In my last post I wrote about one of my first experiences teaching math to second graders. At the time (way back in 1996!), the math adoption we were using was MathLand, which was very conceptually based. I had several teacher friends that were also educators comment that they loved MathLand and felt it really helped their students learn math conceptually and the lessons kept their students very engaged. I agree with them wholeheartedly. The lessons from MathLand were very engaging and grounded in conceptual understanding.
As I detailed in my previous post, my takeaway from my classroom experience was that the lesson did not go the way “I” had planned. I place the “I” in quotation marks because, at that time, the lesson was based on my expectations for my students, which were based on my knowledge of mathematics instead of theirs. I set the task before them to use dinosaur counters, to make up dinosaur stories, and to record their stories through writing number sentences. If I could redo that lesson, I would start by having the students count to find out how many dinosaurs they had and observe how they counted their dinosaurs. Did they count them one by one? Could they keep track of how many dinosaurs they had counted? Did they put them in groups of 2s, 5s, etc. and then count the groups? If I asked them how many dinosaurs they and their neighbor had together, would they have to start counting from one to add the two groups? Or could they count on from one group?
Observing my students’ behavior in all of the above situations would have told me so much more about their mathematics than the task I gave them. If I had knowledge of their mathematics, I would have known what the next best step for each student would have been. At the AIMS Center, I have been studying the work of Dr. Les Steffe, in which he observed how children come to understand number by how they assimilate counting. Based on the student behavior he observed, he was able to develop a progression of how students develop their understanding of the abstract concept of number.
I still love the lessons in MathLand, but I now know the student centered lessons in the adoption, coupled with the observation and understanding of student behavior, would have been even more powerful for myself and my students.