# The Harmony Learning Community Blog

News, Updates, Program Recaps, and Homeschooling Information

### 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…

### Platonic Solids: The First Three Weeks

POLYDRONS (April 5 -19, 2018) In the past, I’ve often made the mistake of getting out “manipulatives”* to help students discover a certain mathematical concept only to find that the students wanted to engage in open-ended exploration. They weren’t interested in my agenda. So, for this course, I put the Polydrons on the table with no guidelines for two weeks….

### The Euler Characteristic for Eight-Year-Olds

(Jan. 25 – March 8, 2018) The five students (plus one occasional visitor) in our math circle spent six weeks doing like mathematicians do – savoring a math problem, learning it in depth before any attempts to solve it. I felt like Andrew Wiles in his decades-long work on Fermat’s Last Theorem. BEFORE THE COURSE: THINKING ABOUT IT I didn’t…

### The Stable Marriage Problem (Gale Shapley Algorithm)

(October 2, 2017) I discovered this problem and was so excited – my students would love it, it directly tied in to the topic of our course, and it was a good example of a mathematical algorithm that all of the students would have sufficient math background to work. I wanted to do it right away, so I discarded my…

### RIVER CROSSING: Missionaries and Cannibals, Polya

(May 19, 2015) Only R and J were there;  the rest of the kids were out sick.  We didn’t want to continue with the Dark Bridge/Unicorn problem without the others, so we tackled the famed river crossing problem Missionaries and Cannibals:  In the missionaries and cannibals problem, three missionaries and three cannibals must cross a river using a boat which…

### PROVING STUFF: Mathematical Thinking with Five-Year-Olds, 3.0

CLOCK JUMPING – SELF-DOUBT, LOOKING FOR PATTERNS (April 1, 2014) Things started out smoothly enough.  The clock was taped to the floor, and the kids were ready to jump on it.  Will you land on every number if you count by four?  They did this without me, and added a new approach:  everyone started on a different number, and half…