Math Classrooms Should Be Places of Surprise and Wonder | Matthew Oldridge | TEDxChathamKent

00:17:59
https://www.youtube.com/watch?v=heAH2PMj0yA

Summary

TLDRThis talk dives into the intrinsic link between mathematics and everyday life, highlighting notable ways in which children interact with math through play and exploration. The speaker expresses concern about how negative perceptions of math can cloud students' understanding. Through various examples, such as the Pythagorean theorem, concepts of infinity, and data interpretation, the speaker illuminates the importance of developing a healthy mathematical mindset in children. The goal is to foster a learning environment where mathematics is viewed as a source of wonder and excitement rather than a tedious academic exercise, encouraging students to see math as a tool to make sense of the world around them.

Takeaways

  • 🏃‍♂️ People take shortcuts in life based on instinctive math.
  • 📐 The Pythagorean theorem can be visualized in everyday paths.
  • 🌈 Allowing children to explore math creatively fosters understanding.
  • 💡 Negative perceptions of math can hinder learning; we need to change this.
  • 💵 Kids learn powerful concepts about value through practical examples.
  • 🔍 Infinity is an intriguing concept that students can comprehend.
  • 🔢 Understanding prime numbers can spark interest in math.
  • 💬 Classroom discussions should encourage curiosity and questioning.
  • ✨ Children should leave school feeling empowered in their understanding of math.
  • 🔄 Math is about extending common sense into larger contexts.

Timeline

  • 00:00:00 - 00:05:00

    The speaker discusses how people instinctively take shortcuts in their movements, akin to a mathematical concept known as the Pythagorean shortcut. This illustrates that humans inherently understand certain mathematical principles through their actions, even if they are not explicitly aware of them. Bringing this concept to children, the speaker emphasizes the importance of exposing them to interesting mathematical problems and encouraging a positive mathematical mindset to counteract negative stereotypes associated with math.

  • 00:05:00 - 00:10:00

    The concept of infinity is introduced as both a number and a powerful idea that can bewilder even children. An example is shared about a thought experiment involving a penny doubling each day for a month, leading to a large amount of money that surprises children when they do the math. The discussion pivots to prime numbers and how numbers can be understood differently, showcasing the unique insights children have about mathematics, which invites exploration beyond traditional arithmetic.

  • 00:10:00 - 00:17:59

    The narrative shifts to addressing math education and the importance of creating classrooms that allow for exploration, conversation, and deeper thinking, rather than rote memorization. Examples are provided of students experiencing 'Eureka' moments when they discover mathematical relationships and concepts independently. The goal is to nurture a sense of wonder about math, encouraging students to connect it to real-world situations and develop their critical thinking skills.

Mind Map

Video Q&A

  • Why do people cut across pathways?

    It's often not laziness, but rather a natural understanding of mathematics and efficiency that leads them to take shortcuts.

  • What is a Pythagorean shortcut?

    A concept illustrating that the direct distance between two points is often shorter than the other possible paths.

  • How can children engage with mathematical concepts?

    By playing with numbers and exploring strong mathematical concepts through curiosity and discussion.

  • What are common negative messages about math?

    Children often say they are bad at math, which can stem from a lack of engagement or negative experiences in school.

  • What is the significance of infinity for children?

    Children can grasp the concept of infinity as something that never ends, which engages their curiosity about large numbers.

  • How does exponential growth work?

    Using the example of doubling a penny over 30 days reveals how quickly values can grow.

  • What is the role of prime numbers in math education?

    They represent indivisible numbers and can spark interest in patterns among numbers.

  • How can we improve math teaching?

    By creating open spaces for dialogue and exploration among students, making math relatable and engaging.

  • What did students say about math?

    Many students expressed that math is a way to describe the world and that it should be exciting and surprising.

  • What is the ultimate goal for children learning math?

    To leave school feeling empowered with mathematical thinking and the ability to extend their common sense through mathematics.

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  • 00:00:00
    [Music]
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    you
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    [Music]
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    so we begin here and I'm out for a run
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    or a walk and as I often do I look down
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    the sidewalk I want to go this way and
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    this way and then this way do I go this
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    way and then this way no way I cut
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    across just like you would and you know
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    you would and what's the reason for that
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    if you look closely in the shadows you
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    can see there's a warn path just like in
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    every field in every Park there's a warn
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    path where people have cut across so do
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    you think to yourself after all your
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    years of schooling do you think hey
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    that's the Pythagorean shortcut probably
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    not okay so why do we do that the answer
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    is not because humans are lazy it has
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    more to do with as the rapper most def
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    put it it's strictly mathematics okay so
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    we don't think to ourselves
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    hey that side length is shorter than the
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    other two side lengths put together or
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    we don't say to ourself the square on
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    the hypotenuse is equal to the sum of
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    the square and the other two sides right
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    we just cut across because we know that
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    it's faster and it is mathematics here's
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    another example right beside my kids
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    lovely school an example of the
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    Pythagorean shortcut on a hill okay but
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    this time is stretched in in three
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    dimensions and wouldn't that blow kids
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    mind if you were to draw that triangle
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    on a balloon for example what happens to
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    the angles but this blue kids Minds
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    right because they never thought of the
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    mathematics this way okay that
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    Pythagorean shortcut is in every
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    textbook in the last hundred years but
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    it's also in our world secondly when we
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    let kids play with interesting math this
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    sort of thing happens so all I did was a
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    kid put these we were playing with the
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    squares right so again the sum of the
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    two squares equals the sum of the other
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    squares but he said okay these three
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    squares can't make a right angle
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    triangle and truly they can't okay but
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    this is an example of the sort of thing
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    that kids wonder if we let them because
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    you know none of us get out in the world
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    and we say I just really really stink at
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    reading we don't tend to say that the
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    negative messages about mathematics are
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    a little more common and we don't want
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    that so Stanford education professor Joe
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    bowler has been quite influential in
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    that she talks about mathematical
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    mindsets and we need to have them and we
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    need kids to have them so negative
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    messages like this don't help us
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    so with my own children inspired by my
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    own practice I was thinking you know
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    what happens when we just play with
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    numbers okay and none of us remember
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    this but we learned to count we're born
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    with something inside us some sense of
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    number one few many depending on what
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    culture were born into but so I said
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    what's a big number and I got five
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    because they were both quite little and
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    then I got ten so this 10 Ness we can
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    count out 10 objects kids learn to do
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    that sometimes by rote then they know
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    that 10 objects is 10 ok having 10
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    cookies is a good thing so this is how
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    they get along their way and then
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    eventually they learn that numbers get
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    bigger and bigger and bigger
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    so we were just playing around on a
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    piece of paper and I said you give me a
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    big number so finally I got million out
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    of them right and so I said well okay
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    what if you add 1 ok well that's a
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    bigger number and then we started
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    talking about what happens if you add
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    some zeros and they were seeing that
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    this you could have this long string of
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    numbers
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    and that surprised them because they're
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    so little and they don't understand
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    place value the number system anything
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    like that we were just playing
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    but then so kalam in his room he emptied
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    his piggy bank because he just couldn't
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    keep that you know 2 dollars and 42
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    cents in so he's he dumped it on his bed
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    for some reason I don't know why he was
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    naked at the time but and so he says I
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    have infinity money I have more money
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    than I can count so he's counting it
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    he's like like a young Scrooge McDuck or
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    like a young Montgomery burns or even
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    like a young Donald Trump and he's
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    counting it right and so isn't that an
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    interesting definition of infinity and
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    we don't teach that in school trust me
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    we don't so now if you think of infinity
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    is more than you could ever count in an
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    infinite number of lifetime's this
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    lifetime or any other that's a pretty
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    interesting definition he has no
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    training in math he wasn't in school yet
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    and then just from two days ago I got
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    this from Twitter because that's how I
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    operate I said what do kids say about
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    infinity and so Jennifer sent two Osos
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    grade sevens in Peel District School
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    Board said this and I give Cole Griffin
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    and Owen a lot of credit for this it's
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    the thought of a number that never ends
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    but because it's so indescribable as the
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    equation shows it doesn't matter if we
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    add one subtract one or add one same
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    thing it's still infinity so all of a
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    sudden is something gigantic and massive
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    that you can wonder about something that
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    mathematicians work on but yet twelve
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    year olds can grapple with
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    just another example of a problem that's
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    out there so I give you one penny
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    actually I give you the proposition I
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    say I'll give you a penny now and then
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    I'll give you two more tomorrow do you
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    want that for 30 days or do you want a
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    million dollars
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    and kids are always all like just give
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    me the million bucks right now and they
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    tell you what they're going to buy but
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    it when they start doing the math
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    they're surprised right so after ten
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    days you have two dollars or something
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    but after 30 days you have this pile of
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    pennies where it's around ten point
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    three or ten point seven million dollars
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    and so that's the power of exponential
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    growth but they don't know it as that
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    but they're surprised and it's an
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    interesting result
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    just another example of something that's
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    interesting
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    numbers themselves ok so 100 squares
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    pretty common in school we teach kids to
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    count by twos count by threes factors of
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    24 but what's pictured in yellow are the
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    prime numbers so those indivisible
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    little atoms of numbers you know and so
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    there's no real visible pattern okay if
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    we did multiples of 2 there'd be a
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    pattern there would be columns it'd be
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    nice and neat kids are really interested
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    in that in my experience they seem to
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    get more spread out as you get along the
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    number system so interesting and so
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    intriguing
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    and so what do kids think when they get
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    to school
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    one kid in grade six said math is a way
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    of describing this world and she wanted
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    to go to things like money but how much
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    and then baking but how long in these
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    things important well they're
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    quantifiable right and do we want kids
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    to come out of come out of school and
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    come home and say I had math today we
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    learn how to describe our world or do we
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    want to leave grade 12 or college and
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    university we leave all our schooling
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    and we say hey I learned math I learned
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    how to describe the world I think that's
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    a pretty good outcome
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    but what are my own children say so
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    column on the top I'm just admitting it
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    right now I said what is math he just
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    repeated that back from a couple weeks
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    before he doesn't know what multiplying
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    is infinity times infinity is still
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    infinity but that's what he said math is
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    which is fun but so aleck in the bottom
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    left he said 1 plus 1 is 2 try it if you
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    know a 3/4 five-year-old say what is
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    math kindergarten age students they'll
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    sit they'll give you an example of
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    arithmetic and math surely is arithmetic
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    but it's a whole lot more of that than
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    that
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    arithmetic is interesting kids will say
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    that they'll just give you that one
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    example of the fact they know
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    just one of those mic drop moments so I
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    put it out to Twitter and so Malka
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    Rosenfeld's daughter lzd said space and
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    time any distance and numbers ok so
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    again do we want kids to come home from
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    school and say I use math today it's all
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    about space time distance in any numbers
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    I think we'd like that I'd be pretty
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    amazing but sometimes what does happen
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    ok and so Jamie Mitchell great teacher
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    in Burlington his daughter Stella and I
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    hope you don't feel this way he says
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    math is numbers she says math is numbers
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    and annoyingness and hatred I want to
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    start the hashtag save Stella and all
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    the Stella's out there because math is
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    more surprising wonderful and
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    interesting than that somehow she's got
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    there in her school experiences and her
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    math teacher father's quite heartbroken
  • 00:08:44
    about it but I love this quote because
  • 00:08:46
    no not all kids feel that way but some
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    do okay and that's a problem so
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    what if every kid came out of school and
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    they said math is surprise and Wonder
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    and playing with number and a whole lot
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    more than that but what if they said
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    that that would be a pretty great
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    outcome
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    and
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    so taking you through where I sit as a
  • 00:09:10
    teacher of mathematics in the school
  • 00:09:13
    system so this is school board materials
  • 00:09:15
    from 1991 and what they're basically
  • 00:09:18
    saying is teachers aren't going to teach
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    like you were taught and that's true and
  • 00:09:23
    sometimes parents want to come in and
  • 00:09:25
    get mad about us and we've all seen
  • 00:09:27
    maybe those like Common Core math things
  • 00:09:29
    that go viral and Facebook parents get
  • 00:09:31
    mad okay so back up to 1957 Russia
  • 00:09:35
    launches a satellite called Sputnik the
  • 00:09:37
    space race has started America says
  • 00:09:39
    we're not good enough we're not as good
  • 00:09:40
    at the Soviets as math good at math as
  • 00:09:43
    the Soviets and so they invent something
  • 00:09:45
    called the new math 1957 so almost 60
  • 00:09:48
    years later we're still fighting this is
  • 00:09:51
    right after 1989 the details don't
  • 00:09:53
    matter but continent-wide Reform
  • 00:09:56
    National Council of teachers of
  • 00:09:58
    mathematics in the United States we
  • 00:10:00
    decide we want to change it we decide
  • 00:10:02
    the old ways won't do
  • 00:10:03
    1991 okay we still have these same
  • 00:10:06
    conversations so there's new math
  • 00:10:08
    there's old math there's new old math
  • 00:10:10
    there's old old math and we're still
  • 00:10:13
    fight okay sometimes we do call it the
  • 00:10:15
    math wars and so what happens how are we
  • 00:10:18
    portrayed in the newspaper you know I
  • 00:10:21
    track this stuff people say don't read
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    the comments I say always do under every
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    article about math test scores math
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    teaching it could hold me to this kids
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    these days they can't make change
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    it always appears and people get mad
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    about it so you know math is about a
  • 00:10:38
    whole lot more than just making change
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    and yes kids should be able to make
  • 00:10:42
    change accurately but we have machines
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    called cash registers just to do that
  • 00:10:46
    and we're better at thinking and cash
  • 00:10:49
    registers are good at carrying out
  • 00:10:50
    routines
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    so what do we need in our classrooms we
  • 00:10:55
    need kids to be skilled with number
  • 00:10:57
    concepts we need them to be skilled with
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    arithmetic but we need them exposed to
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    the big powerful and interesting
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    concepts make no mistake about it and we
  • 00:11:05
    need our classrooms to be wide open
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    spaces for students thinking okay
  • 00:11:10
    because we're born into it that's our
  • 00:11:13
    human birthright an uninterrupted stream
  • 00:11:16
    of consciousness that were born into
  • 00:11:18
    from birth until death
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    we have that we have our power of our
  • 00:11:23
    thinking and so do we teach primarily
  • 00:11:25
    through worksheets or wonderings
  • 00:11:28
    probably a little bit of both kids want
  • 00:11:30
    to know if pie ever ends I know because
  • 00:11:33
    we had a Wonder wall and some kid just
  • 00:11:35
    stuck that to it I didn't write that
  • 00:11:38
    that's what kids want to know they
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    wonder and I want for our classrooms
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    that they're talking spaces kids should
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    talk to kids so math just doesn't happen
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    between me and my textbook or me and my
  • 00:11:51
    teacher I talked to other kids talking
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    changes everything in my experience
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    they should be wide open spaces for
  • 00:11:59
    thinking as I said and kids should get
  • 00:12:01
    to conjecture which is to map as
  • 00:12:03
    hypotheses to science right just
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    advancing these powerful conjectures
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    with their own thinking and finally
  • 00:12:11
    wondering and grappling with really
  • 00:12:13
    really big ideas
  • 00:12:16
    like what makes a circle a circle and
  • 00:12:19
    one kid wondered that and it's actually
  • 00:12:22
    a really profound question so we can say
  • 00:12:24
    it's the most perfect expression of
  • 00:12:27
    circumference compared to diameter and
  • 00:12:29
    that ratio is PI but I don't know if
  • 00:12:31
    that's satisfactory to a kid or not or
  • 00:12:34
    what happens if you slightly deform it
  • 00:12:36
    you know we all know what happens to our
  • 00:12:38
    car tires if it starts going flat for
  • 00:12:41
    example kids want to know kids want to
  • 00:12:43
    know things like this how many people
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    have lived on this planet we can apply
  • 00:12:47
    mathematics and reasoning to this so we
  • 00:12:50
    can come up with an estimation tool we
  • 00:12:52
    can look up a few facts and it's
  • 00:12:54
    checking for that reasonableness and
  • 00:12:56
    kids could come up with an interesting
  • 00:12:58
    number really interesting question this
  • 00:13:02
    one you probably can't read but it says
  • 00:13:03
    if you divide a number up so much that
  • 00:13:06
    it equals zero is that number actually
  • 00:13:09
    infinity okay so you can't actually
  • 00:13:10
    divide by zero but you imagine if if I
  • 00:13:13
    divide any number like eight and I
  • 00:13:16
    divide that number by the number next to
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    zero for all intents and purposes I
  • 00:13:20
    would have an infinite number of parts
  • 00:13:21
    and this kid was reasoning that through
  • 00:13:23
    but that something happens at zero right
  • 00:13:26
    you just can't do it and kids want to
  • 00:13:28
    know and it's not in our curriculum but
  • 00:13:30
    it probably should be and so I say to
  • 00:13:32
    you let kids lead with the power of
  • 00:13:35
    their thinking because they have it and
  • 00:13:38
    they must okay our classrooms must be
  • 00:13:41
    thinking spaces for children for all our
  • 00:13:44
    students
  • 00:13:45
    and let's student thinking lead is kind
  • 00:13:48
    of my philosophy and it's the reason why
  • 00:13:50
    there's so many seemingly messy photos
  • 00:13:53
    of student work because when you get in
  • 00:13:55
    that moment and you get talking with
  • 00:13:57
    them and you see that work develop it's
  • 00:14:00
    just amazing okay they start to find a
  • 00:14:03
    pattern as it says at the bottom they
  • 00:14:05
    lead with the power and strength of
  • 00:14:07
    their thinking this was a project we did
  • 00:14:10
    for the Ministry of Education so loving
  • 00:14:12
    the math living the math that was called
  • 00:14:14
    and this picture I always loved because
  • 00:14:17
    it's all these different solutions to
  • 00:14:19
    the same problem they look different
  • 00:14:21
    they are different they're reasoned out
  • 00:14:23
    differently there's different
  • 00:14:25
    mathematics in a lot of them so we had
  • 00:14:27
    some teachers in a room looking up and
  • 00:14:29
    we said what's all the different ways
  • 00:14:31
    this question could be answered and
  • 00:14:32
    there was still more okay and that's
  • 00:14:35
    surprise on the teacher end we thought
  • 00:14:37
    we knew what they were going to do and
  • 00:14:39
    they did something even better than that
  • 00:14:42
    astonishingly diverse and then you get
  • 00:14:45
    kids like this one his insight so we
  • 00:14:47
    have this triangle pattern he saw it as
  • 00:14:50
    groups of three being stuck on the side
  • 00:14:52
    that's what he's circled but he had to
  • 00:14:55
    explain it to his classmates it was
  • 00:14:57
    about to burst out of him okay and other
  • 00:15:00
    students saw the pattern differently
  • 00:15:01
    maybe growing up or down and that's how
  • 00:15:04
    he saw it and he needed to share it but
  • 00:15:06
    these sudden startling insights these
  • 00:15:08
    Eureka moments where they're surprised
  • 00:15:11
    and stunned even by the power of their
  • 00:15:13
    own thinking we need that this is one of
  • 00:15:17
    my favorites so if I offer you $20 off
  • 00:15:20
    or if I offer you 20% off and you have
  • 00:15:23
    to pick well he reasoned out that $100
  • 00:15:26
    was the tipping point for that so where
  • 00:15:29
    the discount becomes better basically
  • 00:15:31
    and this was his hypothesis but if the
  • 00:15:34
    story is a little better okay the
  • 00:15:35
    teacher in that classroom said he's he's
  • 00:15:38
    on special education support he never
  • 00:15:40
    talks this kid hates math but he was the
  • 00:15:43
    one and he was working with a couple
  • 00:15:45
    other kids he needed to share this so
  • 00:15:47
    badly because his thinking was activated
  • 00:15:50
    okay he understood the context I guess
  • 00:15:53
    about shopping he understood he had this
  • 00:15:55
    insight and he needed to share it and
  • 00:15:57
    that's what we want those reluctant kids
  • 00:15:59
    that are just it's bursting out of them
  • 00:16:02
    to share their thinking and they
  • 00:16:04
    surprised us the teacher was surprised
  • 00:16:06
    and this happens over and over and over
  • 00:16:08
    again when you let kids talk to each
  • 00:16:09
    other and we want all of us saying this
  • 00:16:12
    I know when I'm being ripped off and so
  • 00:16:14
    would we want our sons and daughters
  • 00:16:16
    nieces nephews and friends we want from
  • 00:16:19
    ourselves that we come home from school
  • 00:16:21
    and say I learn how to use mathematics I
  • 00:16:23
    know when I'm being ripped off I think
  • 00:16:26
    that's pretty good I just had to do with
  • 00:16:28
    soft drinks pop so but they said they
  • 00:16:32
    reasoned ever they said I can't take
  • 00:16:33
    this it's a ripoff and that leads to
  • 00:16:35
    this next one is one of my favorites I
  • 00:16:37
    walk down the hall and I said a buck 54
  • 00:16:39
    32 grams of baked potato chips are you
  • 00:16:42
    kidding me nobody even likes those and
  • 00:16:43
    so I came up with this problem right
  • 00:16:46
    what's a fair price and so kid one kid
  • 00:16:49
    said 27 cents and they looked up a bunch
  • 00:16:52
    of chips on the internet and some flyers
  • 00:16:53
    and 27 cents was what they came up with
  • 00:16:56
    and then they knew from the power of
  • 00:16:59
    their own mathematics suit I'm assuming
  • 00:17:02
    they never bought these again and so
  • 00:17:06
    great book how not to be wrong by Jordan
  • 00:17:09
    elenberg there's no equations in it I
  • 00:17:11
    highly recommend it but he called
  • 00:17:13
    mathematic mathematics the extension of
  • 00:17:16
    common sense by other means and I would
  • 00:17:19
    love for all of us if we say hey I went
  • 00:17:20
    to school I learned math I learned how
  • 00:17:22
    to extend my common sense by other means
  • 00:17:24
    and those means are mathematics I would
  • 00:17:27
    love that for all of us and for all the
  • 00:17:29
    children out there I would like it very
  • 00:17:33
    much if we saw mathematics as a source
  • 00:17:35
    of surprise and Wonder and not just
  • 00:17:37
    something that happens in textbooks are
  • 00:17:39
    not just something that happens in
  • 00:17:41
    schools and I'll give the last word to
  • 00:17:44
    kids as I always like to do because they
  • 00:17:47
    often say it best so one kid in grade
  • 00:17:50
    six said math is the most powerful force
  • 00:17:53
    in the universe use it wisely thank you
  • 00:17:56
    very much
  • 00:17:57
    you
  • 00:17:58
    [Applause]
Tags
  • Mathematics
  • Education
  • Children
  • Curiosity
  • Learning
  • Pythagorean Theorem
  • Infinity
  • Exponential Growth
  • Engagement
  • Mindset