse to offer third graders algebra for three main reasons:

Elementary schools do not bother to check if a child is ready for algebra. Most schools do not really try very hard to distinguish among kids who are succeeding. Some kids getting an A in math are encountering challenging material, mastering it, and getting an A- they're correctly placed and thriving. Some are bored out of their mind and turning in the assignment in five minutes, while looking up in their free time how to compute a derivative. I expect the vast majority of kids who are ready for algebra are never given a chance to prove it, and their parents don't even know they should advocate for it. In part this is because...

Elementary school teachers are not usually good at math. They often exude a palpable terror of it. They often feel stressed out and threatened when kids know more of it than they do. It's hard to hire competent math teachers, and there will often be no one at an elementary school qualified to teach algebra. 

But if this were the only problem, then all schools would do what LEARN did, which was notify me that (as third grade is the highest grade offered at LEARN and C the only child ready for algebra), they can't offer it this year, and schedule a meeting to talk about our options to ensure she's getting the math material she's ready for. We discussed some options, and decided I'll be stopping by for an hour during the school day each day to teach her myself. I know other parents who asked schools if they could do the same thing for their ready-for-algebra kids, and were rebuffed. Which makes me suspect a third reason:

Once an option exists, parents get weird about it. I did not relentlessly push C to be ready for algebra; it was a surprise when she tested ready for it. I don't want to bring about a world where taking algebra in third grade is a baseline expectation for entry into the good colleges and the upper middle class; that would genuinely be deranged. But we can't simply be normal about what kids can and can't do. If some third graders are taking algebra, parents will stress out about why their kids aren't ready for algebra. I strongly suspect that if a gifted school did offer algebra for elementary schoolers, they would within days be fielding queries from parents about why their kid isn't in algebra.

For this reason a lot of gifted schools, as a matter of written or unwritten policy, basically teach the same curriculum as normal schools but a year or two ahead (and, they’ll often argue, ‘in more depth’). They are not actually well-suited to help kids move at their own pace, and actively avoid making it apparent when some kids are much faster than others.

I don't think this is a good reason, to be clear. The correct response to those parents is that the school offers every child a challenging curriculum paced according to their own needs, and the parents should focus on whether their child is encountering material that is challenging and satisfying for their child. Trying to push kids into the most 'advanced' class that exists is genuinely a bad idea, even though offering algebra to 8yos who are ready for it is not. But I think a lot of schools want to avoid this complication, and so avoid offering anything 'too' advanced.

Anyway, LEARN's thesis here is pretty simple: it is good for all children to study material that they are prepared for and that is challenging and interesting to them, at the pace that is right for them. This is true for students who struggle academically, and it's true for children who are advanced academically. Parents should not add 'fret about my elementary schooler not taking algebra' to the already-too-long list of things parents fret about, but if a child is ready for algebra, then fully and justly educating that child requires offering that child algebra. 

In future posts I'll discuss the different self-paced learning options we explored for C and their upsides and downsides for young advanced learners.