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#155347  05/02/13 10:11 AM
Re: DS loves advanced math concepts but not practicing
[Re: Licorice26]

Member
Registered: 12/29/09
Posts: 250

DD is like this, too. She begs for new and exciting math concepts and terms, and totally gets them, but doesn't show her teacher she really knows subtracting within 20! She recently got interested in poetry again, which was her obsession last summer/fall, and because she hasn't thought about it since then she was excited all over. She was figuring out how many lines in different forms and rhyme scheme patterns, which she also did last fall. I mostly figure, eh, she's passionate about learning so that'll see her through. I wonder if its just asynchronous behavior, like she relishes these big concepts and patterns but the grind of committing them to automaticity is just not part of her mindset right now.

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#155360  05/02/13 10:42 AM
Re: DS loves advanced math concepts but not practicing
[Re: 22B]

Member
Registered: 02/05/11
Posts: 5181

I'm sorry to rain on the parade, but some things don't sound right here. What does it mean to "practice concepts"? It makes sense to "practice methods (or algorithms)" and it makes sense to "understand concepts".
Also it is concerning when you say "we go back to previously learned concepts it appears that he has forgotten how to use them". Why does this happen?
I'm concerned that the approach to mathematics may be wrong, and that there may be too much rushing ahead without a solid foundation. Though to be fair, this does fit nicely with the apparent "vision" for teaching science and mathematics now in primary and secondary. (Actually, teaching pretty much everything in K through 12.) I interpreted this as a reluctance to practice application of concepts. That is, watchandlearn = fine, and leads to happiness, a single demonstration or application, fine again, but do this slightly different application, "I'm bored with this now and I don't want to." It's probably at least partly a matter of metaskills being underdeveloped. Kids at this age are not very good at KNOWING when they actually have mastery and when they could use a little more practice/reinforcement. It's a hard target to hit with HG+ kids, though, because they really DON'T need as much repetition as most learners, but they still need (on average) a bit more than they like.
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#155373  05/02/13 11:34 AM
Re: DS loves advanced math concepts but not practicing
[Re: 22B]

Member
Registered: 09/19/08
Posts: 1898
Loc: Scotland

Exactly what 22B says. The way to practise a technique, and reinforce a concept, is to use it in nonroutine contexts. Sometimes routine contexts make good warmups, but most children here probably get way too many of them. Here's a cute problem you can solve using a quadratic. Incidentally, if anyone can solve it without a quadratic, let me know! I saw it elseweb, and the discussion there gave circumstantial evidence that it should be possible,but noone found how. It feels like the kind of problem that might be trivial if you look at it right. A column of vehicles 10km long drives 24km in a straight line at a constant speed and then stops. A police car starts from the back of the column and drives to the front, turms around and drives back again. It arrives at the back of the column at the instant the column of vehicles stops. Assuming the police car travels at a constant speed and turns around instantly how far has the police car travelled?
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#155386  05/02/13 01:07 PM
Re: DS loves advanced math concepts but not practicing
[Re: ColinsMum]

Member
Registered: 02/10/13
Posts: 1228

Exactly what 22B says. The way to practise a technique, and reinforce a concept, is to use it in nonroutine contexts. Sometimes routine contexts make good warmups, but most children here probably get way too many of them. Here's a cute problem you can solve using a quadratic. Incidentally, if anyone can solve it without a quadratic, let me know! I saw it elseweb, and the discussion there gave circumstantial evidence that it should be possible,but noone found how. It feels like the kind of problem that might be trivial if you look at it right. A column of vehicles 10km long drives 24km in a straight line at a constant speed and then stops. A police car starts from the back of the column and drives to the front, turms around and drives back again. It arrives at the back of the column at the instant the column of vehicles stops. Assuming the police car travels at a constant speed and turns around instantly how far has the police car travelled? Interesting, ColinsMum. Does "solving it without a quadratic" disqualify you from using Pythagoras?

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#155387  05/02/13 01:12 PM
Re: DS loves advanced math concepts but not practicing
[Re: 22B]

Member
Registered: 09/19/08
Posts: 1898
Loc: Scotland

The same circumstantial evidence  the q was set for 13yos  probably means Pythagoras wasn't intended to be needed, though I'm a bit vague about what gets taught when normally, so I'm not sure. However, I'd be interested to see a solution using Pythagoras!
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#155388  05/02/13 01:41 PM
Re: DS loves advanced math concepts but not practicing
[Re: Licorice26]

Member
Registered: 02/10/13
Posts: 1228

Actually I'm kind of bluffing. I changed 10 to A, and 24 to B, and equated some ratios, which became a quadratic, and solving that (and dismissing the "" solution) gives that the police car travels
A+sqrt{A^2+B^2}
This hints that there may be some kind of slick geometric argument that involves a right triangle with sides A, B, C=sqrt{A^2+B^2}, but I did not actually try to find one.
In general, the answer will involve a square root, but it just happens that if A=10 and B=24 then C=26, so you don't see the square root in the given specific problem. So in some sense, "solving a quadratic" is necessary.
I wonder if it was a multiple choice question, in which case one could just check which option works (which is still not totally trivial).
I think Pythagoras is roughly grade 6, and solving quadratics is roughly grade 8.
Edited by 22B (05/02/13 02:17 PM) Edit Reason: Changed a B to an A.

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#155393  05/02/13 02:25 PM
Re: DS loves advanced math concepts but not practicing
[Re: 22B]

Member
Registered: 06/25/12
Posts: 978
Loc: BC, Canada

I'm sorry to rain on the parade, but some things don't sound right here. What does it mean to "practice concepts"? It makes sense to "practice methods (or algorithms)" and it makes sense to "understand concepts".
Also it is concerning when you say "we go back to previously learned concepts it appears that he has forgotten how to use them". Why does this happen?
I'm concerned that the approach to mathematics may be wrong, and that there may be too much rushing ahead without a solid foundation. Right... exactly. Wouldn't the solid foundation come from solving multiple equations/problems using the already understood concepts until they're embedded in memory? But when your 7 year old isn't fond of repetition, this becomes an onerous killthejoy task that dissuades the kid from wanting to do more math, and as a parent you don't want that, so you teach him whatever he's curious about, and not worry too much about him remembering because it's way above grade level anyway, but then a year later when he's forgotten you wonder if you did the right thing by not "drilling & killing" ... (Not that I have any experience with that ) <sarcasm, in case anyone missed it!! It's so hard to know what the right thing to do is.
Edited by CCN (05/02/13 02:29 PM)

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#155394  05/02/13 02:30 PM
Re: DS loves advanced math concepts but not practicing
[Re: Licorice26]

Member
Registered: 07/13/12
Posts: 1478
Loc: NC

I debate whether to sometime mention to DS to notice when Pyhagoras triples show up in problems as a clue to a solution approach. Or maybe that is something one should have the fun of selfdiscovering.
By the way in Common Core they have Pythagoras in 8th grade and Quadratics in 9th. Progress, I suppose, I know decades ago I had it in Geometry which I took in 9th grade (which was the only acceleration they offered.)

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#155543  05/04/13 12:05 AM
Re: DS loves advanced math concepts but not practicing
[Re: Licorice26]

Junior Member
Registered: 12/08/09
Posts: 36

I just got back to the post and was truly impressed how many people are trying to help me ! Thank you so much for your ideas and thoughts! It also really helps to know that I am not alone. I agree  it is hard to know what the right thing is. Some other math tutor tried to do the "only if you get 95%+ correct can you move on" and it killed his desire right then. I very much like the idea of trying to apply the concepts. Someone else also mentioned that giving him an answer to a problem and telling him to show me how to get there might work  I tried this today and it surprisingly worked quite well. I am wondering if knowing the answer makes him less answer focused/ stressed and thus allows him to think more clearly about the steps to get there. For right now, we have decided to let him explore things that he loves and as someone mentioned  given that he is ahead  if he has to get back to things in a while, it should be still ok (or so I tell myself ).

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#155548  05/04/13 04:54 AM
Re: DS loves advanced math concepts but not practicing
[Re: Licorice26]

Member
Registered: 01/14/08
Posts: 1579

DD is now doing CTY grade 5 math, which has moved off from EPGY. I love the new format.
And it builds quickly. So a mathy kid can listen to the videos, do the exercises, then the test and move on. But the next section builds. I admit we are not far into grade 5 math, but so far it works well for that style of teaching and retention.

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