What is mathematics?

I was one of those students in school who always ask "why?". Sometimes I didn't get an answer as to why things were they way they were, sometimes I did get the answer and even sometimes I got a delayed answer that may have just had to wait a class or two. My experiences growing up were good and I was really interested in math, so when I got older and went to university I decided to find out "why" for myself. After four years of a math degree I still can't give you an exact definition of what math is because math is complex and many people look at math in different ways.

Throughout elementary school students were expected to learn how to add and subtract, and multiply and divide using a given algorithm to find an answer and then they were tested with pencil and paper on how well they had mastered this procedure. The same is true for junior high and high school. Math wasn't made to be fun, it was taught as one subject that was separated from all other subjects. Students mostly thought that math was memorizing formulas and then solving problems with these formulas to get one particular answer. Chances are if you were a student who solved a problem in a different way then was expected, you may have gotten it marked wrong. But the truth is that math is not a subject that should be separated from everything else and it's not just having a formula and answering a question to produce an answer, in fact there are many branches of math such as geometry, patterns, counting, sequencing, algebra, graphing, etc.. Some of these involve formulas and some don't, and if they do involve formulas then there may be more then one way to solve the problem. Many students would try to memorize what they were doing and not fully understand it, therefore they would get very confused and end up not liking math.

In his talk "What Kind of Thing is a Number?", Reuben Hersh states "Mathematics is neither physical or mental. It's part of culture, it's part of history, it's like law, like religion, like money, like all those very real things which are real only as part of collective human consciousness". I think this is a good way to describe math, it is not internal or external, it is both, it's a concept that people follow, and it's involved in your everyday life whether you realize it or not. He later states "A good math teacher starts with examples. He first asks the question and then gives the answer, instead of giving the answer without mentioning what the question was." As a teacher I hope to give my students the ability to understand what it is they are doing and let them think for themselves, I would like to per mote cooperative learning and let the students discuss among themselves why things are they way they are, and make meaning of the answers they are producing. I will at first give them a question and give them time to think about it before talking about the question as a whole and then showing them the solution.

During class we read the book "Math Curse" by Jon Scieszka and Lane Smith. I highly enjoyed this book, I usually get excited when I see books directed at younger children about math. The main reason for this is because I don't remember reading anything like this when I was young and I think it is a great way to get young students involved and interested in learning math. Math is a universal concept that is involved in everyday life and this is represented in the book when Mrs Fibonacci tells the class "You know, you can think of almost everything as a math problem..." This book has one student in a whirl-wind of thoughts about math and she thinks about EVERYTHING as a math problem.

These are my thoughts and views on what math could be but there is still alot to learn and knowledge to be gained in the coming years of my career.