David,

I've come to the view that the underlying problem is the concept of grades -- i.e. stratifying students in school based on birthdates when they're four or five and expecting their academic skills and achievement to follow a "normal" track for the next 13 years. Every child in school ought to be learning the next thing -- what he or she doesn't yet know. This is true of the quickest as well as the slowest.

It is quite possible, given the right teaching materials and the right training for teachers, for a large room of students of different ages to be working each at his or her own level on material that he or she hasn't mastered yet. This has been the case for years in Montessori primary and elementary classrooms and is what happened in the old one-room schoolhouses. Montessori classroom teachers and one-room school teachers would not expect to teach everything the students learn -- they meet with students regularly (daily), monitor and note progress, introduce new lessons, point in the right direction. They depend on having the right teaching materials at hand and on an atmosphere conducive to work.

There are many advantages to this sort of model: a student's choice who to sit with at lunch isn't tied to the level of academic work he or she is doing in the classroom. So a kid can be in a small math group with 11 and 12 year-olds but eat lunch with his or her 8-year-old buddies. Also kids who plod along slowly for a while, then become inspired to move ahead quickly (because who knows -- family problems at home have lifted, something they didn't get finally clicks, the right teacher inspires them) can move ahead without having already been placed on the slow track. And kids who skip ahead academically can still, if they want, participate in school sports with kids their own size and ability. (One result of a multi-grade skip is that it almost always eliminates the possibility of being competitive in school sports. Another whole topic I know.)

I think some "experimental" attempts to conduct multi-age classrooms fail because the teachers really aren't trained for them. They're still in the mindset of "3-4th grade" or whatever, so it's great for the slower 4th graders or brighter 3rd graders. Or the teachers don't know how to teach the kind of self-discipline kids need to work on their own, and the atmosphere becomes chaotic. Perhaps students' lack of self-discipline and ability to work hard on their own is the biggest obstacle to differentiated learning.

While a standard curriculum like the old Ray's Arithmetic series (counting through calculus) or the Mc Guffy Readers that were used in public schools in the 19th century certainly had limits and would not have met the needs of the brightest students for more depth, they were quite demanding and straightforward compared to many contemporary school textbooks that I've seen. The kids who worked through the 8th grade level (in however many years that took) were both literate and numerate at a surprisingly high level.

I'm not of course advocating a return to one-room schoolhouses, and I'm not sure the Montessori model has been adequately extended to higher grades, but I do think there should be ways to train teachers and to structure schools that would allow for a more individually differentiated approach to academics. And I think this could be done in ways that would tend to defuse rather than inflate social pressure against high achievement (and hopefully also be more encouraging to students with a record of low achievement).

Imagine if school systems now, instead of buying new, slightly varied and perhaps slightly dumbed-down versions of the same textbooks every few years spent much of that money on improving the quality of their library offerings, so that students who were moving through the standard texts (chosen for basic solidity and durability) at a good clip would have somewhere to turn for more depth or breadth, and students who needed more work at the same level before advancing could supplement the textbook with well-written materials at an appropriate level.

With computers and textbook curricula such as AoPS available now, it really ought to be possible to keep any students challenged. But teachers need to be trained to work with bright kids who are working on their own -- to recognize that even bright kids need to be accountable to someone and need to learn such skills as meeting appropriate deadlines, explaining what they've learned, writing out problems or demonstrations for an audience, answering aloud as well as in writing thoughtful questions about something they've read. Teachers would need to realize when to set a challenge for a student and to have the self-confidence not to be put out by a bright kid. In general teachers would be freed from having to come up with a daily lesson plan to address some 20-30 diverse, wiggly, often inattentive kids and could instead focus on their own mastery of content and understanding of the progression of knowledge that children need to make -- so for each child they could help clear up confusions, recognize legitimate leaps forward, identify and help fill in "gaps," keep the big picture in mind.

At the high school level, things are different -- specific subject courses probably work best with whole groups (especially lab sciences, but also art classes, history classes, language classes). But in a high school of reasonable size it's pretty easy to have courses taught at different levels and to divorce school "grade" from the level of course taken. At least, it seems a lot less problematic for brighter students to move ahead in some subjects without age or grade being an issue. The problems in high school, so far as I can tell, mostly come from the fact that there are students who don't want to be there at all and know they're reaching the end of their days of compulsory school attendance. (Some of these I guess are the ones who would have hung around after class to beat up the schoolmaster in the good old days.)

In the "real" world as it were -- the choice to skip or not to skip seems to me a highly individual one. For some kids, subject advancement seems to work well -- say, skipping up in math only but staying in the same grade. For others a whole-grade skip works better. For a very bright kid I know of locally, a two-grade skip from middle-school (where he was being harassed) to high school (where he was young, but being tall and physically mature didn't stand out too much) apparently worked well. The young man ended up being a leader on the local First Robotics team, and since some of his younger friends are still in high school he still helps to advise the team from college in another state.

With my older son the public schools, clearly reluctantly but based on compelling aptitude and achievement test scores, offered to test for grade advancement the summer after the first grade (not sure why that required a further round of testing). In the best guess of the teacher who would have done the testing it seemed he might place into the fourth grade -- possibly beyond -- as a not-quite 7-year-old. We ended up declining the testing, working out a suitable plan with his second grade teachers that involved illicitly bringing him home early 4 days a week to do math, then we started homeschooling the following year. As for the proposed two-grade skip -- he was working on his own through an 8th grade prealgebra/pregeometry text by January of the second grade, after four 45-minute math lessons a week the previous fall (I was careful not to "punish" him with extra math time but he never had to be taught anything twice). Since he'd been in daycare/preschool since he was two, full-time homeschooling was not an entirely satisfactory arrangement, but neither was school. In (a Montessori) kindergarten he'd been known to set 3-week projects for himself, and having unstructured time to do his work suited him very well. But I don't think that even a heavy schedule of play groups and extracurricular classes entirely made up for his being home with mom and baby brother most of the day.

Now in the 9th grade (just turned 14), he's taking three courses at the local high school (90 minute classes back-to-back every other day), one course at the state university, foreign language with a private tutor, math through AoPS and on his own, English with his parents. Plus an extracurricular schedule that has us drawing a roadmap every morning. One more school class and he'd be eligible to play sports should he choose, though rec-league seems to be more his style. It would be convenient, to say the least, if he could get everything he needed in one place, but we have options that a lot of people especially outside larger metro areas don't.

Sorry this is so long -- it's a complicated topic!