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