Classroom Discussions - Chapter 9
This whole chapter is about effective lesson planning. The four components for a good lesson plan would be identifying the mathematical goals, anticipating confusion, asking questions, and planning the implementation. After talking about each of these tools, the chapter delves into a lesson that a teacher has made according to the knowledge she has about her students. The chapter also takes into consideration the improvisations a teacher may need to make based on the way the lesson is going.
Kazemi - Discourse That Promotes Conceptual Understanding
This article is about two classrooms that were observed and studied to see what the classroom norms were, attitudes towards math, and overall math learning in the two classrooms. Both teachers had different teaching styles although they were both exhibiting similar actions (i.e. praising correct answers, probing further into the math) but with different strategies.
Putting the Umph into Discussions- Stein
This article is about moving away from teacher led classroom discussions but more into student led classroom discussions. There are certain questions that a teacher may ask that leads the students in class to pay attention to certain important details and what their classmates are saying- as in actually processing and thinking about the classmates ideas as opposed to just listening and not understanding. This is going to lead the students to not rely on the teacher to give the answer as much but to work through the problems as a productive class.
Tuesday, October 5, 2010
Monday, October 4, 2010
Blog # 3 "Big Ideas"
Classroom Discussions: Using Math Talk to help Students Learn
Chapter 9 in “Classroom Discussions” focuses on planning lessons incorporating mathematical talks, in order to foster student comprehension. Touching base on four effective components and providing specific examples. It states that structuring a lesson in this way is extremely beneficial for students to reflect on their reasoning. It is important for teachers to anticipate some of the possible questions, concerns, and misconceptions students may have beforehand.
Mathematical Argumentation: Putting the Umph into Classroom Discussion
In this article, written by Mary Stein, it uses the research collected from a middle school study to try and move instruction away from the teacher-centered type of structure to student centered discussion. Stating that students get more out of mathematical lessons, by engaging in discussions where students explain their ideas, listen to one another, and evaluate both their and their classmates’ arguments. Therefore, challenging one another in a safe and respectful environment in order to better understand the material.
Listening to Students: The Power of Mathematical Conversations
In this article, Atkins provides a series of journal articles that contain conversations between 4th grade students. From these articles the power of mathematical conversations are proven. Within each of them, it goes on to further describe how each conversation offers insight into students thinking about math. The conversations are used as a tool to understand a students thinking and interactions with others.
Discourse that Promotes Conceptual Understanding
In this article, Kazemi compares two classrooms of students, sharing similarities and differences of the way mathematical concepts are discussed. One class was evidently stronger in presenting consistency with pushing students to conceptually think about mathematics. In doing so, students were achieving higher in terms of problem solving and comprehension.
Chapter 9 in “Classroom Discussions” focuses on planning lessons incorporating mathematical talks, in order to foster student comprehension. Touching base on four effective components and providing specific examples. It states that structuring a lesson in this way is extremely beneficial for students to reflect on their reasoning. It is important for teachers to anticipate some of the possible questions, concerns, and misconceptions students may have beforehand.
Mathematical Argumentation: Putting the Umph into Classroom Discussion
In this article, written by Mary Stein, it uses the research collected from a middle school study to try and move instruction away from the teacher-centered type of structure to student centered discussion. Stating that students get more out of mathematical lessons, by engaging in discussions where students explain their ideas, listen to one another, and evaluate both their and their classmates’ arguments. Therefore, challenging one another in a safe and respectful environment in order to better understand the material.
Listening to Students: The Power of Mathematical Conversations
In this article, Atkins provides a series of journal articles that contain conversations between 4th grade students. From these articles the power of mathematical conversations are proven. Within each of them, it goes on to further describe how each conversation offers insight into students thinking about math. The conversations are used as a tool to understand a students thinking and interactions with others.
Discourse that Promotes Conceptual Understanding
In this article, Kazemi compares two classrooms of students, sharing similarities and differences of the way mathematical concepts are discussed. One class was evidently stronger in presenting consistency with pushing students to conceptually think about mathematics. In doing so, students were achieving higher in terms of problem solving and comprehension.
Sunday, October 3, 2010
Blog 3- This Week's Readings
Chapter 9 of Classroom Discussions. This chapter provided advice and examples for including productive discussions in math lessons. One of the most important pieces of advice was to carefully plan where discussions would be introduced in the lesson by noting where students would likely be confused, creating high level questions that require students to form a response about their reasoning, and planning out the talk moves to use. The chapter also discussed the best situations to use different talk formats such as small group, partner, and whole-class.
Atkins- “Listening to Students”. This article presented a case study of an educator introducing discussions to groups of fourth grade students and what she discovered from listening to their responses. She presents summaries and some transcripts of mathematical discussions with these students based on the meaning of volume, negative numbers, and how angles are measured. Important ideas she highlights are how conversations can help reveal students’ mathematical misconceptions, the way the layout of the class for conversation can influence interaction, and the importance of student-student interaction.
Stein- “Mathematical Argumentation: Putting Umph into Classroom Discussion”. This article provides ideas for encouraging more student discussions in middle school math classes and moving away from teacher-centered lessons to one’s where students work together to make meaning. Stein says that the task to be solved greatly influences the quality of discussion and gives an example of one task she believes is good for sparking discussion. The article also provides ideas and examples for facilitating a good discussion and reviews some of the research on the benefits of discussion in math classes.
Kazemi- Discourses that Promote Conceptual Understanding. In this article, Kazemi compares the type of classroom talk observed in two teachers’ classrooms. She describes how both teachers approach discussing the same mathematical task with their students. One teacher demonstrates “high press” with her students, the act of constantly questioning them and encouraging them to explain their thinking and justify it, while the other teacher does not show the same level of questioning. Kazemi explains the benefits of using “high press” in math lessons. The article ends with advice for teachers in examining their practice and implementing “high press.”
Atkins- “Listening to Students”. This article presented a case study of an educator introducing discussions to groups of fourth grade students and what she discovered from listening to their responses. She presents summaries and some transcripts of mathematical discussions with these students based on the meaning of volume, negative numbers, and how angles are measured. Important ideas she highlights are how conversations can help reveal students’ mathematical misconceptions, the way the layout of the class for conversation can influence interaction, and the importance of student-student interaction.
Stein- “Mathematical Argumentation: Putting Umph into Classroom Discussion”. This article provides ideas for encouraging more student discussions in middle school math classes and moving away from teacher-centered lessons to one’s where students work together to make meaning. Stein says that the task to be solved greatly influences the quality of discussion and gives an example of one task she believes is good for sparking discussion. The article also provides ideas and examples for facilitating a good discussion and reviews some of the research on the benefits of discussion in math classes.
Kazemi- Discourses that Promote Conceptual Understanding. In this article, Kazemi compares the type of classroom talk observed in two teachers’ classrooms. She describes how both teachers approach discussing the same mathematical task with their students. One teacher demonstrates “high press” with her students, the act of constantly questioning them and encouraging them to explain their thinking and justify it, while the other teacher does not show the same level of questioning. Kazemi explains the benefits of using “high press” in math lessons. The article ends with advice for teachers in examining their practice and implementing “high press.”
Blog #3
In Mathematical Argumentation: Putting Umph into Classroom Discussions, the main idea was orchestrating classroom discourse away from teacher-centered to a classroom centered on student thinking and reasoning. Classroom discussions are looked at as encouraging students to come up with and evaluate their own knowledge. In order to construct these types of discussions, a good task is necessary. This will promote student thinking and discourse. These tasks should be instructional tasks that probe students to take different stances and find different solutions which will in turn hopefully lead to a rich discussion where students are listening to others opinions, defending their own ideas, and using evidence to support their views.
In Discourse That Promotes Conceptual Understanding, the main idea was "when teachers help students build on their thinking, student achievement in problem solving and conceptual understanding increased." Sociomathematical norms help create a high press for conceptual thinking. The four main norms discussed in the article include a) explanations consist of mathematical arguments b) errors offer opportunities to look back a problem and think about it in a different way and explore new strategies c) mathematical thinking involves understanding the relationship between different strategies and d) working together involves individual accountability and reaching an agreement through mathematical argumentation. "When teachers create a high press for conceptual thinking, mathematics drives not only the activities but the students' explanations as well."
In Classroom Discussions: Using Math Talk to Help Students Learn, there are four components for effective lesson planning. They are a) identify the mathematical goals b) anticipate confusion c) ask questions and d) plan the implementation. By planning a thoughtful lesson it will ensure that the discussion remains focused on students' understanding of the mathematics that you want them to learn. It is necessary to generate good questions that promote productive talk, always plan for high-level questions. It is also important to include a summary rather it be in the middle of a lesson, at the end, or the next day. "The importance of summary cannot be overestimated. It is through this process that conclusions are drawn and shared meaning among the students is developed" (187).
In Discourse That Promotes Conceptual Understanding, the main idea was "when teachers help students build on their thinking, student achievement in problem solving and conceptual understanding increased." Sociomathematical norms help create a high press for conceptual thinking. The four main norms discussed in the article include a) explanations consist of mathematical arguments b) errors offer opportunities to look back a problem and think about it in a different way and explore new strategies c) mathematical thinking involves understanding the relationship between different strategies and d) working together involves individual accountability and reaching an agreement through mathematical argumentation. "When teachers create a high press for conceptual thinking, mathematics drives not only the activities but the students' explanations as well."
In Classroom Discussions: Using Math Talk to Help Students Learn, there are four components for effective lesson planning. They are a) identify the mathematical goals b) anticipate confusion c) ask questions and d) plan the implementation. By planning a thoughtful lesson it will ensure that the discussion remains focused on students' understanding of the mathematics that you want them to learn. It is necessary to generate good questions that promote productive talk, always plan for high-level questions. It is also important to include a summary rather it be in the middle of a lesson, at the end, or the next day. "The importance of summary cannot be overestimated. It is through this process that conclusions are drawn and shared meaning among the students is developed" (187).
Wednesday, September 29, 2010
Blog # 2
"In our work with teachers, we have found that they do not always agree with one another - or with us - on how tasks should be organized." (pg. 345, Smith & Stein)
This is a great insight to the notion that all students are different, therefore they learn differently. All tasks might not work for all students. This is something that I have been thinking a lot about because of the fact that in my classroom, a textbook is used. Although that might limit some teachers to only using the text giving, my teacher has so many resources that she pulls from to allow high level math students to perform tasks at their level specifically. It's only the 3rd week or so, and she has already sent home alternate homework that she thinks would better suit the students, explaining that the homework given in the teacher book is far too easy for these students to get anything out of it.
I am a little skeptical to see how she makes this work throughout the school year when the students levels will really begin to differentiate and they will be learning something that might be a little different than other students at the same time, being tested at the same time, and still be at a third grade level. I didn't realize that my teacher would send home alternate work so early in the school year, but these student so far have really proved themselves to be at that level, finishing the homework faster than I ever expected.
This is a great insight to the notion that all students are different, therefore they learn differently. All tasks might not work for all students. This is something that I have been thinking a lot about because of the fact that in my classroom, a textbook is used. Although that might limit some teachers to only using the text giving, my teacher has so many resources that she pulls from to allow high level math students to perform tasks at their level specifically. It's only the 3rd week or so, and she has already sent home alternate homework that she thinks would better suit the students, explaining that the homework given in the teacher book is far too easy for these students to get anything out of it.
I am a little skeptical to see how she makes this work throughout the school year when the students levels will really begin to differentiate and they will be learning something that might be a little different than other students at the same time, being tested at the same time, and still be at a third grade level. I didn't realize that my teacher would send home alternate work so early in the school year, but these student so far have really proved themselves to be at that level, finishing the homework faster than I ever expected.
Monday, September 27, 2010
Blog # 2 "Groupwork"
“Clearly the choice of task depends on what you want the students to learn…When objectives are conceptual rather than routine, you will want to find or create a rich multiple ability task: a task with a wider range of intellectual abilities than conventional school tasks (Cohen, Ch 5, pg. 67-68).”
This quote from the readings reminded me of how important it is for students to know why they are working on something. Especially in math, it is the one subject where you can constantly hear students asking or whispering about why they need to learn this or what the point of the activity is. During my time of really observing and getting to know the students and the classroom, I noticed how often he would say “the point of this lesson is…” or “I want you to be able to …after the completion of this lesson”. That was something that even my field instructor commented on, that the students always know what the objective is during his lessons.
The students work a lot in groups in math, and science. The groups change, but they were initially created based on the assessment given the 1st week of class. They really work well and I believe this is mostly because of the way classroom expectations were set up at the beginning of the semester. They were consistently talked about for a week and situations and expectations for working in groups were talked about in depth.
This week our topic in math was place value, each pair of students were given a sheet of paper and dice. They would take turns rolling and recording numbers and then putting them in respected places on the worksheet ultimately making a number in the millions. Each group would create different numbers, there was more than one correct answer, and it involved taking turns so that one member was not dominating and doing all the work. The children really understood their role and work well in pairs and small groups, and I think a major reason is because they know why they are doing it and what is expected from the teachers.
This quote from the readings reminded me of how important it is for students to know why they are working on something. Especially in math, it is the one subject where you can constantly hear students asking or whispering about why they need to learn this or what the point of the activity is. During my time of really observing and getting to know the students and the classroom, I noticed how often he would say “the point of this lesson is…” or “I want you to be able to …after the completion of this lesson”. That was something that even my field instructor commented on, that the students always know what the objective is during his lessons.
The students work a lot in groups in math, and science. The groups change, but they were initially created based on the assessment given the 1st week of class. They really work well and I believe this is mostly because of the way classroom expectations were set up at the beginning of the semester. They were consistently talked about for a week and situations and expectations for working in groups were talked about in depth.
This week our topic in math was place value, each pair of students were given a sheet of paper and dice. They would take turns rolling and recording numbers and then putting them in respected places on the worksheet ultimately making a number in the millions. Each group would create different numbers, there was more than one correct answer, and it involved taking turns so that one member was not dominating and doing all the work. The children really understood their role and work well in pairs and small groups, and I think a major reason is because they know why they are doing it and what is expected from the teachers.
Sunday, September 26, 2010
Blog 2- Cohen, Ch. 5
“You want to pose questions for students that will stimulate them to discuss, to experiment, and to discover. Don’t be afraid to use big, interesting words; as long as someone in the group can read them and as long as someone knows what they mean (or can look them up), the group can function very well.” (Cohen, Ch 5. p. 72)
This quote reminded me of the fact that sometimes the best learning students can have is when they learn from each other. In the chapter, this quote refers to the task directions given to students. Cohen says that teachers shouldn’t be afraid to give complex directions. As long as each group has a student or students with enough prior knowledge to understand the directions they can communicate to the rest of the group. (Cohen, p. 72). Beyond just the task directions, I think this quote can apply to the task as a whole. I also feel that this quote could apply very well to potential group work situations in my class. There are several students in my 3rd grade class who are higher performing. These students have a great deal of prior knowledge across subject areas and are also very resourceful about finding new information when they need it. For group work tasks I would make sure that these students are divided up among the different groups. Groups can be given more challenging tasks and group members who understand the task better than others have the responsibility to explain their understanding to the rest of the group. This allows students who struggle sometimes to still have access to the task while challenging the higher performing students through having them help their classmates. In theory this sounds like a good idea, however there is always the potential for more competent students to simply take over and exclude others from any involvement. Prior instruction on how to help others without giving away the answer and creating assignments designed to require the involvement of all group members could help prevent some of these problems. These are possibilities that I will need to look into before planning group work tasks in my class. So far I have not seen any group activities done in my class, but I am interested to see how my CT plans to handle these issues in group work lessons later on.
This quote reminded me of the fact that sometimes the best learning students can have is when they learn from each other. In the chapter, this quote refers to the task directions given to students. Cohen says that teachers shouldn’t be afraid to give complex directions. As long as each group has a student or students with enough prior knowledge to understand the directions they can communicate to the rest of the group. (Cohen, p. 72). Beyond just the task directions, I think this quote can apply to the task as a whole. I also feel that this quote could apply very well to potential group work situations in my class. There are several students in my 3rd grade class who are higher performing. These students have a great deal of prior knowledge across subject areas and are also very resourceful about finding new information when they need it. For group work tasks I would make sure that these students are divided up among the different groups. Groups can be given more challenging tasks and group members who understand the task better than others have the responsibility to explain their understanding to the rest of the group. This allows students who struggle sometimes to still have access to the task while challenging the higher performing students through having them help their classmates. In theory this sounds like a good idea, however there is always the potential for more competent students to simply take over and exclude others from any involvement. Prior instruction on how to help others without giving away the answer and creating assignments designed to require the involvement of all group members could help prevent some of these problems. These are possibilities that I will need to look into before planning group work tasks in my class. So far I have not seen any group activities done in my class, but I am interested to see how my CT plans to handle these issues in group work lessons later on.
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