> So, this is my very early attempt to be a math tutor. I already have > a basic question. I know that a lot of tutors say that they adapt to > the style of the student (different students have different learning > styles). While that may be very important, I wonder if it's also > important to recognize that mathematicians think and learn in ways > that make math easier, and maybe we should be helping students to > practice those ways. > > In the art world, I'm thinking of that book "Drawing on the Right Side > of the Brain" which pointed out that people have both a left-brained > way of seeing the world and a right-brained way. The conclusion of > the book was not "embrace your half of the brain"---no, it was > "Artists use the right brain--so we'll teach you to do it, too." > > So what thinking/learning style is math? I've encountered some evidence > that math involves a lot of visual thinking. I know in myself that I have > a mental picture to go along with most math concepts, sometimes a mental > animation. When I start to work a problem, I develop a sense of where > equations are laid out on the page. > > So one obvious thought is, I could, perhaps for certain problems, teach > my student to think like me. And I did a little of that. She wondered > why multiplying by a number less than one would make something smaller > (because MULTIPLYING makes things BIGGER, right?). I created an animation.. > three bars going up and down. The left two bars are the multiplicands, > and the right bar is the result. Usually the middle bar is fixed, and > the leftmost one varies between 0 and 2, passing through 1 on the way > up and again on the way down. My student could see that as the left bar > approached 1, the result approached the fixed center bar -- and she > already knew that "anything multiplied by 1 is itself," so this confirmed > it. When the bar dipped below 1, it made complete sense that the result > bar would go down and get smaller than the fixed multiplicand. And when > the left bar got to 0, then you could see WHY "anything multiplied by > 0 is 0." > > It took her about five seconds to grasp this and she said "Oh, now I > know what multiplying by less than 1 makes something smaller."
In class and in talking to students outside of class (early 1980s to mid 2000s; I no longer teach) I often made comments such as such-and-such was a left brain approach (or a right brain approach). The following math-teach post is an example.
I think your animation idea with the three bars is a great idea. However, only a miniscule number of teachers could probably carry this out, or even have time to carry out if they could do it. But apparently you do, so I would encourage you to do others if you're up to it. There are a lot of YouTube videos on math, and while I've only watched maybe a handful of them (literally, as in 5 or 6), it seems to me that the overwhelming majority are simply videos of someone lecturing or videos of someone writing something. What you described is at a much more helpful level, like the many math Java applets I've seen over the years.