Games played by children and mathematicians Nordin Zuber, North Sydney Boys High School.
April 2014
[email protected] @enzuber exzuberant.blogspot.com 2014 This work is licensed Creative Commons CC-BY-NC-SA. http://creativecommons.org/licenses/by-nc-sa/3.0/ You are free to share, copy, or modify this work for non-commercial purposes so long as: (i) You attribute the source : enzuber (ii) Share all derived works under a similar CC license.
Jacob Bronowski “The Ascent of Man” Episode 2
“Now we have a square on the hypotenuse, and we can of course relate that by calculation to the squares to the two shorter sides…” “but we don’t need any calculation.” “A small game …. … such as children … and mathematicians play…
will transpose that triangle there … and this triangle here..”
Games played by children and mathematicians
Young children … •
Not afraid to experiment
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Not afraid to ask “Why?”
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Demonstrate surprising concentration and persistence when problem solving.
I think it’s important to bring play and “childishness” into our high school mathematics classrooms.
A favourite lesson: Vi Hart’s “Wind and Mr Ug”
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An intriguing narrative
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A “sense making” challenge
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A surprise twist
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A motivation to explore
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Deep mathematics underneath
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An instant 30 minute lesson
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Just add paper, glue and scissors.
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Your students will go home and share with their family…
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… and look for more Vi Hart videos.
“Doodling in maths class”
Take a piece of paper ….
We need more paper folding!
Demonstrate the index laws
Explore zero folds, and negative one folds! 1 Demonstrate 20 = 1 and 2−1 = 2
Based on an idea from Peter Hickey
http://exzuberant.blogspot.com.au/2011/04/take-piece-of-paper.html Google: “take a piece of paper exzuberant”
Explore inverse relations and inverse functions You will need: • a piece of square paper, • a lead pencil, • a coin. Start with 𝑦 = 2𝑥
Try this with 𝑦 = sin 𝑥 YouTube “Graph of a function and its inverse”
http://www.youtube.com/watch?v=0ImB4PTrxyY
Paper folding proof of Pythagoras’ Theorem – Vi Hart
Explore circle concepts using …. circles!
Image: Wikipedia – Jim Belk
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Year 8 circle terminology
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A terrific way to teach Year 10 5.3/Extension 1 Circle Geometry
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And don’t forget fractions work!
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The famous exploration of 𝐴 = 𝜋𝑟 2
Sesame Street
From the sublime : “Fish,fish,fish”
to the ridiculous: James Blunt “My triangle”
The most dangerous, infectious song you can show your Year 10 class:
Numberphile
Dr James Grime
Exploring the mathematics in “Good Will Hunting”
Is it just “Math-o-tainment”?
Is it just “Math-o-tainment”? Introduce students to topology
Deeper thinking about mathematical abstraction Steven Strogatz : From Fish to Infinity
http://opinionator.blogs.nytimes.com/2010/01/31/from-fish-to-infinity/
Deeper thinking about mathematical proof
Develop narrative in mathematics
Physically explore spatial transformations Create memory prompts for key ideas
Explore mathematical language
That’s for little kids!
What about senior classes? High achieving classes?
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Many of these students have never done these type of activities.
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You will need to convince them.
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Encourages collaboration, encourages creative thinking.
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Helps create memorable lessons – improves recall.
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Helps reduce stress.
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You will be amazed how far these students can extend the lesson.
My goals for an “inner child” lesson activity •
Activity must be engaging
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Students must actually “do” something. Turn “fun maths videos” into activities
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Must have potential to be extended.
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Encourage mathematical thinking through active questioning
Role modelling •
You will get excited by the activities.
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Students will see your emotional involvement in mathematics.
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Perfect opportunity to model open learning without fear.
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Creates an atmosphere of enthusiasm and energy.
Homer visits The Land of Chocolate
Seymour Papert and “Mathland” "If we all learned mathematics in math land, we would all learn mathematics perfectly well".
“How can we create mathland? That’s what it’s really about".
YouTube: “Why Learn Math and Science Seymour Papert”
Numberphile on You Tube New episodes every week. A terrific source for lesson ideas
Jacob Bronowski “The Ascent of Man” Ep. 2 (1973) You Tube: “Bronowski on Ptythagoras’ Theorem”
Vi Hart on You Tube YouTube: “Why Learn Math and Science Seymour Papert” Steven Strogatz “From Fish to Infinity”
exzuberant “Take a piece of paper”
James Blunt “My triangle”
MANSW Facebook group Ask for an invite!
Nordin Zuber, North Sydney Boys High School.
[email protected] @enzuber
Peter Weatherall “I am a parallelogram”
exzuberant.blogspot.com 2014 This work is licensed Creative Commons CC-BY-NC-SA. http://creativecommons.org/licenses/by-nc-sa/3.0/ You are free to share, copy, or modify this work for non-commercial purposes so long as: (i) You attribute the source : enzuber (ii) Share all derived works under a similar CC license.
