Gifted Issues Discussion homepage Forums Recommended Resources Math intuition, math without books

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.

EandCmom: I read that VCI (on the WISCIV) correlates with ability in algebra while PRI correlates with ability in geometry. It goes along w/ what Cathy said earlier about the verbal side of math. I don't know if that's accurate or not but could explain the cases you were referring to.

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.

Nope, squirt. I think that if he's happy, let him go to it! Child-directed 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 pattern-loving boy would totally adore!!! Thanks for the tip!

YEs I'd like to hear/read more about numerical analysis as well.

A quick and dirty description is on Wikipedia http://en.wikipedia.org/wiki/Numerical_analysis

Here'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

Barging in here, Kriston, you have the VSL angle correct, that Silverman says auditory-sequential 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 auditory-sequential 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.pdf

thanks for all the food for thought!

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.

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.

BTW, my son is sitting on the living room floor doing a math workbook right now. It's way too easy for him but he gets satisfaction out of it and I suppose it's reinforcing those thought pathways... Oh heck, at least he's not watching the TV