The Harmony Learning Community Blog

News, Updates, Program Recaps, and Homeschooling Information

Meta-Pedagogy

Everything has something to do with math.   “What do pick-up sticks have to do with math?” asked one of the kids.  We were playing this attention-focusing game as people arrived for Math Circle this week. “Everything has something to do with math,” I posited. “What does a butterfly have to do with math?” countered M.  Once everyone had arrived…

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Math Circles: Two Weeks

No one had any clue what the rule might be.   We started last week’s Math Circle with 2 rounds of “Tens Concentration.” This arithmetic game is also a mindfulness practice, focusing and sharpening attention. You could have heard a pin drop as the kids tried to remember the location of that other card that would create a sum of…

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Red Bunny and the First Contestant

This question was first asked nearly 800 years ago.   “In a land far away, King Fudge and Queen Ramona, guided by the wisdom of Red Bunny, peacefully ruled their people.” So began the first session of our spring Math Circle for young children. With the help of my assistant R, I told the story of this land. The first…

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Dissent and DC

Kids were experiencing math collaboratively without my help.   In DC this past weekend, I gave a taste of our Math Circle to some of the 350 children who participated in the 2012 Circles on the Road Workshop. While our Circle informed that workshop, that workshop also informed our Circle, which I led 2 days later. In DC, Blake Thornton…

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Francs, Fractals, and Kovalevsky

The idea that math is an art and not a science is not a new idea.   Today we examined the life of mathematician/writer Sonya Kovalevsky. We first talked about some of the childhood experiences that shape her life, then took a break to watch Vi Hart’s film “Triangle Party.” This overwhelming film may be my favorite Hart film: 6…

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Fibonacci

What are the numbers in the Fibonacci sequence? What’s the difference between a sequence and a series? Is it still the Fibonacci sequence if you start with a different first number (or two)? What phenomenon in nature prompted Fibonacci to study these numbers? How is the first number in a sequence determined? What is that first number called? How do…

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When Cake is 20, Pie is 5

The arbitrariness of variable names.   When cake is 20, pie is 5. When cake is 100, pie is 85. So pie = cake – 15, or p = c -15. The students named these variables, figured out the rule, and created the equation after we had first done a traditional function machine and then discarded the conventional language (‘”in,out”…

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Infinity Fwomps

Kids inventing their own algebra.   How do you represent an infinite sequence or series in mathematical symbols? Our group attempted to answer this question in preparation for viewing Vi Hart’s video “Infinty Elephants.” So again we began with function machines. Once the students deduced three relationships between input and output numbers, I told them that my hand was too…

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The Skills We Bring to the Circle

Experience the joy of discovery.   • the sense of humor to say “I want to whisper the function in your ear because I’m too lazy to do the math.” • the honesty to say “I want to whisper the function in your ear because I need help with the math,” and quite plainly, “I have no idea.” • the…

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The Platonic Solids: Never Mind

Developing collaborative problem-solving through the joyful art of mathematics.   Since Euler codified the concept of functions, we started with a function machine. It was challenging to get past the design phase to play with the math, but after applying a chimney to a fish, we did. The first rule was quickly deduced: “It makes it half; it takes half…

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