Chapin, S. H., O’Connor, C., and Anderson, N. C. (2009). Classroom discussions: Using math talk to help students learn.
The basis of chapter nine is help teachers plan discussion rich math lessons. Four main components aid this: 1) Identifying the mathematics goal – what do you want your students to learn and talk about? 2) Anticipating confusion – thinking ahead will help you keep you students on track 3) Asking questions – developing high-level, open-ended questions. 4) Planning the implementation – How’s it all going to shake out? Also addressed is when to use which talk format (partner talk, small group, whole class) and how to generate those good questions.

Stein, M. K. (2001) Mathematical argumentation: Putting the umph into classroom discussion.
This article shows you in depth how to facilitate a classroom discussion where the students lead. All the time students hear teacher’s asking them explain there thinking. This, it seems, is not enough to get students truly thinking about their answers. But phrased in the context of a debate of sorts, where students must defend their thoughts from questions from students with opposing views, students will examine in depth not only why wrong responses are wrong but why correct responses are right.

Atkins, S. (1999, January). Listening to students: The power of mathematical conversations.
This article I had no problem viewing. It takes us through a couple of different classroom settings. In each situation a discussion is happening. In a situation where the students are all plopped on the floor not facing each other the researcher finds that the discussion is directed through her. When arranging the students on the perimeter of a carpet, however, the researcher finds the discussion to be student directed. Students learn better and form collegial relationships when the teacher does not lead the discussion but rather is a member just like any student.

Kazemi, E. (1998, March). Discourse that promotes conceptual understanding
Okay blogmates, you’ve confounded me. I searched this article five different ways and could not find it. From the looks of it though I’d say that the main point of this article is to try your best to elicit an explanation behind a response and then let the student or class work through why it is or isn’t correct.

Chaplin, S.H., O’Connor, C., and Anderson, N.C., (2009). Classroom discussions: Using math talk to help students learn. Chapter 9:
Chapter 9 of Classroom discussions: Using math talk to help students learn discusses the proper ways to plan and draft effective math lessons. It gives four components to creating an effective lesson plan, which include identifying the math goals, anticipating confusion, asking questions, and planning the implementation. The chapter also covers the process of generating high-level questions to promote a productive conversation between the students and teacher and the ability to respond, modify, and improvise a lesson as it is being instructed.

Stein, M.K., (2001) Mathematical argumentation: Putting the umph into classroom discussion: Mathematics Teaching in the Middle School. 110-112
This article illustrates different techniques for promoting more student involvement in classroom discussions. The techniques used help to decrease the teacher’s instructional “talk and chalk” teaching strategy and increase the students’ involvement in discussing the processes used to find an answer, justifying why their answer is correct, or reasoning why an answer is incorrect. This technique allows students to learn how to defend their answer and learn from other people’s opinions and processes.

Atkins, S. (1999, January). Listening to students: The power of mathematical conversations. Teaching Children Mathematics, 289-295
The main idea that I grasped from this article is the importance of math conversations that take place in the classroom environment. I liked how the author placed importance on the equality between student-student conversations and teacher-student conversations. It is just as beneficial for a teacher to join the conversation, rather than leading it and simply spitting out the information. The article also touches on the idea of promoting a rich conversation between students that is more meaningful and promotes accountability as the students are challenged to be able to justify their answers.

Kazemi, E. (1998, March). Discourse that promotes conceptual understanding. Teaching Children Mathematics, 410-414
Kazemi’s article discussed two different classroom scenarios and the importance of “pressing” students, or making them justify their answers with reasoning rather than simply stating their answer. The two classrooms had a different degree of “pressing” and the students in the classroom with a higher degree of “press” were able to correct their own mistakes and gain a deeper understanding of the processes that they included in the math problems they had.

Seminar 4 - Amy Benson

Chapin, S.H., O’Connor, C., and Anderson, N.C. (2009). Classroom discussions: Using math talk to help students learn. Sausalito, CA: Math Solutions. Chapter 9-Planning Lessons

This chapter talks about the importance of anticipating discussion while planning lessons. The chapter talks about when each type of talk (full class, small group, and partners) works best, and how it’s okay to veer off track if you feel like the class is taking a turn you didn’t see coming. The chapter finishes by suggesting that you keep notes on what worked well and what you want to add when you try a lesson again in the future.

Stein, M.K. (2001). Mathematical argumentation: Putting the umph into classroom discussion. MathematicsTeaching in the Middle School. 7(2), 110-112.

This article gave an example of a middle school task and possible correct and incorrect responses. The article suggested how to handle a situation like this- have students explain their reasoning to other students in the class. The students with the incorrect answer went first, and the rest of the students were expected to ask questions if they didn’t agree. The correct answer students went second, and the other students were will expected to ask questions. Eventually the entire class worked towards the correct answer, without the teacher having to ever give it explicitly.

Atkins, S. (1999, January). Listening to students: The power of mathematical conversations. Teaching Children Mathematics, 289-295.

This article gave four examples of mathematical conversations in classrooms. In each instance, the teacher asked students questions that helped them find the flaws in their own reasoning. In one of the examples, the students began to lead the math conversation themselves without much help from the teacher. Students can ask each other questions and explain their reasoning to each other. This meaningful discussion allows students to reflect on their own understanding.

Kazemi, E. (1998, March). Discourse that promotes conceptual understanding. Teaching Children Mathematics, 410-414.

This article compares two classrooms: one where the teacher presses students to think about math conceptually and one where the teacher doesn’t. The first teacher asks students to explain their answers to problems (correct and incorrect) and think about the processes they are doing. This way allows students to catch their own mistakes and learn from them. The second teacher allows students to talk and share answers, but often corrects mistakes herself and doesn’t let the students work through their own errors; their understanding may not be as deep.

Seminar 4 Post- Kendall Philip

-Chapin (Ch. 9) - The main points of this chapter pertained to how to plan an effective math lesson for students. I thought the breakdown of the four components for lesson planning were significant and relative to what I will be doing in the next few weeks. In order to plan the best lessons possible for my students, I need to identify the math goals, anticipate confusion, ask questions, and plan the activities that I will use. Another important part of this chapter talked about how to generate good questions and really get students to participate in productive mathematical discussions. According to page 181, it is important to "plan for high-level questions- the low-level questions tend to take care of themselves". I plan to come up with the more in depth questions to push my students thinking and to allow them to develop a deeper understanding of the material.

-Stein, M.K. "Mathematical argumentation..." I liked the second page of the article about classroom discussions. I see my CT use the strategy mentioned - “open up the discussion by asking, “Does everyone agree with _______?” If not, I should see your hand up, ready to ask a question.” I think this is a great way to allow students to form their own ideas/responses and support them by articulating their reasoning to the class. It allows students to question one another, and learn from one another’s ideas. This strategy also facilitates discussion, and encourages students to defend their thoughts and ideas.

-Kazemi “Discourse that promotes conceptual..” The most important information I took away from this article related to balance in the classroom. I think it is important to provide students with opportunities to participate in conceptual thinking in order to build on math concepts. The conclusion of the article talked in more detail about the importance of teachers creating “a high press for conceptual thinking”. When we, as teachers, work to hold students accountable for defending their ideas and thoughts in discussion setting, we are promoting well-thought out discussion between students.

-Atkins “Listening to students...” This article taught me a lot about the importance of teaching methods. Providing students with opportunities to engage in richer and higher level thinking works to promote an all around better mathematical learning community. I really like how the article talked about the teacher becoming a part of the conversations and discussions, rather than the one leading the discussion. Sometimes it is most beneficial for the teacher to take a student role during conversations (to sit back and observe and contribute to keep the conversation moving). This way, the discussion feels like a safe place for all students to participate. Similar to the Kazemi article, this article talked about the importance of student accountability. To promote rich discussions, students need to practice defending their own ideas and challenging their peers’ ideas as young as at an elementary level.

Sem 3

"If you assign a group a task from regular academic work, the student who is seen as getting the best grades in that subject is likely to dominate the group. Even if you think you have picked group members of similar ability, the students are likely to make very fine distinctions about who is the best student in the small group." p. 29 Cohen, Chapter 3

What made this quote pop for me was my questioning of it. Like many things in these Cohen chapters, I read this and kind of agreed based on my past experience, but then mostly disagreed based on what I am seeing in my classroom. I am wondering what you guys are seeing in your classrooms and whether or not you think this quote pertains to it. It is true that in my classroom I do see some of the same people continually leading small groups, but at this grade level I’m not convinced that its do to their “expert status”. I’ve got a lot of big personalities in my room and I feel that dominance in small groups is more often a product of personality groups than achievement. In fact I regularly have an outgoing girl leading her small groups even though her achievement is lower than other members within the groups. Are you guys seeing similar things in your placements (or is my classroom just an anomaly)?
I get the feeling there may be something more going on here…and I think I know what it is: multiage classrooms (I am in a 3/4 at Deerfield). One of the ideas of the multiage curriculum is that students who don’t normally get to be leaders amongst those of their grade will automatically shoot to the leadership position in a group with mostly younger students. I think this may be what is happening in my classroom to make it seem as though my kids are not choosing experts based on how good a student is, there is something more to consider, seniority. I mention this because again, although I kind of agree with a lot of Cohen’s points…I also disagree with them too and I’m wondering if this is the result of the multiage factor.

Seminar 3 Blog

"When classifying a mathematical task as "good", that is, as having the potential to engage students in high level thinking, we first consider the students - their age, grade level, prior knowledge and experiences - and the norms and expectations for work in their classroom." (pg. 344, Smith and Stein)

I found that this quote really stuck out to me while reading this article because it incorporates the essential information that is needed to be evaluated in order to fully engage a student at the level of thinking necessary to successfully learn and develop. I find it extremely important to assess a student's prior knowledge and experiences before beginning the majority of the class's curriculum and that is why I found that assessing my fourth graders using the DRAs was very beneficial. It was really interesting to see the different levels of reading that my students had. If we hadn't assessed them to find out these different levels and abilities, we would not have been able to teach to each specific ability and therefore, it would have been very difficult for all 25 of the students to be fully engaged or challenged in the curriculum and reach the necessary level of reading for their grade.
Smith and Stein provided an example of giving a task of adding five two-digit numbers together and explaining the process to fifth and sixth grade students (who had access to a calculator and feel comfortable explaining processes and their reasonsings) and second grade students (who had little prior knowledge regarding two-digit numbers and a different perception of explaining your reasoning). (pg. 344-345) The fifth and sixth grade students would be more capable to completing the task because those kinds of questions were commonly found in their daily curriculum. That level of thinking would be considered too high for a second grader to complete.

Blog for Seminar 3 - Kendall Philip

In Ch. 3 of Cohen (pg. 37) and under the section titled “Educational Disadvantages of Dominance and Inequality,” I found the following quote to be very interesting: “Group interaction offers a chance to attack these prejudices, but the teacher must do more than simply assign group work tasks.”

According to Cohen, group work allows students to get to know one another and interact more closely. This gives them an opportunity to challenge and question cultural prejudices that may exist. I believe that it is the job of the teacher to give students opportunities to work together to change some of the prejudices students may have entered school with. For example, “if the leadership position in groups always falls to boys, it will reinforce the cultural belief that “girls can’t be leaders.” Group work and group tasks give all students an equal goal to work towards. If structured properly, each student will have an opportunity to contribute and be a part of the final product. I think an excellent way to use groups is to give each student a different role for the various tasks; that way, each student will get the opportunity to try a new and different role. Hopefully, each student within the group will have tried one or two roles where they felt comfortable, confident, and competent; thus, affecting the overall quality of the final group product. This also gives students time to get to know their peers as well as each of their strengths rather than simply weaknesses. Sometimes it is difficult to change what the prejudices of students, when what they think they believe is something heard from a parent at home. It is important to establish and create (with students) a community of learners in the classroom. This will work to ensure safety and comfort among students.

For Seminar 3 - Amy Benson

“The most common error in writing instructions is to provide too much detail, as if teachers were instructing an individual on how to carry out a technical task step by step. This approach, designed to provide as much certainty as possible, has a deadening effect on group discussion- there is nothing left to discuss”.

This quote stood out to me because I often notice myself making this mistake. I haven’t yet developed any lessons that include group work but I think that this could still apply. For example, during writing time I usually circle around the room answering any questions that the students may have. A lot of students have questions about how to spell words and I typically catch myself giving students the answers instead of encouraging them to look it up in the dictionary. Now that I’ve been catching myself I’ve been trying hard to not let this continue. I think that sometimes it’s easier to just give students the answer than deal with the frustration that comes with pushing the student a little harder.

Now, back to group work. The article is advocating for the importance of full group participation, and I agree. If we oversimplify instructions, the students won’t need to communicate in order to complete the task. Understanding this will be useful in my classroom as I begin to write lesson plans. My class has been doing a lot of “team building” exercises where students need to work together as a group to design or build something. There have been a few groups who struggle to work well together (one student is too bossy, one student is left out, etc.) and in the future I will try to develop tasks that require all students to participate. I think that one of the best ways to do this is to give each group member a part of the job that they are in charge of, but then hold all group members accountable for the final product. This will hopefully encourage all students to not only play a part, but also to communicate so that everyone understands how the group got from point A to point B.

Talk Moves

The talk move that seemed most natural for me to use as a teacher was the repeating move, where you ask your students to restate another student's answer or reasoning. I find this talk move to be very important in conversation between teachers and students because it lets the teacher know which students are paying attention to the discussion and how the students are interpreting the information provided. This talk move may motivate more students to pay attention because they are nervous that the teacher may call on them to restate what was just said by another student. So instead of not being able to recall what was said by their fellow students, they will pay careful attention to understand every comment made (a useful classroom management tool).

I can see myself using this talk move the most because I find it provides importance to the student who gave the initial response. Once a student begins to feel more confident about answering or contributing their opinions into a classroom discussion, they are more likely to continue this contribution, which is ultimately what every teacher would like to achieve. To have every student have the confidence to speak out loud or answer a problem or question is what makes for a successful classroom discussion and an excellent assessment for the teacher to determine what the students are learning and how engaged they are in the lesson.

Another reason I find this talk move to be of importance within classroom discussions is because it offers another version of the response for the students to comprehend. By giving the students this other rendition, they will have a greater chance of understanding what is being conversed within the class.

The talk move that stood out the most to me was asking a student to repeat another student’s idea. The reason that this initially jumped out at me is become I’ve seen this utilized in my classroom. However, the way my CT uses this talk move is not the way I envision its use. She is an excellent classroom manager, and this talk move is used primarily as exactly that: a management tool. She will see a student who isn’t participating or paying attention and then, after another student has spoken an idea, will ask the spacey student to repeat the latter’s comment (sorry that was confusing, but I think you know what I mean). This usually leads to the kid getting embarrassed and being unable to proffer an answer. This does get them paying attention though.

I see this move used differently, more like how the authors envision its use. I can especially see myself using this in math, but I think it’s effective in all subjects. Paired with the use of the smart board, which makes students loooove to share their ideas, having another student come up to explain in their own words another’s idea becomes a powerful tool. Like the authors say, often a great idea can be lost on some if the language to explain that idea isn’t clear, but it only takes one student who understood the idea, with the ability to articulate it, to make it known to all.

Talk Moves- Amy Benson

Though I thought this week’s reading was helpful, I was a little surprised by the topic. Since we are being taught to teach in a “new age”, I feel like a lot of these strategies have already been engrained in us. I didn’t realize that these strategies had categories and names; I simply thought that education was moving in a more student led direction in general, and that over time teaching has reflected these changes. It is hard for me to choose one strategy that stood out to me the most, as I think the chapter illustrated that they all seem to flow smoothly together. I think the strategy that comes the LEAST naturally for me is Wait Time. I’ve heard over and over again, from countless CT’s, that it is so important to develop Wait Time. As a new teacher, I think the idea of Wait Time is a little scary. It all sounds great, but when you’re actually doing it, it feels like failure. It is hard to allow the room to sit in silence for minutes without feeling like you must have done something wrong or not explained something clearly enough (I actually think Wait Time is also a great, but somewhat unnatural, strategy for classroom management as well). The talk move that seems the most natural to me is Adding On. I think that I am always pretty conscious of which students have spoken during discussion and which students haven’t, and I’m always trying to make sure that everyone has a turn. I think it is important to make sure that every student feels like an important part of the conversation and that the rest of the class is interested in what they have to say. I really like that Chapin highlighted the importance of establishing a classroom community in which “all students have the opportunity to engage in productive talk about mathematics”.

First Blog Post- Talk Moves

While reading about the five productive talk moves in Chaplin, one of the moves stood out more than the others to me. The talk move, revoicing, seems to be the one I would be the most comfortable using. Whenever I am in front of a class, whether I am teaching math or any other subject, I find revoicing to be very natural for me. When students tell me their thoughts or explanations, it is very natural for me to repeat what they are saying. I revoice in a way that allows the entire class to hear the particular students answer, in a way that checks my understanding of the students explanation, and in a way that allows the student to hear his/her explanation again.
As Chaplin mentions, the content of mathematics can me make it difficult for students to explain and formulate their ideas. As a future teacher, I believe it is my responsibility to facilitate math discussion by revoicing students’ ideas. Chaplin writes, “deep thinking and powerful reasoning do not always correlate with clear verbal expressions.” This sentence really hit home for me. In any learning environment, I think it can be difficult to take all of the thinking that has been going on in our heads and reproduce those thoughts/ideas orally. Revoicing, in my opinion, is a great talk move to keep all students engage and on task. In a lot of ways, I think of this move as simply reiterating what the student said. As a future teacher, I plan to use revoicing, as I have tried now, to restate what the student said as a way to keep all students in the class on track, to help clear up any misconceptions by asking questions (e.g. is this what you mean? so you are saying....?), and also giving the student who gave the answer an opportunity to hear it back. In my mind, this will give the entire community of learners in my classroom, including myself, time to clarify what has been said.