How did you learn arithmetic? By that I mean basic multi-digit computation, such as subtracting with regrouping, multi-digit multiplication, or “long” division. I learned totally by memorizing a series of steps for each operation. The teacher demonstrated the steps, and we practiced. I’m at good memorizing, so I was able to successfully compute. I’ll be honest in saying that I had very little understanding of what I was actually doing. It was not until I became a teacher and had to explain the process to my students that I realized the complexities of computing with numbers and the need to better understand the math operations, and I am constantly looking for better ways to teach for understanding. Enter Graham Fletcher.
Graham has produced an amazing series of “progression” videos that illustrate how teachers can develop an understanding of the operations (and fractions) by moving through a progression of steps that build understanding. Each vertical progression allows you to meet your students exactly where they are. This week, I am working on division with my 4th graders (whole numbers) and my 5th graders (decimals). I literally studied Graham’s progression for division last week and took screenshots of his illustrations! Here’s a collage showing some of this work.
If you’re ready to delve deeper into the progressions, here is the link to the library of progression videos.