It all began in elementary school when we started talking about long division. While I couldn't really remember the multiplication tables and that made multiplication and simple division somewhat difficult, I wasn't really bothered until we got to long division. I was utterly lost. My teacher started saying something about the leftovers when you break up a six-pack of cokes, or a dozen eggs. I don't remember exactly what I was thinking but I know that I was completely lost. Like, spooky island with a hatch, lost. We were in completely different hemispheres.
I'm not really sure that I actually gave up at that point, though it is clear that this was that point at which I started to find myself completely unconcerned when I didn't have a clue what the teacher was talking about. Not understanding? Why be concerned? There wasn't anything new about it.
I did find that I liked Geometry. As a sophomore in high school I took an advanced geometry class and I loved it, even though it was really hard for me and I still didn't get everything. I liked how ordered it was and how spatial. I could picture the problems in my head and usually I could get myself from point A to plane X, though often, I couldn't explain how.
My first teaching job was to teach 5th graders math and social studies. I loved it. It was logical, systematic and rewarding. Who doesn't get a kick out of helping a kid understand something that they never thought they could understand.
Today I was listening to Science Friday on NPR with Ira Plato. I'm not really sure how the segment had been introduced, but there was a mathematician talking about how people resented math because they often didn't understand it and they felt excluded from it. I immediately perked up.
"Yeah! That's right!" I was thinking.
A caller came on from Tulsa, OK and she said that she was really excite that they were discussing that particular topic because she used to teach math and she always got frustrated when her students asked her when they were ever going to need that stuff. Her response? You will always need problem solving skills. It's helpful to know that, in life, when you need to find X, you should always list what you know and what you do not know and work from there.
She kept talking but I was having an epiphany and didn't catch all of it. As they went on to discuss other aspects of math I started to think of it as problem solving instead of the Dreaded Discipline of Numbers. That's when I knew she was right. Life needs math. When we can learn to look at our problems systematically we can solve them so much easier. We have to remember that with anything (everything!) there are rules we must respect, that govern the way things work. If we can learn those rules we can use them to our advantage and we will realize that we know much more than we thought we knew.
So how do you solve a problem?
Identify what you know from what you don't know. This can be really hard because sometimes we think we "know" something, but the truth is that we assume it, or we don't really understand the information we have. Always verify what you know.
Identify the problem. Somethings are algebraic equations where X is known and Y is unknown, but some things are word problems and you have to learn how to identify the problem and separate it from the extraneous information. That extra information might seem important or interesting or compelling, but usually it's just distracting you from the most important thing. If you can weed out the junk information and get a good look at the actual problem, you've got a good start on things.
Figure out the rules. There are rules for everything. Know what they are and you can use them to discover all sorts of new things that you didn't know you knew.
Simplify! Use a little logic to make things easier to understand. Every problem is a series of smaller problems and if you can take them each one at a time you will find that the larger problem is less frightening than you thought.
You are never done with a problem until you go back and make sure your answer makes practical sense. It's easy to get bogged down in numbers and rules, so when you make a decision about the answer, step back and look at it closely to make sure that it makes sense.
And my favorite...
Don't be afraid to make mistakes. Because you are going to. It's not the end of the world, and the truth is, you will learn a lot more from making mistakes than you ever will from getting it right the first time.