Thursday, May 9, 2013

2013 NCTM Conference: "Exploring the Common Core Practices in Secondary Classrroms"

2013 NCTM Conference (4/19/13 - 3:30 pm - Kristen Bieda and Samuel Otten):

My intention in this session was to learn more about the Common Core Mathematical Practices. Kristen and Samuel provided details on these practices embedded in the standards, but even more importantly, they suggested ways of implementing the standards in a high school mathematics classroom.

The Practices are defined as follows (the links were not provided in the session):
  • Standard 1: Make sense of problems and persevere in solving them 
  • Standard 2: Reason abstractly and quantitatively 
  • Standard 3: Construct viable arguments and critique the reasoning of others 
  • Standard 4: Model with mathematics
  • Standard 5: Use appropriate tools strategically 
  • Standard 6: Attend to precision
  • Standard 7: Look for and make use of structure
  • Standard 8: Look for and express regularity in repeated reasoning

  • Kristen and Samuel noted that these practices require students to "do" mathematics rather than just following mathematical procedures laid out by the teacher. They suggested that "doing" mathematics requires the following:
    • Students participate in complex and non-algorithmic thinking.
    • Students explore mathematical concepts.
    • Students self-monitor their problem-solving processes.
    • Students access relevent knowledge.
    • Students examine task restraints.
    • Often, students will experience a level of anxiety as they wrestle with mathematics in a more real way.
    Kristen and Samuel focused on the implementation of the 3rd standard (construct viable arguments and critique the reasoning of others) which may be one of the most difficult to implement. They stressed the importance of reasoning and proving for students to meet this standard. To participate in reasoning activities, students must generalize mathematical relationships, evaluate arguments, and discuss assumptions and what they are based on.

    Kristen and Samuel promoted the importance of modifying tasks to promote mathematical reasoning. They provided several ideas for doing so:
    • Ask students what happens in the nth case of a pattern.
    • Ask students to justify their conjectures.
    • Reduce scaffolding, so that students are prompted to seek out strategies for problem-solving.
    • Ask students to identify prior knowledge that they assume is true and justify the use of this knowledge.
    • Ask students to define key mathematical objects.
    • Ask students to model a problem through visual representations.
    Kristen and Samuel suggested that if students are actively "doing" mathematics, they will cover all the Common Core Practices. The Practices are interconnected and naturally work with each other.

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