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.   

The K Team

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

The 4 lead teachers on the kindergarten team share the same smart goal. As I discussed in my last post this is around enhancing student’s ability to explaining their thinking clearly and articulately and increasing student to student discourse. I am thinking that it would be useful to focus the coaching cycle with the K team on number talks. Although I have done work around number talks in other coaching cycles I have not yet made it our sole focus. Can I do this? I like the specificity of it but am wondering if the teacher will not feel supported in their workshops. How can we translate our work in number talk to the math workshop without losing focus?

The other piece I am thinking about is working with this team as a whole. At the moment my meetings have been individually based or co-teacher based. Since they all have the same goal it seems purposeful to be planning and reflecting on number talks as a team. I think this would also create a great opportunity for teachers to observe each other’s number talks and learn from each other.  When the team had worked with Iva during their literacy coaching cycle they had given feedback that they would have liked more team planning. They shared a literacy smart goal as well. Iva had done two meeting as a team, one at the beginning of the cycle and one at the end. I am wondering how often we should be looking at number talks as a team. Is it just a few times throughout the cycle or do we try to make this our regular practice?

Her Smart Goal Matches My Research

How does supporting teachers in implementing number talks inform my coaching practice?

Sharron, a kindergarten teacher, and I just completed our first planning session in our new coaching cycle. Sharron’s smart goal for the year is about supporting students to explain their mathematical thinking. In our conversation Sharron revealed that she had read most of the number talk book and watched the videos and felt inspired. She feels lucky to have a designated time in her week to have number talks with her girls. What a great opportunity for me and my research!

During our conversation I wanted to dig into her smart goal a bit. I set up my agenda as follows:

·         What does "explain their mathematical thinking" mean to you?

o   What does it look like, sound like, feel like?

o   Is this orally or in writing

o   Why is this goal important to you?

·         What have you and your studnets done so far in terms of explaining math thinking?

o   What are some highlights?

o   What are some aspects that you are thinking about?

Sharron shared a lot of valuable insights about where students are and where she would like them to go in terms of explaining their thinking and discourse. I feel that my agenda helped me gather the information I was looking for. I know that Sharron is seeing that some of her students get lost in the excitement of number talks and don’t often have the time they need to think or the opportunity to share. Sharron is planning on trying some parallel taught number talks with her fellow teacher. We also discussed students using the quiet thumb sign and teacher’s responsibility to provide think time. Some questions I am thinking about that may support Sharron in thinking more about this idea: Does math have to be done quickly? Why or how could speed support a student’s math ability? How do they develop that speed? When does speed enhance the learning when does it not make sense?

I had to explicitly ask Sharron to share something positives that she sees in her number talks or math class in general. It’s not that she was being negative but simply that she was focused on the things she is thinking about. It’s great that she is reflecting this way but I want her to also reflect on what is going well too.

Feedback I Recieved

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

In my mid-coaching cycle feedback form I asked:
What’s missing for you in this cycle? Any suggestions for how this cycle could be improved?
The response I got was:
Mollie (co-teacher) and I have lots of great math conversations and number talks. I remember you saying that number talks should be short. Our talks usually go over 10 minutes. I’m also concerned about engaging all learners into our rich conversations. I’d like to see you model a number talk.

I suppose working with these teachers around their number talks has not yet informed my coaching because we haven't really begun. However, the simple fact that they are asking for support with number talks does inform my coaching. I am excited that they are thinking about and grappling with number talks.

Questions I would like to ask or am wondering about: How long do their number talk generally run? Who is doing most of the talking? How do you two  (co-teachers) plan a number talk? Why might it be important to keep number talk short? Have you ever seen a number talk in action other than your own?

Debriefing a Model

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

Last week I had a the opportunity to debrief with two 2nd grade co-teachers for whom I had done a model number talk the week before. Originally I had planned to use the guiding questions I provided for their observation as the guiding questions for our debrief. However, when the time came it just felt better to ask them for highlight, suggestions and questions. I had them bring their notes from the observation  to support our conversation.

The teachers had a bunch of interesting observations but one of their reflective comments really stuck out to me as informing my coaching.

One teacher said she was surprised that I was able to get to all four problems in 10-12 minutes. She noticed that I would ask for only 2-3 students to share their strategies, maybe have the other girls comment or ask a question, and then move onto the next problem. She said that often they only get to 1 or 2 problems because they are trying really hard to make sure everyone understands. This conversation made me realize that, as their coach, I need to pay more attention to their pacing during number talks as well as mini lessons. As they are planning are they making predications about student's possible misconceptions? What questions do they ask when a student does not understand during a number talk or mini lesson? Does the student not understand or are they just having difficulty explaining their thinking? In addition we may need to dig further into the purpose of number talks. What do you think the benefits are of providing girls with a short amount of time each day to do mental math? Why is it important to get through each of the problems in the number talk? What do you need to understand in order to facilitate a purposeful 1-15 number talk?   

Models and Reflection

Yesterday I modeled 2 number talks. One in a 2^nd grade classroom and the other in a 3^rd grade classroom. I had not had the opportunity to observe whole class number talks in either room. I would have liked to have had this opportunity so that my planning could have been more focused but scheduling was just tight. In the end I just decided to jump in and do the number talk. I hoped that teachers would see this as my willingness to take the risk. I also thought that I could write some reflective questions that addressed the appropriateness of the number talk. Was it rigorous enough? Were students able to access the math? Was it connected to the content being taught and learned in math workshop? Were my expectations and routines consistent to what was already established?  Also, having been in both classrooms for math workshop and having had planning meetings with the teachers I had some idea of what was happening during number talks and what would provide opportunity for teacher reflection and growth.  

I provided guiding questions for the teachers to use as they observed me. I pulled them mostly from the Number Talks book but felt that they connected well to thinking these teachers are engaged in terms of math content and pedagogy.

·         Do students use one problem to help them solve the next? How?

·         What strategies do you hear students using? Is this what you expected?

·         What models do I use to show student thinking? How do these models support student understanding/development?

·         How do the sentence prompts help students discuss the problem with each other?

The last question was one that I added. Supporting students in talking to each other about their ideas and strategies, rather than just to the teacher, is an aspect of the routine that both classrooms are working on. I wanted the teachers to start thinking about how sentence prompts could help students create math conversation amongst themselves. I did a simple introduction with the prompts and had them hanging for the girls to see. That was it during the number talk.

In the debrief meeting I will ask teacher reflective questions around the prompts. Which prompts do you think will be easiest for students to use? Why? Which will be most difficult? Why? How will these support students in talking to each other about their thinking? Are there any students who will struggle to use the prompts? Why do you think they will be difficult for these students? What else could we do to support these students? Are there other prompts that could be useful? Are there other tools that we could use to create discourse? Below are the prompts that I wrote out on a chart.

·         I agree with _________ because ___________.

·         I do not understand ____________. Can you explain this again?

·         I disagree with __________ because _________________.

·         How did you decide to __________________?

Adjustment to Methodology

I need to make an adjustment to my methodology. My intention was to work with the same 5 teachers throughout two 5-week coaching cycles. This has proved very difficult. As I switched from cycle 1 to cycle 2 the group of teachers I work with changed. I thought I would be able to continue to work with the first group of teachers just around their number talks but the scheduling is nearly impossible. They are now in a coaching cycle with the literacy coach and I need to be respectful of their time. I want this work to be meaningful and useful to them not a burden. As such I am now working with my new group of teachers around their number talks. I do not think this adjustment will be a problem as the process, no matter who I am working with, is informing my coaching.

Small Group NT Model

Before the holiday break I had modeled a number talk for a special education teacher in one of our CCT classrooms. Let’s call her Sarah. Sarah had been concerned that during whole class number talks a select group of girls, all with IEPs, were unable to engage with the content and discussion. At that time, the class had been working on visualizing doubles and near doubles addition combination on a double tens frame.  This small group of girls was missing the opportunity to develop new mathematical understanding and skills related to being a mathematical community member. Sarah was becoming unsure that these students would ever be able to talk about their math ideas clearly. I wanted her to see, that when provided with accessible but challenging work, her girls would be able to talk about math in meaningful ways and develop new understanding through their conversation. I also wanted Sarah to see that there is flexibility in the approach to a number talk.

We decided to do some small group number talks with this group of girls that focused on subitizing small numbers. I would model the first one around seeing 4. I decided to also video tape this number talk so that during our debrief Sarah, her co-teacher, and I could talk about what we noticed. It was a good opportunity for them to see me reflect on my process and question asking in a critical but positive way and use that information to inform my instruction. 

Highlights from the Debrief:

·         Sarah shared that she was surprised girls were able to articulate their ideas in a clear way.

·         Sarah said the girls shared strategies that were more efficient than what she had expected.

·         Sarah reflected on my ability to stay calm and said that sometimes after a long day working with the girls she can get frustrated by the challenges they face to in terms of attention.

·         I was able to point out a specific aspect of my number talk that I would have done differently.

·         It informed out instruction in the sense that this approach and content was appropriate.  

Frustrations from the Debrief:

·         It was difficult to hear the video.

·         I should have put together thoughtfully chosen clips of the video and created questions around those clips.

·         I am not sure how useful the process was for Sarah’s co-teacher.

This week I received Sarah’s Mid-Coaching Cycle Feedback. In response to the question “What’s missing for you in this cycle? Any suggestions for how this cycle could be improved?” Sarah wrote that she would like me to model some number talks with the whole class. I have not seen a whole group number talk and asked that I see one first and then we plan the model together. I am interested in what they are working on in number talks and how they are feeling about the small group of girls participating with the whole group. What skills or understanding have the girls developed that will allow them to participate with the whole group? What did you do to support them with this development? Are there any supports you can provide while the girls work with the whole group?  

Literature Review 3

Richardson, K., (2011) what is the distinction between a Lesson and a Number Talk. Retrieved       

July, 2011 from http://www.mathperspectives.com

            In this article Richardson (2011) addresses a question that teachers often face when thinking about number talks: “What is the distinction between a lesson and a number talk” (2011, para. 1). She argues that lessons are goal oriented and often relationships that the teacher wants students to see are made obvious. A number talks, on the other hand, Richardson sees as “an opportunity for children to learn that they can figure things out for themselves in the way that makes sense to them” (2011, para 3). Although I appreciate Richardson’s distinction I am wondering if providing students time to grapple with problems, invent strategies and construct solutions are solely aspects of a number talk. Shouldn’t students be doing this type of thinking in their daily lessons as well? I am interested in thinking about and discussing the difference and similarities between daily lessons and number talks with teachers. I to support teachers to transfer the rich thinking and problem solving involved in number talks to their regular instruction?

Literature Review 2

Parrish, S. (2010). Number talks: helping children build mental math and computation

strategies, grades K-5. California: Math Solutions.

In chapter 1 Parrish (2010) discusses the rationale for practicing number talks in the elementary math classroom. She depicts mathematics education as historically misconceived resulting in a math-phobic nation unable to meet the demands of today’s informational world. Parrish argues that math is a door to opportunity and one key element is to provide students with opportunities to develop their quantitative reasoning skills so that they may compute accurately, efficiently and flexibly. Parrish (2010) outlines five key components of number talks as “classroom environment and community, classroom discussions, the teacher’s role and purposeful computation problems” (p. 10). Lastly, she provides some useful dialogue of an actual number talk as well as examples of recording student’s strategies. 

Parrish’s (2010) key components to number talks will guide my reflection, planning and coaching work around number talks. Time, misconceptions, asking open-ended questions and crafting purposeful problems are closely interwoven sub-areas that Parrish discusses and that I foresee as potential opportunities for my work with teachers. “In number talks, wrong answers are used as opportunities to unearth misconceptions and for students to investigate their thinking and learning from their mistakes” (Parrish, 2010, p. 11). This has potential to be a huge shift in thinking and practice for a teacher. It asks her to invest in creating a safe learning community where risk taking is valued and provide students time to think. Additionally she will “engage in listening to and learning about students’ natural thinking through asking open-ended questions” (Parrish, 2010, p. 12). I believe Parrish’s ideas extend beyond number talks and are integral aspects of any math teaching and learning opportunity. 

Literature Review 1

Math Perspectives Teacher Development Center (2007). Number talks. Retrieved from

http://www.mathperspectives.com.

Number Talks is an informational text produced by Math Perspectives Teacher Development Center (2007). As its introduction indicates, this text answers the question, what is a number talk, by outlining four main components: goals, computational fluency, format, and teacher role (Math Perspectives, 2007). Math Perspectives (2007) states, “The primary goal of number talks is computational fluency” (p.1 ). The article goes on to discuss how students develop computational fluency, what it means to be computationally fluent and the mathematical understanding an individual would have if he/she were computationally fluent. Additionally this article provides a skeletal framework for number talks as well as a vision of the teacher as a facilitator of mathematical discussion rather than giver of information.  

Number Talks addresses some big ideas related to teaching and learning mathematics. These are the same big ideas that I believe will come to light as I support teachers to implement number talks. As such, the article influenced me to compose thoughtful questions that will allow me to better understand the teacher’s belief system around math. The better I understand her beliefs the more thoughtful I can be in my coaching processes. Math Perspectives states, “A number talk is a powerful tool for helping students develop computational fluency because the expectation is that they will use number relationships and the structures of numbers to add, subtract, multiply and divide” (2007 para. 1). Why is computational fluency important? What does computational fluency allow students to do? As an adult learner what is your comfort level with number relationships? Are you able to mental compute efficiently and accurately? The authors go on to state, “Children develop computational fluency while thinking and reasoning like mathematicians (2007 para. 3)”.  What are the qualities of a mathematician? What does mathematical thinking and reasoning look and sound like? What do students need in order to use their thinking and reasoning skills?       

Methodology

During the course of two 5-week coaching cycles, I will work with 5 teachers around implementing number talks. Our work may include, but will not be limited to, co-planning, co-teaching, modeling, observation, shared reads, and video analysis. This work will be the basis for my data collection.

Throughout the coaching process I will keep a journal that will include my planning notes, notes from observations and notes from debrief conversations. In addition to my journal I will be blogging my research. This is where I will be reflective of my work in relation to my question. I will use my journals as a reference as I blog. My intention is to post at least two blogs a week. My guiding questions for those reflections are:

·         How has coaching teachers in implementing number talks provided momentum for my work?

·         How has coaching around number talks helped me understand my role as a coach?

·         What evidence do I have that this work informed the teacher’s practice and understanding of meaningful math instruction?

I believe journaling and blogging are essential aspects of my action research. My question is focused on how this work influences me and my work as a coach. As such, I must include self-reflection in my process.   

Lastly, I will ask teachers two reflective questions at the end of each coaching cycle.

·         Has focusing on number talks brought any new questions to your mind about your role as a math leaner and teacher? What are they?

·         Has focusing on number talks helped you solidify the ways your math coach can best support you? What are those ways?

I am interested in the impact this work has on a teacher’s perspective of the coaching process, coach-teacher relationship and teacher’s role in meaningful math instruction. I will journal and blog about teacher responses.

What is a Number Talk?

This post is for those of you who are reading my blog and have never heard of Number Talks. My dad read my post and commented, "Morgan I read the blog and do not have a clue as to what you are talking about. Math instruction has certainly changed." I thought a brief definition might help.


In her book, Number Talks, Sherry Parrish states: "Number talks can be best described as classroom conversations around purposefully crafted computation problems that are solved mentally. The problems in a number talk are designed to elicit specific strategies that focus on number relationships and number theory. Students are given problems in either a whole-or small-group setting and are expected to mentally solve them accurately, efficiently, and flexibly. By sharing and defending their solutions and strategies, students have the opportunity to collectively reason about numbers while building connections to key conceptual ideas in mathematics. A typical classroom number talk can be conducted in five to fifteen minutes" (p. xviii, 2010)

A NT Observation and Debrief with Ms. Brown

Last week I observed a first grade teacher, Ms. Brown, facilitate a Number Talk around seeing 6 on a ten frame. We are currently in a coaching cycle and I had asked her if Number Talks were an aspect of her math class around which we could focus our work. She was enthusiastic about this idea. I explained to her that it would be helpful if I could see a NT in her room so I could get a sense of what was happening so far. She was open to the observation. As a side note, Ms. Brown had watched me facilitate a model NT in a different first grade class a couple weeks earlier.  

It was clear that there were established routines and expectations for Ms.Brown's NTs. Students were sitting in rows facing the teacher, independently using mental math to problem solve and raising their hands. Students were using varying strategies to figure out how many dots in all, sharing their answers and explaining how they saw the dots. Students were engaged when it was their opportunity to share their thinking and were having mathematical conversations with the teacher. There was lots of opportunity for students to engage in deep mathematical thinking and ideas.

I wanted to focus our debrief session on shifting the conversation during a NT. What I noticed most in my observation was that students were mostly talking to the teacher when sharing their thinking and the teacher was always the one clarify and reiterating the ideas. Now that Ms. Brown had set up a general system and structure for her NT, I wanted her to now think about engaging students in mathematical conversations with each other and her role as a facilitator rather than a giver of information. I wanted her to think about who was doing most of the talking and why math talk is important for students. Some of my guiding questions for our debrief were:

• Would sitting in the circle change the dynamic in anyway? How?
• Are there hand signals that students use to communicate with each other? Can hand signals communicate thinking in anyway?
• Other than when a student shares an answer or the way she solved, how can we provide students other opportunities to talk during a NT?

Ms. Brown thought that sitting in a circle would probably change the dynamic but she wasn't really sure how. I also asked her why she had her students sit in a circle during morning meeting. She said that way students could interact with each other, smiled and said she would try a circle during her NT. I explained that Ms. Rodriguez, another first grade teacher, had tried a circle, didn't like it and went back to rows. I didn't want Ms. Brown to feel that she had to do NTs in one prescribed way. We also discussed using questioning as a technique to get students to be the ones who are doing the thinking and talking. Some questions that we thoughts about were:

• Who else started the problem this way? What did you do next?
• Can anyone build off that idea?
• Can anyone explain that strategy to me?
• Can anyone tell me what she said?

Lastly, we talk about tools and models that support students in explaining their strategy. Many of the girls were mentally moving dots on the ten frame so they could solve more efficiently. However girls had difficulty explaining their thinking because the dots didn't actually move. I suggested, and Ms. Brown liked the idea, that she laminate some tens frames and use Velcro dots. The other "tool" that I noticed Ms. Brown already using was naming strategies. I told her I really liked that she was doing that and but didn't actually ask her why she thought that was important. I would like to address this question at some point.