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#14519  04/23/08 05:11 PM
Re: Math intuition, math without books
[Re: EandCmom]

Member
Registered: 05/26/07
Posts: 1783
Loc: West coast, USA

Geometry has never been a passion for me, although I liked doing the proofs and writing them out neatly and logically. It seemed satisfying. Algebra just seems like a means to do calculus, which I love. Abstract algebra (rings, fields, etc) I can do in a mechanical sort of way but it doesn't seem intuitive to me at all because all I can think about is blobs with arrows pointing to them. Algebraic geometry is similarly opaque My degree is in applied math and the way I think about math is mostly visual. Numerical analysis makes a lot of sense to me. By the way, that's something that can be understood with relatively little algebra skills. You need to learn about infinite series which are usually intriguing to kids and full of interesting patterns.
Edited by Cathy A (04/23/08 05:15 PM)

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#14527  04/23/08 06:13 PM
Re: Math intuition, math without books
[Re: EandCmom]

Member
Registered: 03/31/08
Posts: 323
Loc: Back in Texas, alas!

LOL Cathy! Most people I know who were good at geometry weren't so good at algebra and people who were good at algebra weren't as good at geometry. I personally LOVED algebra and although I did well in geometry I hated proofs with a passion. I saw absolutely no point in them. Anyone else out here love one and disliked the other or is that just a phenomenon I've noticed in the few people I've discussed this with??? I loved Algebra but saw absolutely no reason for the proofs in geometry. I mean, really, we know what the angles are and which is which and how they relate, so what's the point? After having read all of this thread, I like the theories of teaching math but I have a question. If my guy LIKES doing workbooks, is there any harm in that? Will it stifle his love of learning or will he eventually get bored with them and want to move on to other things. I don't actually teach him out of them  just provide them.

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#14531  04/23/08 06:55 PM
Re: Math intuition, math without books
[Re: squirt]

Member
Registered: 09/19/07
Posts: 6145
Loc: Midwest

Nope, squirt. I think that if he's happy, let him go to it! Childdirected is what it's all about, I think. Especially at a young age.
Mine's just bored and antsy.
And Cathy, can you tell me more about numerical analysis. What is it? Can you point me to any resources for it? It sounds like something my infinity and patternloving boy would totally adore!!! Thanks for the tip!
_________________________
Kriston

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#14536  04/23/08 07:35 PM
Re: Math intuition, math without books
[Re: Dazed&Confuzed]

Member
Registered: 05/26/07
Posts: 1783
Loc: West coast, USA

A quick and dirty description is on Wikipedia http://en.wikipedia.org/wiki/Numerical_analysisHere's a description of Newton's method for finding roots of equations. http://en.wikipedia.org/wiki/Newton%27s_method If you apply this to complex polynomials you can generate really cool fractal pictures like the one at the bottom of the page. I love fractals, too. Check out the Mandelbrot set: http://en.wikipedia.org/wiki/Mandelbrot_set
Edited by Cathy A (04/23/08 07:36 PM)

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#14537  04/23/08 07:40 PM
Re: Math intuition, math without books
[Re: Dazed&Confuzed]

Member
Registered: 02/24/08
Posts: 361

Barging in here, Kriston, you have the VSL angle correct, that Silverman says auditorysequential learners are better at arithmetic and algebra while VSLs are better at geometry except for the proofs, which are sequential. Also keep in mind that the auditorysequential person is supposedly better at rote memorization, while the VSL learns best by seeing relationships. And remember, the right brain is the place for intuition You may have seen this article before, but I'll throw it out here for you just in case any of the points seem relevant to your current thought process: http://www.visualspatial.org/Articles/algebra.pdfthanks for all the food for thought!

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#14538  04/23/08 07:45 PM
Re: Math intuition, math without books
[Re: squirt]

Member
Registered: 05/26/07
Posts: 1783
Loc: West coast, USA

After having read all of this thread, I like the theories of teaching math but I have a question. If my guy LIKES doing workbooks, is there any harm in that? Will it stifle his love of learning or will he eventually get bored with them and want to move on to other things. I don't actually teach him out of them  just provide them. I don't see how it could be harmful. It can be a kind of play and it can be satisfying to figure things out and fill in the blanks. Ask him about what's going on in his mind when he's figuring things out. It's a good exercise to verbalize your thinking process and you may be surprised at what he tells you. My son comes up with all sorts of ways to do problems. Sometimes it's a way of looking at things that I haven't thought of.

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#14539  04/23/08 07:48 PM
Re: Math intuition, math without books
[Re: snowgirl]

Member
Registered: 05/26/07
Posts: 1783
Loc: West coast, USA

... the auditorysequential person is supposedly better at rote memorization... My theory on this is that they are better able to retrieve the floating info by using auditory cues (like whispering to yourself, "6,8,48.") It gives them a hook to hang that info on and find it again. Eventually, they can just hear it in their minds.
Edited by Cathy A (04/23/08 07:50 PM)

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