Both Laura Sommariva and Nancy Benerofe see maths in the elementary school as significantly more than arithmetic and the memorization of facts. These things are, of course still important but can be so much more easily and effectively learned if they are associated with interesting, relevant and meaningful activities such as those Laura and Nancy advocate for. There's another person I should add to the group too, Karyn Vogel, the BSD math coach who also speaks our language.
Come to think of it, I think we should add Vi Hart to our group as she was probably the one who started it all. Interestingly the Khan Academy lists Vi Hart's work under the heading "Recreational Math". One day, I am certain, the educational community will wake up to find that fractals and numerically and spatially defined patterns will form the basics of what we consider to be math education at the elementary school level.