Interesting feedback

I modeled a number talk for a kindergarten teacher the other day and am really interested in a piece of her feedback and how it can inform my coaching work with her as we move forward. “We will be working on keeping the same level of excitement while maintaining a respectful listening environment.  Students were not as engaged as they usually are -- well behaved but not as excited.  Tricky balance!!” I wonder what engage in a leaning environment looks and feels like to her. I am wondering if she would feel the same way if she were teaching 3^rd or 4^th grade. Would her expectations be different? What are her goals for her girls as mathematicians? What does it mean to be a mathematician? What does a classroom of mathematicians look like, sounds like, feel like? What is her role in this classroom of mathematicians? What is the difference between engagement and entertainment?  

Seeing results...

How will supporting teachers to implement number talks in their math classrooms inform my coaching practice?

I am not sure if this post is really supporting my question but I want to share the experience anyway because it just so awesome to see. If anyone can ask questions that would support me in connecting this experience to my research question it would be appreciated.  

As I was shadowing my principal the other day we went into a kindergarten classroom just as they sat down for a number talk. This was not planned. This classroom is a CTT room. However, on this day, only the special ed. teacher was present. This teacher is new to number talks and at the beginning of the year questioned their purpose and effectiveness.

The number talk that she facilitated on this day was amazing. It was a quick image number talk around seeing six. Students were listening to each other, sharing their thinking, and reasoning about the parts they saw and how they related to the total. I truly wish I had videotaped it. The teacher asked thoughtful questions of her students that pushed them to make connections and articulate their ideas clearly.

It was beautiful!

Models?

I did another model number talk yesterday; this time in a different K classroom. However, after reading Robin’s comments about modeling versus collaborating I am wondering if this was the best decision. Some of the reason I have done models, both in the past and the one yesterday, are:

·         The teacher has asked me to and says that she learns best by watching

·         To build trusting relationships  by reversing the role of facilitator and observer

·         To  provide teachers the opportunity to see me critically reflect on my teaching

·         To model a strategy, technique, or process with which the teacher does not feel comfortable

·         To practice my own skills

Some models have turned out well. Teachers have reflected that seeing me do a number talk made the process and work much more clear. They were able to focus in on specific aspects of number talks, like questioning and recording, on which they want to work. I think the model supported them in coming to a new understanding of their own practice.

 However, having said all this, I realize that modeling could be holding a teacher back from meaningful growth. There is potential that a teacher feels nervous about being observed (I can certainly empathize with this) and it is less scary to have someone model. If this is the underlying reason for the model I am afraid that learning will not happen. I am going to assume the best intentions though; teachers are not asking me to model so they can get out of teaching. I believe this! All of the teachers I have modeled for lately are present and have insightful reflections when we debrief. They view the model as a learning opportunity.

I think as a coach I need to get better at collaborative co-teaching. Ironically I would like to see this type of work modeled for me. I am not sure I have really experienced, as a teacher or coach, true collaborative teaching. How do I do this so the teacher doesn’t feel like I am correcting her? How do I manage this in the short time we have for number talks? Does it happen organically or do we plan who will take on certain parts of the number talk (this seems more like a modeling to me). What planning and preparation goes into this work and how is it different than regular planning? What does it look like? Sound like? Feel like?

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.     

Number talks are not easy....

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

Recently I have noticed that many classrooms are using their number talk time for conversations that do not truly fit the definition of a number talk. I am concerned about this but at the same time, at least for now, I am not exactly sure if this is a big deal. We are in the process of figuring out this approach. This is where we are right now but with continued practice and reflection we will develop and grow our number talk practice.

Number talks are supposed be work around efficient computation strategies. What I have seen in classrooms are explicit talks about anything from symmetry to place value. Some of the teachers who are using their number talk time with some flexibility are teachers that I have actually done coaching work with specifically around number talks. I believe all teachers have good intentions and the conversations that are being had are purposeful. But, they are not number talks. I think teachers struggle with understanding student strategies, the math that lies within those strategies, and recording those strategies in a thoughtful way.

I am learning that number talks are not easy. Teachers need a lot of time and support while exploring and developing this practice. One five week coaching cycle just isn’t enough.  Since this is a new program for our school and our teachers, I am wondering how the leadership team and I can be more targeted and supportive in implementation of number talks. How can I facilitate continued and regular support even as I progress through my coaching cycles?

Another Question About My Methodology

There is something that is not working about my methodology. I have yet to get feedback from teachers about our work with number talks. I know this is an integral aspect to my research but I am having difficutly making it happen. Sometimes I feel like we didn't actualy do enough for them to be reflective. Although I always find something to be reflective about so why shouldn't they. Othertimes I just feel guilty that I am giving them one more thing to do. Should I have included my reflective questions about working with me around number talks in my general coaching cycle feedback form? I know it may seems silly but I think one form is just less overwhleming.

Learning by Doing

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

I was recently reminded of why doing the math we will teach is so important. Kelly, a first grade teacher and I are members of the same study group. Study groups are a PD opportunity where teachers, instructional leaders, and staff collaborate in small groups to learn about common topic of interest. This year my group is focusing on the Context for Learning program. We agreed to rotate the facilitator role for each study group session and Kelly volunteered to go first.  It was a string talk that she facilitated during our last meeting that provided me with this opportunity to reconnect with the experience of doing math. String talks are very similar to number talks and the reason why this anecdote is relevant to my research.

Kelly’s string talk was about looking at number on a Rekenrek. She did a quick image routine where she would quickly show us her number and arrangement of beads and we had to recreate the amount and then share how we saw it. I think, at first, everyone felt really silly doing this math together. As adults, it wasn’t challenging math. However, as we shared our individual thinking a very important idea about doing math came to light: There are lots of different ways or approaches to solving a problem. Even though the math was basic we were able to have a rich discussion about both content and pedagogy. 

I know logically that bringing a group of educators together to do some math can be a powerful experience but somehow I had become disconnected from the practice. With the very fast pace of our days doing math somehow got put on the back burner.  It has become an afterthought rather than the heart of my coaching work. At times, teachers and I will do math together but it happens off the cuff and usually because we have some extra time at the end of our planning session. I have had many conversations about how doing the math first provides insight and informs our planning but talking about it very different than actually doing it. I need to do better job of providing the time and space for teachers to engage with the mathematics they will teach. I need to support them in internalizing this as an integral part of their planning work by allowing them to experience and reflect upon its process and impact.