# The Harmony Learning Community Blog

News, Updates, Program Recaps, and Homeschooling Information

### Category Theory #2: Grappling with Abstraction

(November 1, 2018) “That’s a pig!” said F, as we all walked over the picnic tables to start our Math Circle outside today. “No, Penelope is not a pig. She is a pig puppet. There’s a big difference,” I replied as we sat down. This seemingly inane comment of mine captured everyone’s attention.   PIG-PUPPET YEARS “You know how it…

### 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….

### Invariants

(3/8/2018) During our course on Invariants, the eight-year-olds spent most of the time exploring the Euler Characteristic (click here for details). This report is essentially a list of other activities we did to start or finish our sessions. An invariant is something that never changes. Piagetian Conservation Tasks – We did every activity in this article: http://www.cog.brown.edu/courses/cg63/conservation.html. Conservation tasks basically…

### Embodied Mathematics

(Nov 2 – Dec 7, 2017) Our 5-7 year olds just spent five weeks experiencing math with their bodies.* You can see some footage of this circle in action on the video we produced during the course. Thanks to all the students and parents who participated. Here’s a list/description of every activity we did.   Role-playing the need for math…

### Algorithms, Algebra, and College Admissions

(October 19 and 26, 2017) “Today we’re going to do something we’ve never done in a math circle here. We’re going to take a quiz.” Stricken looks on faces. “We’ll do it together, it’s just 2 questions, and I think it will be fun.” Relief. “I’m always on the lookout for things related to algorithms to share with you, and…

### CHROMATIC #, WEEK 6: No Mention of Aliens

(April 14, 2015)  In case you haven’t been following along, a bunch of 6-8 year olds have been tackling the Hadwiger-Nelson Problem (to determine the chromatic number of the plane) with the support of a narrative tale about aliens on a planet called Botso.  This week (our final), I dropped all references to the story.  The group engaged in an…

### 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                             …

### Chromatic #, Week 2, Acting It Out

CHROMATIC NUMBER, 2, ACTING IT OUT (March 17, 2015)  “What do you remember of our problem from last week?”  I asked.  The students called out details until the problem was pieced together. THE PROBLEM Here it is in everyday language:  What’s the fewest number of colors an astronaut can use to mark out territory to be sure that you are…