## Thursday, February 15, 2007

### Moving from the concrete to the abstract for small children

Learning their numbers is just one step in coming to an understanding of mathematics.

Young children can comprehend concrete concepts more easily then something abstract. Numbers are an abstraction. They relate a set of objects to glyph. But it is really no great difference from what words we use.

I am sure there are children that once they learn the concept of chair and table look at a stool that has four legs and no back and call it a table. Are they confused when you sit on it? I doubt it. A stool is just a special case of chair that looks a lot like a table.

So for teaching numbers to children we have to make sure we allow for things like that. When we are counting objects we should make sure that they are separated enough so it is visually obvious that they are separate objects.

For example, if we are using index cards we shouldn't allow them to overlap in any way. If we are using blocks we shouldn't stack them until after they have been counted.

All of mathematics is just layers of abstractions and shortcuts. Multiplication is nothing more then a fast way to add a bunch of the same sized sets.

Some people panic when they see something like: 4y = 6y - 4 but it is only because they aren't used to seeing it for what it is. But if you change it slightly then it because something more familiar: 4 times _ = 6 times _ - 4. Then it often becomes obvious what needs to happen. Subtract 6y from both sides: 4y-6y =6y-4-6y reducing to -2y=-4. Then divide both sides by -2: -2y/-2 = -4/-2 and reduce y=2. There is your answer.
Easy, sneezy.

Cent percent agreement. But if the original one would have been something like,

4y - 6y = 4

That would be more obvious to me.