But here's the kicker: when I tried to actually teach the correct definition of a square, students refused to listen, because they acted like it was just my opinion.(Reform K-12, via Joanne Jacobs.)
Obviously. Notions of squareness are historically contingent and culturally constructed. Ninety degrees at the vertices and at the intersection of the principal diagonals? A restrictive conception, possibly at one time useful, but, hey, this is the twenty-first century.
(That the largest returns to schooling are in fields that require technical training, meaning a grasp of algebra, geometry and logic, just doesn't matter to some people.)