What is mathematics anyway??

When I thought about what mathematics is, the first thing that comes to mind is numbers; adding, subtracting, multiplying and dividing.  I also think of problem solving, geometry, and measuring. However, to give an actual definition of mathematics is quite a challenge.  

In our book, mathematics is simply described as “the science of patterns and order”-meaning all mathematics is is simply learning the basic skills and interrelationships between those skills, then building on them.  

According to Van de Walle, doing mathematics is solving problems by generating strategies, applying them and discovering whether they make sense.  To begin this in a classroom, Van de Walle goes on to say that a teacher must pose worthwhile tasks , then create a risk taking environment where students share and defend their ideas. A student can use many was to come up with a mathematical answer.  As long as the process is valid to get the proper answer, this is considered mathematics.

To “think mathematically” means to use mathematical skills and ideas to justify certain things or solve problems.  My son is five and he loves hockey.  When he isn't in school he lives for the sport.  Each morning when he wakes up, he comes into my room and grabs my iPhone to check the NHL scores.  This morning he said “Leafs beat the avalanche 5-2, they got three more goals than the avalanche”.  This was thinking mathematically.  Although he didn't realize it, he was using his numbers and more and less to explain to me the hockey news.  He then went on to tell me that the leafs had now “won six games in a row because yesterday they won five games in a row but they won last night so now it’s six, right Mom?”. We use mathematical thinking so much from the time we play with blocks putting the proper shapes in the holes to fit into a bucket.  We may not realize that this is what’s going on, but it’s such a gigantic part of our society. I think it is natural for people to think mathematically even though they do not know they are doing so. However, as teachers, we have to engage children and make them want to learn more about mathematics so that they can extend their mathematical thinking to solve many problems not only in school and work, but in society as they go through life.