I was awake at 5:30 this morning. Maybe you were, too.
For me, it was because of a math lesson that was coming up in a few hours: subtracting negative integers from negative integers. I wasn’t satisfied. In fact, I was troubled. It was bothering me so much that it had awoken me in the early morning hours.
Subtracting negative integers from negative integers.
Sure I could easily subtract a negative integer from another integer, and I could explain how to do it in just a few moments. But that is not what I was pursuing in the lesson. I wanted the students to have a deep, meaningful understanding of the concept. And as I fell asleep last night, exhausted, I knew that I still hadn’t wrestled the idea to the level of a deep, meaningful understanding that I was seeking.
I’ve been an elementary teacher for 17 years, at grades 2-5, followed by two years as an instructional coach at a K-5 elementary school. This year my district developed a new position: District Math Coach. That is now me. We have 5 elementary schools, one middle school, and one high school.
Early on I decided that I wanted to gain a clear perspective of what it is to teach like from the “front” of the classroom—at all of the grade levels. We all know the “front” actually means the front and the back, the left and the right, and all throughout the middle. When I think of math, I want to think of instruction and how students and teachers wrestle with challenging content. I want the student’s perspective. I want the teacher’s perspective, especially from the grade levels I have never taught. So I asked the teachers from the middle school and from the high school if I could come teach a lesson in their classrooms.
Today I went to the middle school.
Initially, I had been tempted to ask the teachers to give me a somewhat easy lesson to teach so that I could connect it to my own experience. However, part way through that thought, before I could even finish the request, I changed my perspective: No, you know what, give me one of the most difficult lessons you have coming up this week. That is what I really want to experience. That is what I need.
So, last night, after wrestling with the concept for a few days, I went to sleep clearly knowing how to subtract a negative integer from another negative integer, but not fully understanding the concept at a deeply satisfying conceptual level. I had examples and stories ready, I had thoughtfully read the history of lessons leading up to this one, I had discussed the lesson with the teacher (who provided wonderful insight!) and I asked follow-up questions. I had even developed interactive, triggered digital integer chips to use throughout the lesson, but I was still unsatisfied with the depth of my understanding of the concept itself and what it truly meant. So I found myself awake, long before my alarm was supposed to go off, wrestling with the idea, trying to understand it at a very deep level, at the depth that I wanted the students to experience. I knew that the deeper I could reach, the deeper I could clearly see, the better I could lead the students into a place where they could deeply and personally wrestle with the same idea.
Sure I already knew they would be successful with the process, and that I could observe, measure, and mark off procedural success. But that is not what I was looking for. I was looking for the deep wrestle from the students that leads to a deep, lasting understanding that can become the solid foundation for future learning. The kind of wrestle that woke me up.
After all, I cannot expect the students to tangle with this concept at a deep, deep level if I have not tangled with it myself at that very same level. And so I tangled, early in the morning, precisely so the students would have the same opportunity.
Note: This post was written in October as a personal reflection. It was never shared. Yesterday I ready Pernille Ripp’s post YOU CAN’T JUST DO IT TO THEM. After reading Pernille’s post I decided to go back and add this to my blog.