What was your greatest 'learning' this semester with regard to teaching children mathematics? How has your thinking shifted?

This semester, I have experienced a lot of great 'learning' with regard to teaching children mathematics. Math is not just about drilling students by doing facts and worksheets. Math is so much more than completing problem after problem and it took me a while to understand this because that's the way I learned math and that's all I knew math to be. I always knew that I wanted to make learning math fun and interesting, but I had no idea how to do that. Math has always been a subject that I've never enjoyed, even when I did understand concepts, I hated doing the work. 

I learned this semester that math can and should be enjoyable for students because they use math all the time through things like telling time, mental mapping and problem solving, problem solving being a HUGE one because we problem solve every day! Students need to understand the purpose of learning what they're learning, in order to help them completely understand; using everyday examples that create meaning for them, as well as using manipulatives to help demonstrate and to help solve a problem (being something more concrete for them to see) help in amazing ways. I can vividly remember asking my teachers over and over, when am I actually going to use what I'm learning, in my everyday life, and the answer was always the same: "You will. So you'll need to know how to solve it," never ever an exact answer. I would probably be much better at math if we were given the opportunity to use manipulatives and if my teachers found a way to relate what they were teaching, to my life in some way.

Another thing that I learned this semester is that there is never only one way to solve a problem. When I went through school, we learned the proper steps to solve a problem the correct way, even if I could solve it a different way, i had to show how to solve it the teachers way so "that I knew what I was doing." I'm so glad to hear that a lot of people don't see problem solving in that way anymore, we even seen in the curriculum guides and text books that they show teachers and students different ways to solve things such as addition and multiplication problems. This is a great improvement because not everyone thinks the same way, and if someone can solve the same problem differently, but still get the same answer, why would that be so wrong? As well, "problem solving" itself, doesn't just include word/story problems, something very important that I learned. Problem solving is pretty much what makes up mathematics; most everything you do in math is solving a problem in some way. 

I came into this course thinking that I would have to be writing lesson plans for mathematics, and stretching my brain to develop different worksheets and exercises to add to my portfolio for future reference, like I have with so many other courses I've completed. But to my surprise, I found myself learning how to teach math in a very new and different way, a way in which I was definitely not use to. But after completing this course, I now understand that there are better ways to teach math and it can be fun and creative and at the same time allow students to critically think and foster deep learning.