Yes, I agree 100%. And the younger the child, the stronger they should be. That is, I would expect a 16 year old university freshman to be on the strong side (or potentially starting trade school early if interests lie there instead of academic), but I would expect a 12 year old university freshman to be extremely strong and probably beyond most of the standard freshman courses anyway in his area of interest. Why try so hard to get a mediocre education faster?

I wouldn't do it behind his back.

That's just wonderful.

Accidentally store them with a baited mousetrap on top of the pile. When you hear a scream, come running, and say 'Gosh, I'm SO sorry, I thought I might have seen a mouse last week so I set that.'

Pee standing up, then flex in the mirror. Wait, isn't that what they do anyway? :D Amusingly, this topic came up a while back when I was in a bar with a bunch of guys. They said, nearly unanimously 'If I woke up as a woman, I think I'd spend 3 hours standing in the bathroom looking in the mirror jiggling my chest.'

What it actually looks like to me is: A clever and motivated student who can read and understand what they read can make up for a fair amount of missing background knowledge in the humanities courses, by adding some extra reading. Although they'll miss some important allusions, a student who's never read Shakespeare could (hypothetically) move forward through a literature course while adding in reading on the side to make up those gaps. They won't be just stone-cold stopped from reading most other works of literature due to lacking prerequisites. It is extraordinarily difficult, however, for a student who is lacking knowledge in, hypothetically, calculus and physics, to be able to move directly onto a degree which requires a solid knowledge of those subjects. Cambridge's mathematics degree, for example, goes as follows (courses converted to US names): Quarter I -- Linear Algebra, Group Theory, Differential Equations, Intro to Proof (via Number Theory/Set Theory), Mechanics (remedial, if student didn't have those modules at A level) Quarter II -- Analysis I (calculus with proofs), Multivariable Calculus, Probability, Dynamics and Relativity There is NO way someone who was at ALL shaky on any part of high school mathematics through calculus BC could keep up. It couldn't even be fixed by doing a massive quantity of subject reading during the first quarter, as you'd be completely lost in differential equations without calculus knowledge (it'd be like trying to do algebra 2 without understanding algebra 1) and just wouldn't be able to cram it in fast enough. It'd just get worse when you tried to get to analysis and calc 3 in the second quarter.

Either way we went, we'd end up with cases that seem ambiguous. If -4² gave the result of 16, then what about 0 - 4²? Would that give you 0 (since the - would be attached to the 4, we wouldn't have an operator, and juxtaposition indicates multiplication), 16 (treating -4² as +16), or what? In order to make it clear, we'd have to say 0 - (4²). Furthermore, this would also mean that something like 3x² was ambiguous and could mean either 3(x²) or (3x)². In order to make this unambiguous, we'd need to write it as 3(x²). This would honestly make writing polynomials a nightmare.

As well as vitamins, eat some eggs. Good for the hair.

There's no reason he can't do word problems a grade level or two behind his computational skills, or have them read to him. But they ARE important. The point of a word problem is to use the math you know to solve the problem without being told what equation to use or which numbers to combine in which way. It's to ensure you actually know what the operations *mean* and why. If you have six children and each has two cookies, are you multiplying, adding, subtracting, or dividing? Are there multiple ways to solve the problem? Are some ways more efficient than others? etc.

:iagree: with all of the above. The one thing I'd like to add is that I'd really, really like to see more evaluation based on student progress instead. I think if a high school gets a student who is of average intelligence but for whatever reason is reading at the 3rd grade level, and a year later that student is reading at the 6th grade level, I think the high school is doing a good job with that student. But the tests will just say 'behind grade level'.

Lol, this reminds me about the ones I kept getting about 'the warranty on your vehicle may have expired'. I went through the procedure to talk to them, went through as if I were going to get it, then told him I had a 19-year-old vehicle with 350k miles on it (truth). What do you know, he cussed me out and hung up :D

Yeah, they've been moved progressively further apart. If you can find some REALLY old videos, they were just men's parallel bars set at different heights. Then they moved them a bit further apart, and then further again sometime in the 80s. During the intermediate stage, they were just close enough that someone could hang on one bar and wrap their lower half around the other bar, bending at the waist. You'll see it in, for example, Nadia's routine.

:grouphug: Children of the Heavenly Father This youtube link has a version of the song including the lyrics

That is just plain wonderful news.

Yes, this.

Well, y'know. I have a friend. As an adult, her mother was packing to move, and showed her ... a broken condom, and told her it was from the night she was conceived. ...

No -- that's not at all an unusual combination.

You must have mixed this up with another disease. Smallpox is not making a comeback. Polio maybe?

Do you maybe know anyone near you from whom you could borrow one? Theology is SO personal it's really hard to tell.

I had it at 24. My last booster had been at 10-11 (I forgot which?) but anyway definitely pre-puberty.

Gosh that's not at all what I meant, I hope it didn't come across as arrogant. :) I'm really interested in everyone else's 'aha' moments. It's always been something that just makes me wonder, why something is so easy for person A, they see it immediately, and person B struggles and struggles and has multiple explanations and still doesn't grok it.

Yes, me too! I have so many tricks to make things more memorable or to reduce them to something I already have memorized precisely because I'm dreadful at memorizing.

I would absolutely agree with your decision not to hurry to calculus. I think a solid precalculus class that includes algebra review is an excellent idea.

Yes, this.

That's pretty interesting, not a way I would have thought to attack it. I can see since we know ab we're going to get (a-b)^2 by subtracting 4ab from (a+b)^2. It always made sense to me as completing the square with an arbitrary quadratic.