# The Harmony Learning Community Blog

News, Updates, Program Recaps, and Homeschooling Information

### Intro to Voting Theory

(1/16/2020) Our overarching Math Circle goal is for students to invent and discover math for themselves. In this course, the plan/hope is that I’ll ask a bunch of questions and the students will invent their own voting methods before discovering what voting methods people have created throughout history. Pet of the World  “What would happen if you got to vote…

### Category Theory 1: Odd One Out

(October 25, 2018) An important concept in category theory, indeed in mathematics itself, is deciding which attributes to ignore when you conduct mathematics. Context matters. When you’re signing a contract to buy a car, you may not care what color the contract is printed on. But when you’re sending out your wedding invitations, you might care about the paper color…

### 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…

### 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…

### GARDNER #5: Life, Murder, and Box Tops

LIFE (October 21, 2014)  Last week’s boardwork was on display before the students arrived.  M, who was absent last week, was early for class today.  She saw the board and immediately asked, “Why does it say ‘die?’” “Ask them,” I told her, indicating J and L, who were also early for class.  J set the board up for Life1. Then…

### I LEARN SOMETHING: Mathematical Thinking with Five-Year-Olds, 4.0

(April 8, 2014)  We started out playing a few logic games – “Picking Fruit” and “Wearing Hats.”  The students had fun using process of elimination to deduce what couldn’t be seen.  The students announced one conjecture, then would immediately change their minds, then revert, etc.  (Once again, insight is fleeting.)  One student didn’t want to commit to any conjecture. …