Friday, December 4, 2015

Learning Math Through Flawed Teaching

Our staff has been working towards implementing the math CCSS for the past few years. Not only are the standards different from the previous state standards for math, but the practices require teachers to provide different structure and instructional approaches.

One of the reasons that I was drawn to teaching was because I received such incredibly bad instruction in math. As a new teacher, I knew that I’d have to develop a whole new approach to math; one that was very different than I was provided. I wish I knew the name of the book that I read in 1978, my first year of teaching, to help me with my 2nd graders. I only remember that the whole book was devoted to developing number sense. I spent many evenings gluing beans on popsicle sticks to create manipulatives to help my students when they calculated problems. As a primary grade teacher, I continued to provide my students with many opportunities to solve problems using manipulatives and helping them to make sense of what they were doing.
 
This week, I posted an essential question at school in the hopes that teachers and students would consider various responses. Teachers expressed frustration at even understanding the question. So in hopes of providing some clarity, I worked directly with a few to help them see how their students demonstrate modeling math, measuring, and calculating change. I began to realize that a major problem was the mindset of the teachers when approaching the question and choosing a work sample to post on the bulletin board. The sense that the product has to demonstrate perfection, was an obvious barrier.

There is no place for “perfect” in a classroom. Not only are the students learning, which puts them in a constant state of change, the teacher is continuously learning. Both will experience moments of exhilaration, but almost never, perfection. When I came to this understanding, I decided that I would model imperfection (as I do unintentionally every day). 


I wanted to pose a math problem that the children encounter frequently. Our PTA is running a Santa’s Secret Shop next week, so I recorded myself posing problems with two different groups of students.  As you watch these, you’ll see the dumb things I did as a teacher. With the two 3rd graders, I could have posed the question and given the money to them in such a way that would have provided either a little more challenge or a little less challenge. Not knowing the students’ abilities in math, I didn’t realize that one was so capably different than the other. They didn’t really learn from each other. In the 2nd video, the three 5th graders were chosen by their teacher who also recorded the scene. I didn’t tell her not to talk until after she began to help them scaffold the problem. I also didn’t prepare to provide them with multiple tools to solve the problem. There are many more flaws to my instruction; too innumerable to list. But what matters is that I gave the students an opportunity to solve a real world problem, struggle to find the result, talk through their thinking, and use tools strategically. They manipulated numbers into parts and had to demonstrate their understanding of operations to solve the problems.. The students were asked probing questions and the 5th graders had the opportunity to learn from each other as they explained their thinking out loud.
















These recordings of students working can provide great insight for their teachers even with all of my missed steps. Let’s all go forward providing  our students with many opportunities to solve problems. Don’t worry about perfection. Think about all that your students will learn as they struggle through problems. Consider how much more you’ll know about them.