The math curriculum as it is now is pretty damn good, research based, rooted in decades of experience. The curriculum goals tell what should be taught, not how it should be taught. And there's a big problem with how math is taught in the U.S. and many other countries. Assessment requirements drive teaching style - it is easy to teach something to be memorized to get a score on an exam. It is difficult to teach kids to make connections and appreciate structure, especially when these things are not tested well and teachers themselves are often lacking in the skills themselves. Elementary education majors have the highest level of math-anxiety of any college major in the US.

Teaching geometry in kindergarten/1st grade as names of shapes and counting sides is part of the problem. It doesn't matter if a child calls a pentagon a "house shape", what is important is identifying attributes of shapes, how shapes are alike and different, how shapes fit together and can be taken apart to make other shapes, how shapes can be grouped together by attributes and be alike in some ways and not alike in other ways. Geometry should include 2d and 3d shapes. Attributes can be things like "how the shape rolls" with explorations of why cylinders and cones rolls differently. Kids should be exploring shapes in all kind of different contexts and materials and with their bodies and using shapes to make patterns and artwork. There is a huge rich world of shape beyond names and number of sides!

Often neglected is spatial reasoning as well, which is hugely underestimated in the effect it has on all other reasoning, including non-spatial tasks.

At ages 3-6 kids' minds are most fertile for learning the groundwork for geometry and other mathematics, and kids who are behind in 1st don't catch up later. (2012 NIH study, Clements, lots and lots more if anyone's interested).

Sieze the day with the young 'uns! Especially with mathematics! Early numeracy is the greatest predictor of success in school -- quantitative reasoning in kindergarten is an even a better predictor of success in reading in school than reading ability in kindergarten is!! (2008-2011 Duncan et al metastudy of 36000 children in 3 countries)