Date: Jun 13, 2013 12:34 PM Author: Dave L. Renfro Subject: Re: new tutor here Michael Mossey wrote (in part):

http://mathforum.org/kb/message.jspa?messageID=9134056

> 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]

http://mathforum.org/kb/message.jspa?messageID=7056499

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