Conceptual Understanding in Mathmatics

Throughout the math courses I've taken in the K-8 math program here at Lesley University, there is a very common recurring theme that is modeled for us week after week, and concept after concept, and that is the importance of building conceptual understanding with each math concept. This is easier said than done for someone who has been taught all the traditional algorithms, and I can apply them like no one's business, but until I explored some of them at a conceptual level, I was only applying procedural knowledge, rather than doing any higher level thinking. A good example is that I can divide fractions very well, and I always remember how because of the good old saying" Yours is not to wonder why, just invert and multiply." But in a number theory class when we had to use geometry and area models to show we knew WHY rather than how, I was immediately out of my comfort level. Conceptual understanding should be a base that helps bridge the gap between the concrete and the abstract. If we jump right to the abstract, then we are doing a very large disservice to students.
As a math teacher, I was already aware of this, and thought I was doing a fair job teaching conceptual understanding first,and in some cases I was, but there are so many fantastic ways to explore math that appeal to all types of learning styles and provide a very rich, multi-modal way of building on prior knowledge to form new understandings. Just when I think I have great teaching activities, I discover yet another way in one of my classes to explore math. In my Geometry class we were recently exploring copying angles, and I could certainly do this with a compass, but we had to use paper-folding to accomplish this and then explain why it worked. What a challenge! But I learned so many new things by doing the paper folding and it increased my understanding immensely.
As a math teacher, I spend a fair amount of my time searching for,and differentiating activities to reach all learners in my class. I have found that each Lesley class I have taken has handed me a multitude of fantastic activities built upon the premise that conceptual understanding is key, and I get to experience these activities first myself as the student before sharing them in my classroom. What a fantastic learning opportunity this has been. When I look back at my own growth as a teacher in the year I've been in this program, I'm amazed and extremely thankful that I chose the K-8 math class series. Jen Nelson