Reading Recap

Discourse that promotes conceptual understanding

This article really focuses on the social relationship students have with math. Students need to have an open environment, which promotes discussion and dissection of their math strategy. Students also should be able to compare strategies enhancing this idea of conceptual thinking and discussion. As for teachers, teachers need to allow students to explain their thinking and not interrupt their ideas but help them by asking them to restate or putting it into different wording for them.

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

Putting Umph into Discussion

The previous article talks about classroom discussion and critical thinking but this article focuses on what students actually talk about. Teachers need to find interesting problems that students will connect to and invest in, in order to promote classroom discussion. In order to find these tasks, teachers need to know and understand their students because not all tasks will promote discussion. Again this article focuses on more student lead activities than teacher lead activities where students are responsible for the discussion but the teacher is a resource to help.

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

Classroom Discussions: Chapter 6

This chapter was incredibly helpful as a reference for discussion based lesson plans. When planning these types of lessons teachers need to anticipate problems that my arise, plan what type of discussion students will be having weather small group or pairs, and come up with a higher level thinking question to generate conversation. There is a great deal more planning that needs to go into these types of lessons and teachers should prepare for this types of planning.

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

Listening to Students

This article was focused on the listening aspect of student lead discussion. It was shocking to find out that students engaged in a mathematic for over an hour. Often teachers cut off discussion and precede right into explanation but this example teacher allowed and encouraged this discussion. Once again this teacher also came up with intriguing activities and questions to ask her students but she ends the article by saying that this is an “evolutionary process” reassuring other teachers that this technique is a practice for the students as well as the teacher.

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

Summary of Readings:

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

When planning a lesson teachers need to keep in mind that not all students are going to be at the same level and this needs to be considered to make sure that all students are participating in the lesson and comprehending what is being taught. There are four main components for planning a lesson plan that the chapter talks about. These include identifying the math goals, anticipating questions, asking questions and planning the implementation. Each of these goals all work together to help a math lesson go smoothly in all directions. The chapter discuses what ways there are to form good questions that students are going to respond to and link to what they are learning in math, generating questions that will give students assessment type answers that they will have to think about. The chapter explains many examples that teachers have used and how students respond to help tie in each of the four components for planning a lesson and the benefit that the students and teacher will receive.

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

Some main points of this article include getting students to be interested in classroom discussions and the different ways that that is possible. The classroom needs to have a comfortable setting where all students feel comfortable to participate. The article suggests getting students to take sides on different instructional positions in math and having those discussed in the classroom. This gives students something to think about and participate in with their own thoughts and ideas. The article discusses different ways to make sure that all students are incorporated into the tasks and supplies that are needed to work with some tasks because having those supplies is vital to the outcome of the discussion. Walking around the room and making sure that students are working and participating correctly within the math instruction. Lastly it is important to get students involved and enthusiastic in explaining their thoughts and ideas to other students.

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

This article is very insightful and sheds light on the different ways that mathematical conversations can take place in a classroom during a math lesson. This article focus’s on student to student interaction during a math conversation verses a teacher to student interaction. A teacher demonstrates how a math conversation takes place within her classroom about cubes and the faces of cubes. She reflects on the way the two different conversations went and what the students were getting out of the conversations. Students were able to help answer each others questions about angles and cubes through conversation. The teacher was in the classroom but the students were doing most of the talking and learning on their own.

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

This article is about two teachers who demonstrate two different ways to perform sociomathematical norms in their classrooms. The teachers were explaining mathematical concepts within their classroom and both teachers had the same classroom norms but the outcome of the math discussions were completely different as well as the students interest in math. The classrooms were all different in the way that the students discussed math and how math was incorporated into their own thinking processes. Within the article there are four socimathematical norms that are listed within working in a classroom. These include, explanations of math, errors and exploring wrong answers, mathematical thinking and collaborative work. These four discourses are helpful in working with students and math and getting students to think about math in different ways.

Summaries of the Readings This Week

Classroom Discussions Chapter 9:
 This chapter focuses on what makes up a good lesson plan while providing numerous different examples as to how a lesson plan can look or include. Most of the information has already been taught to me like identifying the mathematical goals, anticipating confusion, have questions prepared for discussion, and planning the  implementation (Chapin, 2009). However, I believe that summarizing is something that I have never officially learned and is something that is taken for granted. Summarizing is a useful tool that allows for conclusions to be drawn and shared meaning among students can be developed (Chapin, 2009).

Stein Article:
This article focused on the discourse within that classroom. "Mathematical discourse is the way students represent, think, talk, question, agree, and disagree in the classroom" (Stein, 2001). As I have discussed in previous post, discussion in mathematics has never been apart of my mathematical career. Everything has been lecture based with the numerical answer representing my understanding of the material. It is so important to get children to talk through math together to create a better understanding.

Atkins Article:
Similar to the Stein article regarding communication, Atkins focuses on power of bringing conversation into the classroom. The biggest item that stood out to me was the role of the teacher. Too often teachers are the leaders of the lesson but when discussions are brought into the classroom, the teacher can become a member of the mathematical community (Atkins, 1999).

Kazemi Article:
This was by far my favorite article. I believe that too often math is cut and dry. Throughout my experiences, there is no room for interpretation. However, it is so important to provide students with the flexibility to explore the mathematical world and to create their own arguments. Promoting students to create their own mathematical arguments will eventually foster a stronger classroom discourse (Kazemi, 2001). I loved that this article showed the importance of arguing for it helps students to come up with ideas of their own and to find passion within the material.