Some of the problems that I did not list are in fact algebra and some I did not list because they were either definition problems or basic arithmetic problems. Those (except the actual algebra problems) are important as well but I chose these because they require solving, yet at the same time, don't require algebra.
I think a lot of students and teachers fail to comprehend algebra because they are clueless of its purpose. It might be better said that they have been rendered immune to its purpose. This is the problem with curriculums that are based on procedure only and lack the cleverness that defines higher mathematics. Putting algebra early into an arithmetic curriculum is no fix because the student is even less likely to appreciate it.
My solution is, in addition to the steady diet of fractions and decimals, to begin exposing my son to these types of problems so that he develops an appreciation for the mechanics behind cleverness with the idea that they will be easily recognizable and accessible when he sees them organized and extended in algebra.
What it comes down to in some families is when does junior get private access to a personal computer? Or is the device to be shared by the whole family. Or is there a computer with Internet and another without? Many permutations.
Then there's the television. Are there sibs, do children fight over it? Who controls the remote?
Not that TV and Internet are all that separate. Is there a Netflix account and do kids watch Hulu?
Mom and dad... lets back up. Is it a nuclear family? No? Anyway, when are adults present and what level of availability to the present. Do they have the ability to do elementary and high school level homework? In what subjects? What realities and storylines do these older humans model. Do they "go to work"? Is there a "stay at home" parent? Again, so many permutations.
In terms of crafting an environment in which junior might thrive, I'm for creating safe study spaces. Some kids seek peace and solace in a public library. There's a sense of sanctuary, of asylum. Others see school as a refuge. Others see school as anything but. What a scholar needs though, young or old, is a safe place to be from which one has both access to information, and time to ponder, reflect, practice, contemplate. "Access to information" includes interactivity with peers, teachers, other humans.
The safe space or sanctuary you see around Portland is the "coffee shop". http://www.backspace.bz/ is a good example. Students congregate in clusters or alone. In a college campus, it's more like your student center, student union or whatever they call it, often a large meeting area, but these days with wifi and very possibly with study carrels.
Per my "city as campus" master plans (this goes back to an earlier chapter), more and more coursework will involve scheduling meetings at places like these, then perhaps roaming off on some mission. Or the class will be at a room in this complex, a bevy of offices. CubeSpace was another example, but with an unimaginative landlord that couldn't see an investment banking opportunity (Portland may have no real investment bankers at all, wouldn't surprise me).
Anyway, given today's infrastructure, from young adulthood on it's very possible to construct a college campus like existence where you learn a lot. Events like WhereCampPDX (going on as I write this), other stuff on Calagator. There are meetups galore all over town. But then do you get credit towards some certificate, some credential? It's note always that structured. You've got your live-streaming resume though (e.g. Facebook) so others can see what you've been up to, if you have a habit of updating your friends and associates (LinkedIn, Plaxo, whatever -- I'm on all of the above).
Younger kids looking for role models often find a geek adult in their network who lives a lifestyle similar to the one described.
In my case, I'm doing food services part of the week, engaged in a municipal level first person physics type project to rescue high quality fresh produce from the waste stream and vector back into the food prep / large kitchen / chef / serving circuits. Other times I'm doing committee work for egalitarian adults who practice "management by rotation" and who manage various facilities as well as provide limited services and opportunities, to young people included. My daughter went to Jamaica and Nicaragua with this group. Other times I'm off to Python meetings at Urban Airship.
Clearly I'm a learner as well as a teacher and that's what a teacher is (someone who learns professionally, in order to stay effective as a teacher).
Free junior from too much time in the classroom may be one way to jigger with the mix of responsibilities we stereotypically assign the North American classroom teacher. Teachers like me, living outside that grid, and not college professors either, are role modeling a different lifestyle to even the high school aged, and that helps them see how they too could be these other kinds of teacher. Stereotypes break down and re-form as a result in changes to the ecosystem (biosphere, infrastructure). This happens all the time.
I think the thralldom many experience with the radically out of date and "poor fit" (misfit) school system is coming to an end. It's being corroded from outside more than from within. TV, the Internet, and other institutions, also with teachers, are showing different ways to go. I think our standard ideas about school are coming unglued and will be coming together in different configurations, probably with less age segregation and more "library time" in the sense of learning to study on one's own, in a coffee shop like environment.
School as we remember it from the 1900s will not be as many days a week, if any.
The buildings will be managed and scheduled differently. A lot of these changes will take some people by surprise, but that's nothing new in historical terms.
The changes will be at a different pace in different areas. It's not like all of North America is on the same page. The more futuristic configurations will likely happen on the Pacific Rim more than near the Atlantic seaboard. Illinois has a track record of being open, pioneering. Lots of ideas will be coming from Japan and Alaska. This is sort of how I'm seeing things shape up, even right now.
It'll be different for different people of course. Cascadia is not necessarily marching to the same drummer as the people attuned to Washington DC are (a faraway city that appears to have few bold futuristic ideas about anything, except museums, backward looking (with so many cities to learn from, why put such an unfair amount of stress on that one?)).