The Harmony Learning Community Blog

News, Updates, Program Recaps, and Homeschooling Information

COMPASS ART 6: Do Ghosts Have Guts?

(October 22, 2015) This session was marked, as usual, by question upon question upon question. SPIRALS >What is a spiral? >Can you construct a spiral with a compass? >Can a spiral have any straight lines in it? >How do you make a Baravelle spiral?   EUCLID REVISITED AGAIN We played around with all of these questions until interest in spirals…

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COMPASS ART #3 and 4: Fun with Euclid

(October 1 and 8, 2015) I’m combining 2 sessions into one report,  mathematical conversation topics  grouped by how they went over with the students. LAME Compasses: Some students are struggling with their (and my) compasses.  Parts get lost.  Positions slip.  The leads get lost.  No one agrees on which compass model (and we have about 8-10 of them in class)…

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COMPASS ART #2: The Evolution of a Question

(September 24, 2015) I decided to do something today that I rarely do:   to demonstrate to the students how to do something.  Last week the kids learned a whole bunch of geometry, but the group did not feel cohesive.  Everyone was pursuing different leads and goals, with simultaneous conversations about different topics.  I wanted to move the group more toward…

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COMPASS ART 1: Intro to Geometry

(September 17, 2015)  Our new math circle course on compass art for 9-11 year olds began with a switcheroo activity:  I gave everyone a printout of an image, and about every 30 seconds said “switch!”  I asked them to pass their page clockwise one person.  The images included: Mandalas from various traditions (Celtic, etc), Zarah Hussein’s Islamic art, Native American…

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Dark Bridge, Unfinished

(May 24, 2015)  It was a melancholy day – the last math circle of the year, and also (for those who attend the Day Program) the last day of Talking Stick.  As students slowly trickled in, we warmed up by attempting two of Martin Gardner’s line drawing challenges:  The Fish and The Robot.1  The task is to draw each in…

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Folklore – River Crossing – Collatz – the Elephant – Siri – Cannibals

(April 28, May 5, and May 12, 2015)  We’ve had 3 sessions so far, and I see 3 big themes developing in this 5-session course for 9-11 year olds: Everyone thinks that “Everyone Else in the Room is Better at Math than Me.” Not everyone realizes what math is really about. There’s culture/folklore in mathematics that the kids are starting…

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Chromatic #, Week 4, Coloring the Plane

FUNCTION MACHINES (March 31, 2015)  The first student to present his Function Machine to the group was N.*  He drew the machine, then called on students whose hands were up to suggest “in” numbers.  He stated the out number for each, as follows: IN  OUT                           1                                 118                        20           20,089,000,000                           1                                 129                           2                             …

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Chromatic #, Week 3, The Number Line

(March 24, 2015) “This is the last function machine I will ever lead in this course,” I announced at the start of class.  “After today, you will take turns leading them.”  My function machine of the day produced 7 from 3, 17 from 8, 6259 from 3129, and so on.  In other words, f(x) = 2x + 1. We never…

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ESCHER #5: All About Assumptions

ESCHER #5:  All About Assumptions (February 10, 2015)  I brought in some soccer balls to continue our discussion about which regular polygons can be tessellated.  The kids discovered that the balls were a pattern of both pentagons and hexagons.  The question became “Why?”  Conjectures:  Roundness?  Size? Of course, since soccer balls are 3-D, they weren’t going to answer our question…

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ESCHER #1: What is Symmetry?

(January 6, 2015)  How do you define symmetry?   This question became the crux of our first Math Circle on Escher.  Our 11-13 year-olds debated this question for well over an hour. It all started when I passed a bunch of images around: >beehives and other natural patterns, >examples of Moorish architecture, >various Escher works, and >a guy staring at his…

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