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What is mathematical inquiry? Plenary talk at 2018 IBL Workshop

What is mathematical inquiry? Plenary talk at 2018 IBL Workshop

Plenary talk at 2018 IBL Workshop. This talk was given in June 2018 at the 2018 IBL Workshop, DePaul University, Chicago, IL.

Dana Ernst

June 21, 2018
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Transcript

  1. IBL Workshop
    DePaul University
    June 19–22, 2018

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  2. How logical are our students?
    0

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  3. 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:
    1

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  4. 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
    opposite face is blue.
    1

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  5. 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
    opposite face is blue.
    Which cards must you turn over in order to test the truth of this
    statement without turning over any unnecessary cards?
    1

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  6. 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?
    2

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  7. How logical are our students?
    • When presented the number/color task in psychology
    experiments, only 10% of people selected the right answer.
    3

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  8. 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.
    3

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  9. 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.
    3

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  10. 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.
    3

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  11. What is Mathematical Inquiry?
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  12. 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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  13. Inquiry Framework
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  14. Inquiry Framework
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  15. Inquiry Framework
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  49. Inquiry Framework
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  60. Inquiry Framework
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  61. 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?
    7

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  62. 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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  63. A Non-Mathematical Example
    http://www.sciencebuddies.org 9

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  64. 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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