The Harmony Learning Community Blog

News, Updates, Program Recaps, and Homeschooling Information

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….

Read More→

ESCHER #6: Exploration

(February 24, 2015)  Our last session.  One parent asked – as everyone was walking out at the end – “Did you come to a conclusion in your math circle?”  The answer was a resounding no.  This course was more of an exploration.  We often begin a math circle course with an overarching question.  This time, we had nothing other than…

Read More→

ESCHER #4: Can Any Regular Polygon be Tesselated?

ESCHER #4:  Can Any Regular Polygon be Tesselated? (February 3, 2015)  The story of today’s session can be told by a list of questions the participants asked in response to one question I had written on the board at the beginning of class: Can any regular polygon be tessellated? Resulting questions: >What is a polygon? >Can a line be a…

Read More→

Collaboration via the Cupcake Function Machine

After the total silence that accompanies very hard thinking, the kids were thinking aloud and producing conjectures.   After we played with Polydrons and Schläfli symbols* for about 10 minutes, we created a function machine. The students dictated the machine’s parts (various polygons, a cupcake, and sprinkles) as I drew it. They specified that the “in” number should enter the…

Read More→