Dana Ernst
June 21, 2018
180

# 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.

June 21, 2018

## Transcript

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

2. How logical are our students?
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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:
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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.
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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?
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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?
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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.
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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

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

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.
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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:
• Where is the mathematics?
• Rules, conjectures, proofs,
generalizations?
• Record all mathematical
ideas and questions.
Meta-Process
• Record any mathematical
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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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:
• Where is the mathematics?
• Rules, conjectures, proofs,
generalizations?
• Record all mathematical
ideas and questions.
Meta-Process
• Record any mathematical
make.
• If possible: What is the
motivation behind those
moves?
Ponder: How do your moves look in other mathematical contexts?
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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

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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