Understanding and Recording

How does supporting teachers to implement number talks inform my coaching practice?

Yesterday I modeled a number talk in a 2nd grade classroom. I had offered this to the classroom teachers and they quickly said that it would be helpful. I also asked the teachers what type of number talk would be best. They said the girls were working on finding landmark or friendly numbers and some had begun to explore compensation. I decided to do the following number talk: 40 + 4, 39 + 4, 39 +15, and 39 + 39. The teachers had confirmed that they thought this would be a purposeful talk. In the end I was only able to get through the first two problems but I also feel like the conversation we had about the problems were useful for both the students and the teachers who were observing me. Let me share some of the strategies the girls used to solve the first two problems.

• An open number line.
• start at the larger number and make 4 hops
• each hop is worth 1
• I recorded this strategy on an open number line - exactly as the student had described
• Replace the 0 in the ones place with the 4 ones being added
• I recorded this with an arrow going from the 4 to the 0
• I also asked the girls if this would always work. Meaning if we have a 0 in one’s place and we are adding on ones can we always “just replace” the 0 with the number being added on. There was disagreement from the girls about this and we decided that we needed to explore this idea some more.
• Compensation
• Take one from the 4 and give it to the 39 – then you have the same problem as before
• I recorded this by writing -1 next to the four and drawing an arrow from the 4 to the -1. I then drew another arrow from the -1 to the 39.
• In retrospect perhaps I should have written a +1 next to the 39
• I also had the girls turn and talk about this strategy (what did she do? What did you hear?) and then had a student tell the class about what she and her partner had discussed.
• Making 10
• Break the 39 into 30 + 9 – then take 1 from the 4 and give it to the 9 to make a ten – then put it all back together.
• I recorded this strategy by writing
• 39 + 4
• 30 + 9 + 4
• 30 + 10 + 3

Although I had asked the girls to see if they could use the first problem to help them solve the second problem none of them noticed, or at least didn’t share, that 39 was one less than 40 and that they could use that information to solve quickly. However, I realize that the compensation strategy was getting at this idea – almost as if this was a first step to recognizing and efficiently using the relationship. The student turned 39 into 40 but did not specifically notice or share that the sum of the second problem was one less than the sum of the first problem because 39 is one less than 40.

Although I have not yet had the opportunity to formally debrief with the teachers, one teacher, upon completing the talk commented that it was really helpful to watch me. She said that it helped her hear my questioning but it was particularly helpful to see how I recorded the girls thinking. She added that she sometimes struggles to understand what a given student is saying and, even when she does understand their thinking, it is difficult to organize their thinking clearly on the board. How can I support this teacher to understand the connection between my questioning and my ability to record the student’s strategy? How will thinking about all the possible ways a student may approach the problem, before actually facilitating the number talk, support the teacher in interpreting student strategies? 

I am going to do two more models this week. I will continue to focus on making landmark or friendly numbers for the girls. I will pay attention to the questions I ask to help me understand the student’s strategy and how I record for the teachers. I am thinking about video tapping the talk. I also want to be really purposeful in our debrief. I have not yet planned for that time.

I am thinking that number talks are an excellent way for teachers to develop their ability to interpret and understand student strategies. It also provides teachers time to practice recording student strategies clearly. I am wondering if this practice of recording student strategies will help teachers know how to support students in recording their own strategies clearly. These are all focal points for my coaching.