Turtle Multiplication and Conceptual Understanding
Math teachers love algorithms. I think one of the reasons I love math so much is that there are rules to follow. I know that says a lot about my personality. When I was in the classroom, my students would say, “Just show me how to do it.” I also heard, “I can follow the steps and get the right answer, but I have no idea what I am doing.” Unfortunately, I could relate to these students. Much of my math career as a student was like this. It was only when I began to teach it that I truly understood the whys and hows of math. I think this is one thing Common Core will fix for students. They may hate it and resist it at the beginning, but they will retain it.
When I was in the classroom, I was guilty of reducing mathematics to an algorithm. I taught cute tricks like “Outers over Inners” to simplify complex fractions. I think all teachers are guilty of this at some point. I came across this video in an elementary classroom that testified to this:
The teacher was teaching students how to multiply a two digit number by a two digit number. I had heard from several teachers how great this “new” method was for students. It is so cute! I had to bite my tongue. If you watch the video, my questions are “Why does the turtle drop an egg?” and “Why do we draw a collar on the turtle?” I need students to understand this. What happens if I have a three digit times a two digit? Does turtle multiplication still work? I need conceptual understanding that transcends to problems of varying types.
Here is how I would love to see multiplication by two digit numbers taught:
What are your thoughts? Are we hurting students by teaching cute algorithms in isolation? Is procedure really what matters? What other “tricks” do we teach that hinder conceptual understanding?