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.
Tuesday, October 5, 2010
Monday, October 4, 2010
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.
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.
Sunday, October 3, 2010
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.
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.
Friday, October 1, 2010
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.
-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.
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