[EDIT: Sorry for the long post, basically we agree]

I feel that I deeply understand that the name of the object is not the object, and that naming an object has no bearing on what it is. However, I have seen kids come into classrooms with no idea what a circle is and that is the problem, especially in poor schools. In order to discuss the language of math, you need to have a basis to work with, and as such, at that level counting and shapes seems like a good starting point. Even if it's not mathematics.

(I'm sure you know this, but I'd like to clear it up for someone else who might be passing by): If you and I want to talk about birds, and one of us says chicken while the other says humming, while we're both looking at a robin, we're going to be confused. We need to both agree "This is a robin" then we can discuss the structure of the wings, the red breast, the blue eggs it leaves in the nest.

So, of course I think kids should be able to explore all about the shapes! That is pretty much my whole point. At this time, the student has no choice but to move on to the next subject. They get no time to explore the model they just learned, they test and then move on.

Also, perhaps you are thinking that my opinion is that geometry is not important, or that spatial reasoning would not have a place in my dream curriculum. Quite the opposite! Being able to build and break down shapes, I have found has helped many students in other areas. I would encourage more play with physical shapes. I would not however ask them to calculate mindlessly. I would twist a two dimensional circle, I would ask them if they could find a way that you can twist a band and always end up on the same side! We would explore these things. We would have TIME because we aren't rushing toward the next subject.

In fact one of my favorite authors has a great deal to say about spatial reasoning. If we look at George Pólya's seminal work "How to Solve It" one of the first examples used is that of a parallelepiped wherein the room is used as an example for finding the diagonal.

But it's true we are at a place where most elementary educators fear math, I've heard it come from teachers mouths. They've never been lost while solving something, only to find the answer after a brief night of sleep and a cup of coffee. Alleviating the math anxiety is important to me also. But I can't blame the teachers, I just can't. They already deal with so much, especially in elementary where they have multiple subjects and activities.

Please do not misunderstand me, I am not dismissing current research into mathematics, I am dismissing the rush of administrators in schools to push kids to the "next level" and not give kids the chance to play with an idea. The kids never get to see the fun puzzles that can come because we are all so ready to test them and move on, and it saddens me greatly.

I am not a real teacher, just someone who volunteered for a while with my wife who is a real teacher.