$30 off During Our Annual Pro Sale. View Details »

What is mathematical inquiry?

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.

Dana Ernst

June 29, 2017
Tweet

More Decks by Dana Ernst

Other Decks in Education

Transcript

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

    View Slide

  2. deep practice

    View Slide

  3. deep practice
    Take 45 seconds to look over the following list of pairs of words, but
    do not write anything down.
    bread/b tter ocean/breeze
    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
    computer/chip television/rad o
    l nch/dinner chair/couch
    2

    View Slide

  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

    View Slide

  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

    View Slide

  6. deep practice
    A B
    ocean/breeze bread/b tter
    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
    computer/chip television/rad o
    chair/couch l nch/dinner
    Table: Word list from The Talent Code.
    4

    View Slide

  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

    View Slide

  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

    View Slide

  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

    View Slide

  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

    View Slide

  11. how logical are our students?

    View Slide

  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

    View Slide

  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

    View Slide

  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

    View Slide

  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

    View Slide

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

    View Slide

  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

    View Slide

  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

    View Slide

  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

    View Slide

  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

    View Slide

  21. stepping stones
    10

    View Slide

  22. what is mathematical inquiry?

    View Slide

  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.
    12

    View Slide

  24. inquiry framework
    13

    View Slide

  25. inquiry framework
    13

    View Slide

  26. inquiry framework
    13

    View Slide

  27. inquiry framework
    13

    View Slide

  28. inquiry framework
    13

    View Slide

  29. inquiry framework
    13

    View Slide

  30. inquiry framework
    13

    View Slide

  31. inquiry framework
    13

    View Slide

  32. inquiry framework
    13

    View Slide

  33. inquiry framework
    13

    View Slide

  34. inquiry framework
    13

    View Slide

  35. inquiry framework
    13

    View Slide

  36. inquiry framework
    13

    View Slide

  37. inquiry framework
    13

    View Slide

  38. inquiry framework
    13

    View Slide

  39. inquiry framework
    13

    View Slide

  40. inquiry framework
    13

    View Slide

  41. inquiry framework
    13

    View Slide

  42. inquiry framework
    13

    View Slide

  43. inquiry framework
    13

    View Slide

  44. inquiry framework
    13

    View Slide

  45. inquiry framework
    13

    View Slide

  46. inquiry framework
    13

    View Slide

  47. inquiry framework
    13

    View Slide

  48. inquiry framework
    13

    View Slide

  49. inquiry framework
    13

    View Slide

  50. inquiry framework
    13

    View Slide

  51. inquiry framework
    13

    View Slide

  52. inquiry framework
    13

    View Slide

  53. inquiry framework
    13

    View Slide

  54. inquiry framework
    13

    View Slide

  55. inquiry framework
    13

    View Slide

  56. inquiry framework
    13

    View Slide

  57. inquiry framework
    13

    View Slide

  58. inquiry framework
    13

    View Slide

  59. inquiry framework
    13

    View Slide

  60. inquiry framework
    14

    View Slide

  61. inquiry framework
    14

    View Slide

  62. inquiry framework
    14

    View Slide

  63. inquiry framework
    14

    View Slide

  64. inquiry framework
    14

    View Slide

  65. inquiry framework
    14

    View Slide

  66. inquiry framework
    14

    View Slide

  67. inquiry framework
    14

    View Slide

  68. inquiry framework
    14

    View Slide

  69. inquiry framework
    14

    View Slide

  70. inquiry framework
    14

    View Slide

  71. inquiry framework
    14

    View Slide

  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?
    15

    View Slide

  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.
    16

    View Slide

  74. inquiry framework
    Here is a non-mathematical example.
    17

    View Slide

  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.
    18

    View Slide