Dana Ernst
June 29, 2017
170

# What is mathematical inquiry?

Plenary talk at 2017 IBL Workshop. This talk was given on June 29, 2017, at Cal Poly, San Luis Obispo, CA.

June 29, 2017

## Transcript

1. what is mathematical inquiry?
2017 IBL Workshop @ Cal Poly
Dana C. Ernst
June 29, 2017

2. deep practice

3. deep practice
Take 45 seconds to look over the following list of pairs of words, but
do not write anything down.
leaf/tree music/l rics
sweet/sour sh e/sock
phone/bo k movie/actress
chi s/salsa gasoline/engine
high school/college pen il/paper
river/b at turkey/stufﬁng
fruit/vegetable be r/wine
l nch/dinner chair/couch
2

4. deep practice
Directions
∙ Without looking at the list of pairs of words, write down as many
pairs as you can. You do not need to remember where any missing
letters were nor which column/what order a pair was in.
3

5. deep practice
Directions
∙ Without looking at the list of pairs of words, write down as many
pairs as you can. You do not need to remember where any missing
letters were nor which column/what order a pair was in.
∙ Looking at the table on the next slide count how many pairs are in
column A versus column B.
3

6. deep practice
A B
leaf/tree music/l rics
sweet/sour sh e/sock
movie/actress phone/bo k
gasoline/engine chi s/salsa
high school/college pen il/paper
turkey/stufﬁng river/b at
fruit/vegetable be r/wine
chair/couch l nch/dinner
Table: Word list from The Talent Code.
4

7. deep practice
According to The Talent Code by Daniel Coyle, studies show that on
average people remember 3 times as many pairs in column B, the
one with missing letters. Maybe a room full of mathematicians will
have wildly different results, but …
5

8. deep practice
According to The Talent Code by Daniel Coyle, studies show that on
average people remember 3 times as many pairs in column B, the
one with missing letters. Maybe a room full of mathematicians will
have wildly different results, but …
You are peculiar!
You are peculiar!
You are peculiar!
5

9. deep practice
According to The Talent Code by Daniel Coyle, studies show that on
average people remember 3 times as many pairs in column B, the
one with missing letters. Maybe a room full of mathematicians will
have wildly different results, but …
You are peculiar!
You are peculiar!
The claim is that a microsecond of struggle (cognitive demand)
makes all the difference.
You are peculiar!
5

10. deep practice
According to The Talent Code by Daniel Coyle, studies show that on
average people remember 3 times as many pairs in column B, the
one with missing letters. Maybe a room full of mathematicians will
have wildly different results, but …
You are peculiar!
You are peculiar!
The claim is that a microsecond of struggle (cognitive demand)
makes all the difference.
Ponder: What does this have to do with teaching?
You are peculiar!
5

11. how logical are our students?

12. 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:
7

13. 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.
7

14. 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?
7

15. 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?
8

16. how logical are our students?
∙ When presented the number/color task in psychology
experiments, only 10% of people selected the right answer.
9

17. 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.
9

18. 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.
9

19. 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.
∙ This activity underscores why we need mathematical systems to
support our thinking.
9

20. 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.
∙ This activity underscores why we need mathematical systems to
support our thinking.
9

21. stepping stones
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22. what is mathematical inquiry?

23. inquiry framework
Part 1
Explore mathematical ideas related to Lights On. As you explore,
keep a record of the process:
Explore Lights On
∙ Where is the mathematics?
∙ Record all mathematical ideas
and questions.
Meta-Process
∙ Record any mathematician
moves you make.
∙ Keep track of 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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72. inquiry framework
Part 1
Explore mathematical ideas related to Lights On. As you explore,
keep a record of the process:
Explore Lights On
∙ Where is the mathematics?
∙ Record all mathematical ideas
and questions.
Meta-Process
∙ Record any mathematician
moves you make.
∙ Keep track of the motivation
behind those moves.
Ponder: How do your moves look in other mathematical contexts?
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73. 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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74. inquiry framework
Here is a non-mathematical example.
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75. 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, and
∙ 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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