Seminar 4 Blog Post: Reading Summaries

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 walks us through how to plan effective lessons. Such lesson plans include: identifying the mathematical goals, anticipating confusion, asking questions, and planning the implementation. It describes the importance of using discussion (and different talk formats) to teach mathematical concepts and being open to altering your lesson to respond to what students know or don’t know. To conclude the lesson, summarizing what occurred in the lesson is important in order to solidify students’ understanding.

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

This article describes a real life example of classroom discussion used in a middle school mathematics class. Providing a more open-ended problem allowed individual students to determine the solution method that worked best for them. Then, the teacher facilitated a whole-class discussion in which the correct solution and a common incorrect solution were both presented. It was up to the students to present their arguments, defend their methods, and then decide which is correct. Overall, the teacher used classroom discussion to let students inquire about math.

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

This article discussed a classroom in which the teacher is not the sole source of knowledge. Students can teach each other and learn from one another as well. It focused on the importance of using classroom discussion and student-led mathematical conversation as a tool to promote higher-level thinking in our students.

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

This article talks about ways to promote deeper-level thinking among our students (we must find a happy medium between rote memorization and fun exploration). Again, students were given a problem that allowed the possibility of several open-ended solution methods. After working in groups to solve the problem, each came up with a different strategy and could present and justify it to the class. Then, students could “practice articulating their thinking” by discussing and exploring correct and incorrect solutions (p. 413).

Article Summaries

Chapin, O’Connor, Anderson. (2009). Chapter 9: Planning Lessons – The chapter about lesson plans really lays out the lesson plan that Chapin, O’Connor, and Anderson feel is most effective. The lesson plan that they use has five components, these components are, identifying the mathematical goals, anticipating confusion, asking questions, managing classroom talk, and planning the implementation. This lesson plan focus’ highly on using talk to learn mathematical and how important it is to think about the mathematics prior to teaching the lesson. This in-turn will help keep the focus of the discussion on the students’ understanding and helps the talk move forward so the goals of the lesson are addressed.

Stein, M.K. (2001). Mathematical Argumentation: Putting the Umph into Classroom Discussion – Centering your classroom discussion on mathematical tasks does not have to become a routine, or how Stein puts it, “the IRE routine (teacher initiation, student reply, teacher evaluation)” (Stein, page 110). Instead, as the teacher you can step back and let the students do all the thinking and discussing. The teacher’s role then becomes to simply encourage risk taking and alignment with one position or the other in the debate, or to just be there to revoice and clarify student discussion.

Atkins, S. (1999). Listening to Students: The Power of Mathematical Conversations – This article focuses on the importance of the teacher taking a step back and allowing the students to do more of the talking as well as leading classroom discussions. When the teacher steps back and becomes a member rather than the leader, it opens up more relationship building between the students where they are being challenged and reconstructing each other’s ideas.

Kazemi, E (1998). Discourse that Promotes Conceptual Understanding – In Kazemi’s article, the point that is being made is what it means to “press” students to think conceptually about math. It is important that teachers help students build on their thinking so that their problem solving and conceptual understanding can increase. Kazemi also states in this article the importance of students make use of reasoning that justifies procedures rather than statements of the procedures themselves (Kazemi, page 410).

Seminar 4 Posting- Main Points of 4 Articles

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

                   

This article focused mainly on the ways that you can foster children’s level of discussion in the classroom and how to guide learners in a mathematical community. The article discussed discussion by teachers asking the right types of question to push children’s thinking, as well as finding ways to position students in the classroom to talk to each other and to look at one another.

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

                   

This article focuses on ways to enhance your classroom discussions with mathematics and the roles that students play. This article talked about how students have to be responsible for their reasoning and standing up to defend their answer and correlate it to others. It is the teachers job to come up with a problem that enables students to answer the question in multiple ways and find reasoning differently as well.

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 focuses on the lesson plan format that is helpful to having discussions in class. Some main points include the things that need to be included in the lesson. These things being identifying the learning goal for the lesson, knowing what confusion might occur, asking the correct type of questions for students, outlining how you will implement the lesson as well as identify the type of moves you will use in the lesson ahead of time. It is also important to think about how you will react to questions and comments in the middle of the lesson. It is also important to go back and add notes to your lesson about things that worked and things that didn’t work.

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

                    This article focused on classroom norms that need to be present within a classroom to have thorough discussion and understanding about mathematic topics. These norms are not just norms that you have for classroom management or typical rules. These norms include thinking about math reasoning rather than steps needed to solve a problem, using errors to further understanding a concept, comparing similarities and differences between strategies for problem solving and also accountability for students to think about an answer. Students had to prove their answers were correct and work together until a consensus was reached!