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.  

Resource List

Resources:

Fuson, K., Hufferd-Ackles, & K., Sherin M. (2004). Describing levels and components

of a math-talk learning community. Journal for Research in Mathematics Education, 35(2), 81-116.

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

http://www.mathperspectives.com.

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

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

Richardson, K., (2011). What is the distinction between a lesson and a number talk?

Retrieved from http://www.mathperspectives.com.

Young, C. (2005). Implementing number talks helpful hints. Retrieved from

http://www.mathperspectives.com.

My Question

Question:

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

Statement of Purpose:

I recently, and enthusiastically, became a member of the Girl’s Prep Bronx community in the position of Instructional Math Coach. As I begin this new work I am often considering ways to develop collaborative and thoughtful relationships with teachers in order to support the growth of both teacher and student alike. I am interested in coaching tools and coaching approaches that will engage teachers in a process of reflecting upon and refining their role as math learner and teacher. 
 
Last school year a group of teachers at GPB participated in a study group around Sherry Parrish’s book Number Talks. The teachers had expressed an interest in thinking more deeply about math and Josie, our principal, provided them with this resource. As a result of the positive feedback from the study group, and a generally school-wide interest, GPB has, for the first time, built in a 20-minute Number Talk time to the weekly schedule. As a community we are still exploring and defining how this time is to be used. However, teachers have discussed how this extra time provides girls with lots of opportunity to apply their understanding of number in order to flexibly and efficiently solve problems. I want to support teachers in implementing Number Talks and focus on how this work informs my coaching practice.