I’m coming up on the two year anniversary at my current job and I’ve been reflecting on how my thinking has changed over this time. Before this job, I felt I had a good grasp on teaching math. I had just spent 20 years teaching junior high math. I faced down the torch and pitchfork crowds on a daily basis and even managed to pique an interest in some, entertain others, and teach skills to many. I was told I was a good teacher. I worked very hard at creating lessons that I felt would help make the content accessible to my students. I taught using manipulatives, graphic organizers, discussions, multiple representations, technology, games, and more. I designed my lessons incorporating activities to build what I believed was conceptual understanding. I connected the lessons to prior knowledge. I understood, better than most, the connections between the math operations of adding, subtracting, multiplying, and dividing whole numbers as well as connections between the sets of whole numbers, integers, fractions, percents, and decimals while using the math operations. Most teachers teach exactly the way they were taught, but I was constantly trying to stretch my understanding of the content and improve my teaching practices. However, I didn’t know what I didn’t know.
Even with all I tried to do, I continued to have students in my classes who struggled and were not successful. Worse, I didn’t always know why. I had junior high students who couldn’t subtract or multiply proficiently, many popping up fingers to try and determine a result. Fractions might as well have been quantum physics. I would see students in class who were taking notes, asking questions, completing homework assignments and yet continuing to struggle. Despite my best efforts, I still had students who failed to understand. As much as I learned, and as hard as I worked, I felt something was missing. Again, I didn’t know what I didn’t know.
Since joining AIMS, I have come to know, by reading and understanding research, that success in math begins with a child’s journey in the construction of an understanding of number. As adults we have forgotten our journey. It was so long ago and we have no memory of it. As a teacher, I believed my role was to teach the students skills in mathematics which they operate on numbers. Mathematics is connected ideas and these ideas are based in number. It is not isolated rules or concepts, which is why a problem can be solved multiple ways. Developing an understanding of number provides children with the ability to see and make these connections in mathematics and also develop the skills usually taught. In early education the teaching of math should be focused on the development of number, not only skills. In so doing, children will construct knowledge of mathematics in meaningful ways. I didn’t know what I didn’t know. Who knew?