Peg Tyre is an educator who wrote this article that touches upon Piaget’s ideas that children develop mathematical skills much later than is thought today. Her piece mentions numbers primarily, but the extension to spatial awareness is obvious.
The family next door came over recently, and one of the children took great delight in re-arranging the pieces on our outdoor chessboard. Here is what she produced: It can be a little hard to see exactly what it looks like, so here is a schematic equivalent with what she produced on the right hand side of this image: I have highlighted her reflective and rotational symmetries. The block of eight pieces on the right hand side also show translational cross-matching. The child is only five years old, and watching her with a weather eye made it plain that she was going about re-arranging the pieces with quiet deliberation. Also, this was an activity that she initiated and completed without any external prompt.
The æsthetic appeal of what she had produced caught me immediately when I went and stood beside the chess board. What it has taught me is to be on the lookout for numeracy skills in the children that I meet.