YEAH! I read this tweet and thought, "yes, that is an area where I'm fairly strong!" That doesn't always happen. I remember years ago when I was a math specialist. Math coaching was really a new concept, especially in our district, and my colleagues had varying levels of comfort around being coached. Prior to coaching, I was a young-ish teacher in the district. For some colleagues, I'm sure it felt awkward having the teacher who used to teach across the hall come into their classrooms to coach them. To kind of ease the transition, I used to offer my colleagues a few options. They could teach a lesson and I could observe, focusing in on a very specific goal/behavior/skill they were working on. For some this was asking meaningful questions or engaging all students, etc. Other teachers might not feel comfortable with that model so I'd also offer to teach the lesson and ask my colleague to observe me. During the lesson, I'd ask them to notice and wonder and to share with me, at the lesson's conclusion, what they noticed and what they were wondering about now that they'd seen me teach. The goal after building relationships with teachers through both types of lesson observation was to move to a model of co-teaching where we would plan a lesson together and launch it together and then debrief at the end. I wasn't surprised that many teachers opted to observe me teach a lesson. I was almost always surprised by what they noticed in the lessons.
Of course, I spent a lot of time preparing those lessons. They were standards-based and I worked to incorporate mathematical practices (before the actual math practices were defined). So, I was always a little surprised that teachers were seldom impacted by the math. Instead, they often commented on the non-mathy things that I did. (non-mathy = adjective describing the aspects of a lesson that were not directly related to math.) I remember early on I had visited a sixth grade teachers classroom. He was fairly new to the profession but very talented and passionate. He could not get over the wait time I used. He said it made him feel really uncomfortable. He said it was like an awkward silence that made his skin crawl. He mentioned that he couldn't really breathe until it was finally over and I had called on a kid. They he said that he couldn't believe how I had gotten kids to participate in the lesson whose voices he had never heard in class. He also noted that after I had used crazy wait time for about five of the questions, kids who generally had a had flying in the air right away were holding back a little before raising a hand.. When they were called on to participate, which wasn't nearly as often as when he taught (they had been the only kids regularly participating), their responses were much more thoughtful.
Somewhere along the way I learned something important about teaching. Maybe it was from Marilyn Burns. I'll give her the credit. She is amazing and I've learned so much from her. I bet this came from her too. Anyway, I learned that I don't have to have all the answers to all the math problems. I only need to be willing to do the work alongside my students. I learned that I don't even need to find these answers rapidly. I can take my time to thoughtfully make sense of problems too.
So, when a student shares her response I have no issue saying, "Well, let me think about that for a moment. I've never considered what you're saying before. You really have me thinking." Do you know why I say this? It is not to boost the student up and make him or her feel good about him or herself. I'm not just modeling good math behavior. Here is the thing, I say things like this because everyday I am struck by student thinking and need to take a moment before responding to digest it all and make sense of it for myself. I need to give myself a moment or two to think about my next instructional move. Do I ask a student to sum up what we all just heard? Do I sum it up and follow up with a question? Do I ask a question like, "would your way of solving this problem work for all problems like this?" or "how can you prove that what you've said is true?" In reflecting on my lessons, I sometimes wish I'd played a situation differently but I know that I'd make fewer positive instructional moves if I gave myself less think time.
Honestly, there are days in my fourth grade classroom when a student has presented a way of solving a problem that is so "other" to me. The way the student solved the problem is foreign to me and I NEED the time to figure out what the student did and why the student's way of solving works. I need to make sense of it for myself. When this happens, I'll tell the class I need a moment. I sit down on the floor or in a student chair and I give myself the think time I need. When I'm finally there, I share my struggle with my students. For example, I might say, "I followed Sam up until the point when she said.... but then I got confused when she said...then I realized... now I understand...but what I'm still wondering about is...Does anyone else have something to say about this? Do you have anything else to say or add, Sam?"
It is important to me that I'm modeling good math practices. I want my students to understand that often mathematicians don't "just know" the answers to problems but that we can arrive at answers with perseverance and work. I also want them to know that I take their learning and their thinking seriously and it is worthy of my careful consideration. I want them to see me as a working mathematician who enjoys thinking about math and engaging problems. That this pursuit can be rewarding and even fun. I want them to understand that math intelligence is not something that you are born with, but instead, it can be cultivated. I also want my students to realize that I'm willing to roll up my sleeves and do the work with them. I need to teach them that while correct answers are important, I value the process.
The wait time I use goes a long way in building a positive math culture in our classroom.