Fair or Unfair

The two main talk moves that I noticed from this transcript were revoicing and having the students apply their own reasoning to someone else's reasoning. Mr. D would repeat what the students said or he would also repeat what the student said in the form of a question so as to clarify the point that the student had just made. I think this is a very important and productive talk move because the students then hear the ideas two times, once from the student and then again from the teacher. This could confirm their beliefs or it could give them the opportunity to correct their beliefs or ask a questions if they need to. I also noticed that the teacher asked the students to explain someone else's reasoning quite often. By asking a student if they agree or disagree he is forcing the student to think deeper about what was said. He then asked the student to explain why they agreed or disagreed. This is to force the students apply their thinking to someone else's contribution. Instead of just saying "yes, I agree" they need to dig deeper into their mathematical knowledge and show evidence for their claims. I do not do this enough in my classroom. I think these talk moves take a lot of practice. I think once they are established though they are extremely important in forming meaningful conversations with the students.

Concept Maps in first grade

I think the use of concept maps is very good. In my class we have not used concept maps in relation to a math concept but we had created a KWL chart and also a venn diagram for literacy lessons. I think it would be hard to use a concept map in first grade. I think there would definitely be some concepts that would be better than others to use a concept map with. For example I think it would be possible to create a concept map for addition. You could have the sums in the bubbles and branch off of that the different number sentences that could be created in order to come to that sum. I think another concept that could be used in a concept map would be the geometric shapes. You could have the number of sides in bubbles and branch off of that the different shapes that have that number of sides. The concept maps would not be as intensive as a middle school class would be because the amount of information that first graders knows or is learning is less. The first graders are learning the basics of a larger concept so in the future years they can build on their knowledge and expand their thinking. So over all I think concept maps could be useful tools to use with first graders in certain content areas but for others it might not be very useful.

Concept Maps in Math

In the Baroody and Bartels article it talks about how using concepts maps are an important way to getting students to comprehend different mathematical concepts. It talks about how a teacher could use a concept map to serve as an organizer of the students information. On this concept map there could be different discussion topics, relationships between concepts, or tying ideas together, or a summary of a lesson. Another way that a concept map could be helpful for math comprehension is organizing the broadest topic at the top and then slowly working your way down and getting into the topic. When I was reading this article I thought about the different ways that students problem solve. We present so many different ways to solve problems and expose students to different methods. This made me think of chapter 5 in the discussions books where it talks about the solution methods and problem solving strategies. In this chapter it talks about the four steps to use for solving a problem; understand the problem, make a plan for solving the problem, carry out the plan, look back and reflect on the answer in terms of the initial question. (89). It would be a lot easier for students to use this process if they could have a map of what exactly the lesson is about. This would allow them to look back at all of the different ideas from the lesson and use them for solving a problem. I think this would be another great method for students to use, or a way to help them organize there methods.

Fair vs. Unfair

It was really helpful to have the script of this discussion as opposed to a summary because even when you think you have an idea of how the lesson goes, you still don’t get a real idea until you look at what the students are really saying. I noticed this as well when I wrote my own script. This could happen at parts when you thought it was going really well and you realize that students were not understanding how you thought they were or the opposite where you might have thought the discussion was not going well when in reality students were asking great questions. This also gives the reader a great opportunity to see into the heads of the students and how they are thinking. If there is a misunderstanding then you can see exactly what the student was thinking. At the beginning with the discussion of what is fair or not it was so interesting to see all of the different definitions of what fair meant. If it was just written that students came up with different definitions for the fair, then we would not be able to see the individuality of the answers. For example here is a definition from one student “ It means that there are no tricks to it. Like those amusement park games. You never win those ‘cause there are hidden tricks to them that you can’t see,” and another response “ A fair game is when there is no trick to it. You know all the rules and there are no secrets to it.” (page 259). These are two different definitions of the word fair. From these definitions you also got to see how the other students interpreted them and were able to say them in there own words. I think reading a script is a great way to see into the discussion instead of just brushing the top.