October 4th post

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
Chapter 9 focused in on how to write a quality discussion based mathematics lesson plan, and the importance of a discussion based lesson. The chapter pointed out that the importance of writing a quality lesson plan is to really figure out the intention and purpose of a lesson by making sure to plan ahead of time, the “key concept’s problem-solving strategies, vocabulary, forms of representations, reasoning, and computational procedures that will be presented in the lesson” (Chapin, O’Connor, Anderson, 2009). A strong discussion based lesson plan, identified by Chapin, O’Connor, and Anderson, contains mathematical goals that are clearly identified, requires the teacher to think of potentially confusing concepts that learners might encounter, brainstorming open-ended questions that will further learners thinking ahead of time, and create concrete plan of how to implement the lesson (Chapin, O’Connor, Anderson, 2009). Bringing together all of these aspects in one place, helps to structure a strong lesson plan. The chapter pointed the purpose of a discussion based lesson is based upon the idea that everything that learners do in math is based on what they already know and thus, if they do not understand a mathematical concept fully, they are going to encounter problems (Chapin, O’Connor, Anderson, 2009). Thus the discussion based lesson helps learners work together to create understandings and correct misconceptions, through talk with one another. The main objective while writing a discussion based math lesson plan is to focus on quality big idea questions that will help steer the direction of one’s mathematical talk and help your learners synthesize, apply, make connections, and deepen their knowledge about a mathematical concept.

Stein, M. K. (2001) Mathematical argumentation: Putting the umph into classroom discussion. Mathematics Teaching in the Middle School. 7(2), 110‐112.
The main focus of the Stein article was about putting learners in charge of their own mathematical learning. It was about creating a discussion based math classroom in which learners work amongst each other to construct their own understanding of mathematical concepts while understanding and noticing other classmates perspectives and representations. The article emphasized the importance for learners to learn math through working through their own misconceptions. It talked about the importance of learners feeling okay to take risks and to really delve into the deeper meanings of mathematical concepts; of finding the connections through working through high level tasks. It also talked about providing learners with high level tasks that allowed for multiple representations of solutions, which allow discourse to come forth into the classroom. The discourse is the source of critique and evaluation. The high level tasks are presented in such a way that learners may come up with multiple ways to solve the problem. In this way, learners must then take a position and really stand by their thoughts by justifying their answers. Through justifying their answers they have to provide explanations; explanations that may or may not slowly change their perceptions or understanding of a mathematical concept. Stein mainly focused on having learners work together to understand a various learners’ solutions, justifying their way of getting the answer, and working amongst each other as a class to figure out if a representation is correct or not. Through the discourse, understandings and misconceptions are addressed as learners work together to figure out correct representations.

Atkins, S. (1999, January). Listening to students: The power of mathematical conversations. Teaching Children Mathematics, 289‐295.
The main focus of the Atkins article is ]the importance and the power that can come forth through teaching math through a discussion based lessons. The article talked about the need of strong discourse within the discussions, in which students and teachers and students and students talk amongst themselves in such a way that they listen to one another, and then respond, making sure to ask questions when they do not understand something (Atkins, 1999). It is not a discourse similar to I-R-E, in which teachers present learners with questions that the learners respond to and then are evaluated on by the teacher. Instead, it is a discourse that involves all participants to really listen to what one another is saying and to try and comprehend one’s thinking. It requires the teacher to step back and really hear what a learner understands and what a learner is struggling with. It requires questions to be asked by other learners when they do not fully understand something. When this sort of mathematical discourse is present in a classroom, real learning can occur, for learners hold the power of learning in their hands and they are able to really work through their understandings and correct any misconceptions. Teachers, in this type of discourse, really scaffold learners by listening to what a learner understands and helping to provide guiding questions that make other learners, and the learner with the misconception, rethink the mathematical concept. It places learners in the role of teachers, as they help one another, through presenting counter representations and by requiring their peers to describe their thinking. The article can be best summed up by Ball’s (1993) quote, presented in the article, that reads, “teachers should take a “bifocal perspective—perceiving the mathematics through the mind of the learner while perceiving the mind of the learner through the mathematics” (Atkins, 1999).

Kazemi, E. (1998, March). Discourse that promotes conceptual understanding. Teaching Children Mathematics, 410‐414.
The main purpose of the Kazemi article was to identify the specific type of discourse that is required for a strong discussion based lesson, a discourse that really helps learners to construct a conceptual understanding of mathematical concepts. The article talks about how an effective type of discourse is one in which learners do not just list procedures but, instead, requires them to justify how they got their answer. It is in the justification of what one does that helps them to understand the mathematical concepts, or understand the misconceptions, that they have. The justification helps them to realize truly what did to get to an answer. The article really focused on the idea of “press for learning,” a type of discourse which focuses on students efforts, understandings, and learning of mathematical concepts rather than the correct answer, supports learners in learning how to construct their own understanding, instead of looking at the teacher for all their mathematical knowledge, and emphasizes more of the process that learners use in getting an answer over the correct answer (Kazemi, 1998).