Date: Jun 13, 2013 12:34 PM
Author: Dave L. Renfro
Subject: Re: new tutor here

Michael Mossey wrote (in part):

> 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.

math-teach: The Deprecation of Algebra [3 May 2010]

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.

Dave L. Renfro