Monday, March 18, 2013

Productive Classroom Discussions

I recommend reading the January 2013 NCTM brief "What Are Some Strategies For Facilitating Productive Classroom Discussions?" The research brief provides information on key classroom strategies such as,

Attending to the classroom culture
Choosing high-level mathematics tasks
Anticipating strategies that students might use to solve the tasks and monitor their work
Allowing student thinking to shape discussions
Examining and planning questions
Being strategic about “telling” new information
Exploring incorrect solutions
Selecting and sequencing the ideas to be shared in the discussion
Using Teacher Discourse Moves to move the mathematics forward
Drawing connections and summarizing the discussion

These strategies promoting mathematical discourse are consistent with the MA Mathematics Curriculum Frameworks Guiding Principle #5, Literacy Across the Content Areas and are foundational in developing the Mathematical Practice Standard 3, "Construct viable arguments and critique the reasoning of others".  Respectively these state,

  • An effective mathematics program builds upon and develops students’ literacy skills and knowledge.
  • Reading, writing, and communication skills are necessary elements of learning and engaging in mathematics, as well as in other content areas. 
  • In speaking and listening, teachers should provide students with opportunities for mathematical discourse using precise language to convey ideas, communicate solutions, and support arguments." 
  • "Mathematically proficient students understand and use stated assumptions, definitions, and previously established results in constructing arguments. 
  •  "...making plausible arguments that take into account the context from which the data arose."
  • "Students at all grades can listen or read the arguments of others, decide whether they make sense, and ask useful questions to clarify or improve the arguments."
(source: 2011 MA Curriculum Frameworks for Mathematics)

A good resource of illustrations of the Mathematical Practice Standards with student dialog (currently grades 5-high school) can be found here.

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