The Ways in Which Students Learn Part 1 - Early learning

Although we are looking at grade 7/8 math, I think it is important to remember where kids start with math, and the ways in which they learn early on, and how this may effect the way they learn today.  In teachers college we looked at the order of learning. It was an interesting thing to look at. We were told by our teacher that math learning happens on three different levels.

1. Things
2. Icons
3. Symbols.

We were told that the learning happens in this order. Students begin by learning about things, and develop an understanding of them, but that teaching through Icons and Symbols is very challenging. I think that it makes sense in the fact that students can relate to things that they actually see. If I give a student five cupcakes two initial things will probably happen.

1. That student will recognize that I gave them five of the same things, but each one is classified as it's own
AND
2. That students going to be pretty pumped up about having five cupcakes placed in front of them.

If I were to then take away three of those cupcakes, the student would intuitively know that they now have less cupcakes, and in this way, by showing "things" students can understand the concept (in the cupcake situation, basic subtraction).

It makes sense to me, that icons and symbols would be tougher to teach to children. Icons and Symbols are visual representations of things. I can understand that if you don't know what the "things" are that are being represented, then it isn't going to be easy to understand the icons and symbols. Like in this picture for example...

There are many different symbols being shown, but if no-one explains what they mean, I will make up my own understanding of them, and will base my understanding of them on my previous knowledge of "things" (even if these things may not be what the symbols and icons are representing)
I can understand that in math terms this must be extremely important, because even addition, subtraction, multiplication, division; these basic math concepts are based around an understanding of symbols and icons. Symbols and Icons are important, BUT, and understanding of the things that are happening has to be there, before the symbols and icons can mean anything.




-Jamie