What is mathematical inquiry? Plenary talk at 2019 IBL Workshop

Plenary talk at 2019 IBL Workshop. This talk was given in June 2019 at the 2019 IBL Workshop, Portland, OR.

Transcript

1. 2019 IBL Workshop
   What is Mathematical Inquiry?
   Portland, OR
   June 25–28, 2019
   

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2. What is Mathematical Inquiry?
   0
   

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3. Inquiry Framework
   Part 1
   Explore mathematical ideas related to Blink. As you explore, keep a
   record of the process:
   Explore Blink
   • Where is the mathematics?
   • Rules, conjectures, proofs,
   generalizations?
   • Record all mathematical ideas
   and questions.
   Meta-Process
   • Record any mathematical
   moves you or your peers make.
   • If possible: What is the
   motivation behind those
   moves?
   Our objective is to become consciously aware of the questions we ask and
   moves we make while doing mathematics.
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4. Inquiry Framework
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5. Inquiry Framework
   3
   

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6. Inquiry Framework
   Part 1
   Explore mathematical ideas related to Blink. As you explore, keep a
   record of the process:
   Explore Blink
   • Where is the mathematics?
   • Rules, conjectures, proofs,
   generalizations?
   • Record all mathematical ideas
   and questions.
   Meta-Process
   • Record any mathematical
   moves you or your peers make.
   • If possible: What is the
   motivation behind those
   moves?
   Ponder: How do your moves look in other mathematical contexts?
   4
   

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7. Inquiry Framework
   Part 2
   Now that we have the raw data of questions and moves, our objective is
   to organize our thinking into a visual representation of the process of
   mathematical inquiry.
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8. A Non-Mathematical Example
   http://www.sciencebuddies.org
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9. Inquiry Framework
   Part 2
   Consider the following sources of information about the process of doing
   mathematics:
   • The ideas generated in Part 1
   • Your own experiences doing mathematics for fun/research
   • The behaviors you’ve seen in your students
   The goal is to produce a visual representation for the process of
   mathematical inquiry.
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10. How logical are our students?
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11. How logical are our students?
    Here are four cards lying flat on a table. Each card has a single-digit
    number on one side and one of two colors (blue or green) on the other
    side. Consider the following statement:
    If a card shows an even number on one face, then its op-
    posite face is blue.
    Which cards must you turn over in order to test the truth of this
    statement without turning over any unnecessary cards?
    8
    

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12. How logical are our students?
    Imagine yourself as a police officer in a bar looking for underage drinkers.
    The rule is:
    If a person is drinking beer, then that person must be over
    21.
    You see four people:
    Which people do you need to check to make sure the rule is being
    followed?
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13. How logical are our students?
    • When presented the number/color task in psychology experiments,
    only 10% of people selected the right answer.
    • When the task was reframed in the underage drinking context, 75%
    of people got the right answer.
    • Psychologists: When given abstract tasks, the brain cuts corners and
    we act irrationally.
    • Underscores why we need mathematical frameworks to support
    our thinking.
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