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Clueless mom leads GK (gifted kid) to discover the meaning of fractional exponents by offering an example which reveals its meaning.
She'd like some pedagogical terminology, please. What device did she use?
Here's her blog entry: Deriving the meaning of fractional exponents.
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5 comments:
thanks for pointing this out.
here's a terminological point for ya:
"obviate" doesn't mean "make obvious"
but rather, something more like
"make unnecessary" ... & surely
the meaning isn't made unnecessary
by seeing it for oneself ...
just the explanation!
Thanks! What would be a good word to use instead of my wrong choice?
Suggestions:
illustrate, demonstrate
manifest, reveal, divulge, give away, betray, DISCLOSE
come out, evince, betoken, show signs of, EVIDENCE
bring to light, unearth, DISCOVER
explain, make plain, make obvious, INTERPRET
expose, lay bare, unroll, unfurl, unsheathe, UNCOVER
open up, throw open, lay open, OPEN
elicit, draw forth, drag out, EXTRACT
invent, bring forth, PRODUCE
bring out, shadow forth, body forth
incorporate, incarnate, personify, EXTERNALIZE
typify, symbolize, exemplify, INDICATE
point up, accentuate, enhance, develop, AUGMENT
throw light on, ILLUMINATE
highlight, spotlight, throw into relief, EMPHASIZE
express, formulate, AFFIRM
bring, bring up, make reference to, mention, adduce, cite, quote
bring to the fore, place in the foreground, MAKE IMPORTANT
bring to notice, produce, trot out, come out with, proclaim, publicize, promote, PUBLISH
show for what it is, show up (see SHOW)
solve, elucidate, DECIPHER
"Clueless Mom would like to know the name of this teaching methodology. Yes it's discovery, but what kind? Does it have a more specific name? Is it about recognizing patterns? Extrapolating from examples?"
It's what teachers have been doing from the beginning of time. It's kind of like leading the witness. Sometimes it works and sometimes it doesn't. The key is that the parent led him with the following:
2^3^2 ==> (2x2x2)x(2x2x2)
Some kids need a little bit more leading than others. Some teachers give no clues.
The other problem is that some kids will discover the wrong things. What if you used (3^2)^2 and the child thought you added the exponents. What if you wrote 4^3^2 and the child read it as 4^(3^2)?
Discovery is a nice technique, but it's neither necessary or sufficient. It may be exciting at times (that's good), but it could also be very frustrating. The problem in schools is that it is used as the main teaching technique and is done in child-centered groups, not as a class lead very carefully by the teacher.
There will also be lots of times when discovery won't work, so you can't be a slave to discovery.
Once again, I agree with SteveH. I think "discovery" must be carefully crafted. I don't even like the word "discovery" because it's been so badly done in schools.
And it must be set up so as not to lead your kid astray. And you really have to know the kid to calculate what they know and what kind of a leap they can take.
That's why I trust no one but myself to do it correctly, and judiciously, and appropriately.
I think what SteveH is describing is discovery done badly, and I'm learning that it's done badly A LOT. It's upsetting. It can really confuse kids if you don't know what you're doing.
As for whether it's necessary, well let me just say that the reason I enjoyed math in school so much is because it was delivered with plenty of inductive instruction done well.
Hey, for anybody who knows the island, that was in the Levittown School District. I graduated from MacArthur in 1975. :)
Oh and I hate the child-centered groups. That's precisely the wrong place to use inductive instruction.
LOL
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