[cello music playing]
>>Dor Abrahamson: What is mathematics
if you think about it?
Mathematics is a way of thinking.
It's a way of solving problems.
I'm Dor Abrahamson.
I'm a professor of mathematics education over at U.C. Berkeley.
I study the way that kids learn mathematics.
I'm also an inventor.
I build all kind of gadgets using both traditional
and cutting-edge technology
to help kids learn and teachers teach.
Usually when people think about math, they think about,
you know, X and Y and numbers
and doing all these calculations.
However, mathematics is about making sense of the world
and unless we can sort of ground all of the scribbling
in something concrete that we really get,
we'll never understand what we're doing.
Like adding, you know what adding is.
Take one and one and woo!
You have two.
Or if you think about multiplication,
it's like you take, "what is five times three?"
Three and three and three and three.
You have a sense of what this thing is.
But beyond that, do people have a sense
or are they only scribbling around and getting answers
but not really understanding what these things are?
My job is to help kids connect
between what their brain already knows to do and the math
that they are being taught, so that they can do much more
than just scribble little numbers and symbols,
so that they can really get it.
So they can go out into the world
and identify those phenomena, see those patterns,
use math in their lives to solve the problems
that they care about.
Any researcher of math education can tell you
that the big crisis starts when fractions enter the scene.
Up to then it's just been counting numbers: one, two,
three, four until you get all these weird kind
of relationships where one-half is bigger than one-third,
is bigger than one-quarter is bigger
than one-fifth even though the numbers are going
up the fractions are getting smaller.
Kids flip.
Kids suddenly lose a sense of what these things are.
>>Ratio and proportion are everywhere.
Even on my cello.
When you take a string, play it,
and then you halve it, it's the same note.
What we need is to help kids see the world mathematically.
So our way of going about solving this problem is
to develop what we are calling the
Mathematical Imagery Trainer.
We've set this up so that as long as the crosshair
on the right is double-height of the crosshair on the left,
it's going to be green.
So if I move it this way, it will keep being green.
However, if I find a green spot
and I keep the distance the same, it will go red.
That means we can struggle with the core learning challenge
of ratio and proportion even before we introduce a
single number.
In our lab we are creating all these sophisticated devices.
But we count on teachers
to bring these things alive in their classrooms.
All you need is to be creative as all teachers are in figuring
out how to make these ideas come alive.
So just like with the Mathematical Imagery Trainer,
kids saw how the distances
between their hands keep on growing.
We can show that just with blocks.
We can show the same idea instead of growing
up vertically, going horizontally.
Imagine you're leaving home and you're driving one thing,
say a bicycle, and your buddy is driving a car.
As you're moving along, you're each going at a constant rate
but the distance between you keeps growing.
This guy is moving two units at a time
for every one unit this guy is moving.
That's proportion.
You can use anything.
It's those images that they'll be carrying
out through their lives.
Not the numbers.
They'll forget the procedures.
We want kids to be masters of their mathematical knowledge
so that they can solve the problems of the world.