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To: AmishDude
Is your 11 year old using the definition of the limit (epsilon-delta)?

Yes. The text is Thomas' Calculus and Analytic Geometry. I actually have to limit her on it or she'd do math most of the day. She's enjoying this course more than any math she's done to date.

I made a big deal of rigor in her proofs when she went through intermediate Algebra (a ten year old Dolciani) and made sure she was doing proper diagrams and graphs for each word problem (she already understands an area under a curve as an output variable). In that text, there were perhaps three problems that had us stumped, one of which I know for a fact was an error in the text. As far as units go, well, I'm totally uncompromising there. she's been using dimensional analysis and identities since first grade.

Freeper NattieShea is virtually self-teaching in math at this point. I get to show her how rusty and sloppy I am every once in a while when she gets stuck, but it's a wonderful thing when the ol' man sits down, asks a few questions, and gets her through that, "Oh, duh," moment. I still need to guide her in her writing (she has a "forest for the trees" problem).

Her sister isn't quite as far along. She is nine and has completed one year of high school algebra with an additional course in extreme arithmetic. PowerBaby is probably a better abstract thinker than her older sister, but her sloppy habits will kill her at a higher level. We're working to fix that.

61 posted on 01/16/2004 5:57:31 PM PST by Carry_Okie (If ignorance is strength, we're in a world of hurt.)
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To: Carry_Okie
How did you teach your kids this? Obviously, it wasn't in school.

My son is gifted in math, and he is bored. I just don't know what to start teaching him. There's basics he has never been taught, and I don't know when/what to teach him.

His teacher took off points for him not showing his work on long division. He does it in his head. (Just irked me.)

62 posted on 01/16/2004 6:08:18 PM PST by luckystarmom
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To: Carry_Okie
That is impressive. One of my worries is that young people, no matter how advanced or brilliant, just have trouble with the concepts of things like limits.

You'll find that the geniuses in places like Budapest spent their youth thinking about number theory and discrete math problems. Calculus is something that takes a bit of a leap.

Nonetheless, you should be very proud, she is quite talented, as the link demonstrates. Have you considered something more traditional, like number theory or something more fun, like graph theory?

63 posted on 01/16/2004 6:21:18 PM PST by AmishDude
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