In praise of rock groups

Steven Strogatz' column about mathematics does not disappoint. Look at the enlightening figure above.  It explains why the sum of odd numbers always equals a square.  Read the rest of Rock Groups.

When Iris attended a Montessori pre-K and Kindergarten, one teacher told me that she never understood how to find a square root until her Montessori training.  Huh?

Montessori teaches multiplication as a special form of addition.  And, if you are teaching multiplication with manipulatives (beads and boards to hold the beads in sorted ways to make the abstract concepts concrete), then you can introduce square roots.  So they were teaching 5-6 year olds how to find square roots using beads and boards. 

I borrowed a book about Montessori math from the directress of the school, but it didn't make sense to this math major.  When I saw this figure, I sort of understood the basis.  I have to go back and think about it some more.