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.

Reading-Class connections

In reading “Collaborative problem-solving in mixed language groups,” I was immediately reminded of my students and a conversation I had with my CT. Even though we do have a student who speaks a language other than English at home, the piece of this article that stood out to me more than the ESL piece was the small group interactions. This Wednesday, as a part of a fire safety lesson, we divided the students into groups of three. Pictures of different objects or situation were shown on the overhead and groups were asked to work together to come up with a safety rule related to each picture. Since we have many natural leaders in our class we ran into the problems of students butting heads with other natural leaders in their group; dominating the entire activity; and/or failing to include one member. Our ESL student happened to been in a group consisting of two natural leaders. Near the end of the lesson time, this student approached me reporting that his group was not including him. I joined the group to see what was going on and observed one student writing and drawing as the other student spouted off ideas. I asked why they were not including M and they said they couldn’t hear him. I then suggested that the students take turns writing so that everyone can be involved.
After school my CT and I talked about this. She mentioned how she has heard it said that you should have the same number of jobs within a group as there are students in the group. We tried to brainstorm some ideas, but could only settle on the recorder and reporter rolls. This article seemed to support my CT’s suggestion. In the article it mentioned that the students who improved the most on their math assessment were the ones who had engaged in the discussion and problem-solving process during the collaborative math activity. As an act to engage those students seemed uninterested and scored poorly, the article suggested that you assign jobs such as recorder, checker, summarizer, and materials manager. I know working in groups will be beneficial for my students especially in math, if not academically then surly it will benefit them socially. For future groups, however I will certainly structure it more by making sure each member has a job within the group.

Connections between readings and classroom

I read the article Helping Students with Disabilities Understand what Mathematics Means. In this article it talks about different ways to help students understand math. The first guideline they talk about is to use various models of representation. Educators should represent math in different ways so students have can a variety of ways to visualize a problem. Because many students have a hard time understanding what math means, this could provide many different ways to have students see what the math concept is about. In our classroom we have a couple students with special needs and my CT makes sure to have a lot of different manipulatives and show problems in a variety of ways. One thing I like that my CT and I do is to include movement in a lot of our lessons. For First Grade I think this is really important not only for special needs kids but for all students.

The next thing this article talks about is to consider appropriate structures for teaching specific concepts. This section talks about different ways to present material to students. One way is to have a compare and contrast, another way is to show examples and non examples of things. In my classroom I have found that during some lessons my CT uses these. She does not go as in depth as they do in the article. I think one reason for this is the one student who this would benefit is not always in the room during our math time.

The next part of this article is to consider the language of mathematics. Sometimes language can be something that students get stuck on, especially in math. It may be hard to learn new concepts when you can not understand the words. This article suggests breaking it down in simple language and using lots of examples. My CT does this anyways in First Grade because most of these concepts are new to students anyways.

It is also important to make real world connections and provide detailed instructions. These are important so students know exactly what to do. Also if students can make a connection with something they already know, they are more likely to pick up on the concept. My CT uses these strategies in our classroom not only to support the students with special needs but also in general.

I have found that through this article my CT uses some form of all of these guidelines. I think this article was really beneficial to read to make sure that when you are planning your lesson or your unit you make these considerations.

Components of Lesson Planning

I anticipate that the most challenging of the 5 components of lesson planning will be managing the classroom talk. For one, talk moves are still a relatively new concept for me. Obviously teachers have always been using certain talk moves and I unknowingly had as well, but I had never really paid much attention to which ones or which were most productive in a given discussion until recently. Besides that, I have always liked to be a listener during conversations and discussions in my placements because I find what students have to say so interesting. I'd much rather listen to them talk than think about how specifically I am going to ask them a question to get them to talk. I realize how important it is for the teacher to guide discussions at times so that all students have the opportunity to hear, say, and learn concepts from different perspectives, but it is admittedly taking a lot of practice to remember to think so specifically about what type of talk I am going to use and not just let the students conversations flow.
I worry that I might get stuck in a rut and inadvertedly keep using the same talk move or forget ones that would be perfect for a certain situation.

The book mentions that the "managing classroom talk component would be the time during which you would make notes to yourself about talk such as vocabulary definitions and other related info the students might ask. It is sometimes difficult to anticipate what directs the discussions during a lesson may take and that too makes being completely prepared with all of the information you might need difficult.

Thinking about the Mathmatics

The first three components of making an effective lesson plan all relate directly to the mathematics you as a teacher want to highlight in a lesson. The hardest part for me, in regards to forming productive lessons that include math talk is coming up with the questions that will be asked. If you don’t research the misconceptions commonly associated with the math concepts you are trying to teach, how can you expect to come up with questions that challenge the students to address the errors they may have in their thinking? As the book said on page 175, “student’s comments in math class are largely a result of their current understanding…” We shouldn’t expect students to know their misconceptions or that they misconception will always be revealed without digging for it. The questions are also what guide the conversation and if not though through the questions might quickly take the class away from the objective of the lesson and may actually cause more harm and confusion than good. The level of the question also dictates the depth of the conversation. If purposefully thought provoking questions are not determined before the lesson the teacher might find him/herself asking very basic knowledge level questions. I love how the author gave some strategies and resources that teachers can use to identify concepts that might be problematic for students. Before reading the chapter I don’t think I would have known where to start looking for misconceptions let alone how to address them in the form of a question.

Scripted curriculum and 5 lesson planning goals

I think you could still implement the lesson planning strategies into the classroom even if you have a scripted curriculum. I feel like that is what my CT and I are doing anyways. At my school they have the Everyday math curriculum, which is very scripted. I think this program does a good job anyways of putting the goals at the beginning of the chapter and they are clear so you can see what pre-assessments you need to do, and what the main goal out of all the lessons is going to be. The next component you would have to tweak would be anticipating confusion. This would take more effort from the teacher to sit down read ahead and look at the concepts that are coming up. From there generate a list of potential problems and come up with additional activities to solve those misconceptions. This can be helpful because "you are more likely to make sure that students think carefully about these ideas and procedures during this time," (174). This would also apply to the asking questions component. While I think the Everyday math book does a good job of pointing out little things to ask the students I don't think it goes very in depth and sometimes seems disorganized. This again would take effort from the teacher to sit down and pre-read the chapter to find more engaging questions to ask the students. The implementation is suggested in the book and I do like how it gives you multiple ways to give it.

The hardest part of incorporating this would be the generating questions. Like the books says, "The most challenging questions ask students to explain a complex situation, evaulate the usefulness of a method, or synthesize a set of findings," (180). I think this can easily be done in a scripted classroom but would take effort from the teacher. This is something that I think would be important, to make sure the students get the most from the lesson.

Scripted Curriculums, good or bad?

I think you can definitely still effectively implement each of the five lesson planning goals even if you have a scripted curriculum. At my school our math is scripted, we use trailblazers. At the beginning of each unit in the book it lists the goals for the students for the different lessons for each unit. There are also pre-assessment questions that you can use that include a variety of school the students should already know and adding a few more steps which will lead to what the next lessons are going to teach. I think since the units are scripted the idea of anticipating confusion could go both ways. It could be hard because all of the students learn differently and do things differently. I think it could be easy though because the book prompts you for some questions that the students might ask and it then lists teacher responses for these questions. It could then be hard if a student asks you a question that you are not prepared for you may not have an answer ready. Asking questions would be easy because it gives you sample questions to ask the students in order to guide their learning and their thoughts. In order for a teacher to manage classroom talk it is important to read over the scripted lessons beforehand so that you can maintain the language that they use in the books. It is important to use the same language so that the students will become familiar with it and will eventually be able to use it in their own talk. Planning the implementation would be easy with a scripted curriculum like trailblazers because it gives you worksheets and homework that go along with the lessons. There are small pictures of them in the lesson book and there is also a master book that has the master copies of the worksheets. Using worksheets also is important in a lesson because it gives the students something to use personally in their learning of the ideas versus being in a whole group and looking at the overhead. I think also that have a worksheet gives the students opportunities to use manipulatives and also to practice what they have been learning.

I think a good teacher can make an effective lesson plan with whatever resources he or she has. If you do have a scripted curriculum there are ways to personalize the lessons while still maintaining the value of the lessons.

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Thinking about discussion goals

I think it is very important to think about the math goals prior to beginning a discussion rather than just seeing where the discussion goes. One reason is that I hope if I as the teacher have a clear focus and goal in mind then the students would hopefully see that I am trying to emphasize certain areas and they can focus on that as well. It will also be good practice for when they do small group discussions so hopefully they can realize what being on task looks like as well.

I also know that if I were to let them go off and take the discussion into a different direction it will be harder to get them back on track. I also think it would benefit myself to decide on goals ahead of time so I am prepared and it will help keep me on track too and clearly know my goals for the lesson.

Something I would need to work on and practice and get more experience with determining when a discussion getting off task. There was a couple times in the lesson I observed last week where I thought the lesson was getting kind of off from the overall goal of the lesson and my CT has very good strategies for getting the students to regroup and grab their attention. Kids can get so caught up in their personal stories that I know in my class before we start a discussion and call on kids we remind them if they have a question or a comment or if they actually just have a story to tell that may not be relevant to the discussion. It also discussed in chapter nine due to lack of time it is important to make the most out of your lessons and knowing the goals ahead of time will help in that aspect as well.

Chapter 8 Prompt

Prompt number three focuses on the fact that students must feel that they are in a safe environment in order to have a good class discussion and to get all students to participate and what kinds of school support is there to back up this policy. My CT and I have not used much classroom talk as described by the book, it is mostly the teacher asking a question and calling on a student and then moving on to the next question. The students have not had to really respond to other classmates responses or had to revoice them or build on them. In general they talk to the teacher and the students are not really talking to each other when it comes to academic topics.

As a class we have established our classroom norms and being with first graders we are constantly repeating rules for discussion such as when one person is talking the rest of us listen, raising your hand and just being respectful. These concepts will take a while for the students to really remember and understand and I feel that later in the year after more practice and experience we will be able to move towards discussions where the students can talk to each other more and hopefully really listen and think about classmates responses. As a school there is a big focus on all of us being one community, at our summer staff meetings there was emphasis on every kid in the school being all our kids. Many classrooms also are centered on cooperative learning and groups and sharing. They are trying to instill ideas of respect, being good listeners, trying to do your best and being good learners from the pledge they recite every morning as a school and I think this does help and there have not been too many instances where we have had issues of disrespectful behavior in the sense of saying rude or disrespectful comments. Our disrespectful behavior is more centered around not listening, talking when one person is trying to share and minor things that I will get better as they get used to school and the set up if class discussions.