Knowles Conference Poster

Tara
I was able to present a poster at a Knowles Science Teaching Foundation Summer Meeting about the work Melissa and I had done with Cathy on number talks during the past year. This is some information that I collected in preparation for this presentation and also some thoughts, questions, ideas that I had after talking with other fellows, teachers, and guests at the conference.

Information presented on my poster: 

http://www.scribd.com/doc/101264458

Below are two articles mentioned in the information from my poster on benefits and reasons for doing number talks in high school classrooms as well as one book that was really helpful in our journey this year.

Study by Eddie Gray and David Tall and about the importance of flexible thinking skills in student achievement in mathematics: http://www.scribd.com/doc/101263006

Article in NCTM Mathematics Teacher by James Shultz and Michael Waters (2000): http://www.scribd.com/doc/101265088

A very useful and interesting book Cathy suggested that Melissa and I read, is Building Powerful Numeracy for Middle and High School Students by Pamela Weber Harris. Not only does this have a very clear rationale for the importance of number sense, but it also provides strings of numbers for the different operations (+, -, x, /) that might be useful if you decide to try number talks!

Questions and thoughts that I have following my conversations:

• How can I meaningfully integrate number talks into my classroom without having it be separate from the content of the day? Is this necessary? Or is the process itself worth the time?
• What operation should I start with this year? Addition or multiplication? I think subtraction and division are definitely something that I will want to work towards with students, because they are more difficult to explain and record as well as being more cognitively difficult (or at least I think so!)
• How can I structure conversations or use sentence starters for ELL students? (In my classroom I will have a large percentage of ELL students)
• How are number talks beneficial for the teachers who do them?? This is a question that I heard during the poster session and am thinking seriously about! I have, so far, been critical of how number talks can specifically benefit high school students themselves; however, I truly believe that number talks changed the way that I question in the classroom--a skill that I think is essential to creating a classroom of true inquiry and depth. I think that before I started number talks, it was sometimes very difficult for me to think of meaningful questions to ask my students in class and ways to push their mathematical thinking. However, as I progressed in the series of number talks that I did, I realized that I was growing in the types of questions that I was asking and in how I was posing questions. For example, to a student who solved 8 x 15 by splitting the 8 into 2x4 and multiplying 4x15 = 60, then 60 x 2 = 120, I would ask, "Where did that four come from? In the original problem, I see an 8 and a 15, but where does the four come from?" Questions that may have been obvious to the student explaining, but may not have been obvious to me or their peers. Additionally, it helped me build a repertoire of more open-ended questions that I found were great especially if I was confused about a student response. For example, the phrase, "Can you tell me a little more?" I found to be really useful in situations where I was confused and wanted the student to elaborate on their thinking

          In addition to growing in how I asked student questions, I also grew in other aspects as well. For example, I think I was able to really improve in facilitating large group conversations that everyone was supposed to be involved in (a really difficult task). For example, one thing that I learned was to begin getting students to speak directly to one another. In certain number talks there were times when I asked someone else to rephrase or repeat the strategy of another student. During this time, often my students would start with, "Is she/he saying .....?" Instead of turning to that original student to respond to that question, something both Melissa and I started doing was having the student who was repeating a strategy, restate their question, but directed toward the original student. So, instead of "Is she/he saying...." they would now turn to their classmate and ask, "are you saying....?" For me, I think this was a way to begin having students talk directly to each other, reliving some of the belief that the teacher knows all and would be able to answer this question. Instead, they were now relying on their peers to make sense of a strategy instead of on the teacher--for me, an essential idea I want to build into my classroom.

• Are number talks most beneficial to students who are earlier on in their high school careers or are they just as beneficial to older students in  more advanced courses? 

This is a question that I think often about. And I don't know if I have yet formed an opinion about this. However, I think that number talks can offer so many different benefits and can be used to promote specific goals as well. For example, I might see using number talks in a higher level math course to have students see the value in approaching even basic problems from different levels and also to have discussions about efficiency in choosing a representation or method in mathematics more generally. Also, I think they can be beneficial to any class in building discussion norms and giving students practice and the ability to speak in front of their peers as well as practice listening to the methods of others. (This was also a question I got: Can you ensure that all students are following along? What strategies are there for this?)

As I continue thinking about number talks and how I am going to implement them in my classroom this coming year, these are all questions and thoughts that I will revisit and reevaluate as the year progresses. Any comments, ideas, and/or thoughts about any of these questions and ideas would be greatly encouraged and appreciated!!