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).