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.

Fair and unfair discussion

From reading the Fair or Unfair case study, I have a better understanding of how the talk move of repeating can be used to further students learning. Before reading this case study I had never been able to picture how this talk move would really be helpful. My mentality was more “why have students say something that has already been said?” If done in my class I pictured students repeating verbatim what another student had said or students saying “I couldn’t hear; everyone was talking,” which is already a popular phrase in my room.
In this case study it seemed the students who repeated what their peers said often clarified what their peer had said. It seemed to help the understanding of the class as well as the understanding of the student was being repeated. One specific example of this was during the first part of the discussion when one student was talking about trickery in regards to fairness and another student repeated her while including ideas of having equal chances of winning.
Throughout this discussion, I also noticed how the Mr. Donnell liked to resurface misconceptions that had been brought up earlier. As a teacher I instinctually would want to steer the conversation as far away from these misconceptions as I could. Yet, as I noticed how this lesson unfolded I can see how there might actually be more benefit from addressing these misconceptions right up front than pushing then under the rug. Conveniently in this conversation, all of the misconceptions seemed to be resolved by themselves by the time Mr. Donnell mentioned them again. I think it would have been more interesting to see how the teacher would have handled the discussion had the misconceptions still been prevalent. In my classroom misconceptions seem to die hard. I can see myself getting frustrated and just feeding them what fairness is in a mathematical context. Part of me thinks that first graders just need things stated obviously sometimes while another part of me really wants students to figure deep concepts like that out by themselves. I guess this just goes to show how much I still have to learn as an educator.
For this chapter it was helpful to have a transcript of the lesson rather than just a summary because when lessons are summarized they are often exaggerated or generalized in some way and it is harder to tell what outcomes such a discussion should really produce.

Special Needs

I chose to read the Allsopp article about why students with special needs have difficulty learning math and what teachers can do to help because I thought it was the most relatible to my own classroom. I have one special education student in my classroom whose math scores are so low he actually qualifies for pull out special education math support for a half hour each day. He is however still in our classroom for part of his math instruction and I have seen him struggle to stay focused and keep up day after day. Allsopp also named attention problems as a major barrier for special education students because they often miss important information during instruction. In addition to special education students, I think the majority of us have students who simply have trouble paying attention. As I was reading I found myself thinking not only of my special education students but also others in my class who could benefit from the strategies that they article suggests.
I really liked the examples of how to directly model, let the students use language to describe math, and continue to give meaningful feedback with performance charts. My students have a lot of experience with modeling because of our literacy curriculum and it has been very successful. So I think directly modeling expectations and strategies during math lessons would benefit students as well. Even if the whole class didn’t require it, I could directly model for individual students as they head back to their desk. Not all students need to be dismissed from the carpet at the same time. Those that need more modeling could even stay together for just a few more minutes of instruction. Another option might be to talk with the special education teacher and make sure that we are both on the same page, using similar strategies when the special education student is pulled out for math. One thing that I realized was that my CT and I usually follow the math book very closely, using the examples from the book. I really liked the way the teacher in the article used much more authentic examples for story problems. I think it would really help my special education student if his name and interested were in the math stories he was supposed to solve. Not only would it be more memorable for him but also probably keep his attention longer if we were talking about topics he already knew and liked!

At-Risk Students

I read “Problem Solving and At-Risk Students: Making ‘Mathematics for All’ a Classroom Reality”. This article is about a teacher that was used to teaching students from wealthier, more privileged families and his first year as a fifth grade teacher in an area where the majority of the population is below the poverty level presented many problems for him. I related to this article because about 60% of the students in my class get free or reduced lunch. The small town of Leslie is a poorer town.

The teacher documents a few of his greatest obstacles with the children. Some of the activities that were a snap to his previous classes were really hard for his new class to handle. I really liked the way the teacher handled the challenge that was presented to him. As Robert stated in the article, teachers often time give up on students like these because they think they are “hopeless”. This entire year Robert kept the students in mind. “Children desperately need the chance to explore, create, and resolve conflicts with one another if they are to move beyond the cycle of failure.” There are a lot of students in my class that make comments calling themselves “stupid”. I also do not see a huge amount of student involvement. There are some parents that you can tell are very involved in their child’s education and there are others that I have never met nor heard anything from. Sometimes school is all the student has for support in learning and it is so important for their teacher to give them the support that they need.

The lessons that Robert challenged his students with taught them how to work with each other and how to think critically. He built up confidence in his students by giving them small successes. “The objective of these small steps was not for the students to master the magic square but for them to experience repeated successes in problem solving. My hope was that by accumulating small successes, they would build confidence, perhaps even overconfidence, to approach more difficult problems.” I think it is very important that students feel good about themselves and their accomplishments. Robert notices on the first day of school that the students were intimidated by their math. They said things like “this is too hard” or they would just throw their pencil down and say they weren’t going to do the work. Robert realized that they didn’t believe in themselves. They quit when they were presented with a challenge. Robert turned that around and showed the students that they CAN do it. He taught them that they have the ability to think critically and to accomplish difficult tasks.