Fiona is learning all about math and patterns and geometry and spatial relationships. Not from books or mom-contrived learning games, just through her leisure pursuits which have become incredibly creative and self-directed since her fourth birthday.
Her watercolour painting obsession finally abated after several months. She now sometimes skips a day or two of painting. Instead, she is into cutting and folding and arranging. And taping -- oh, the tape this kid goes through!
Today was typical. She took the padded foam-plastic bag that Noah's CD player had come in and cut one end off. The other end looked a little like a hood. So she sat down with scissors and cut the sides until they fit like a vest around her torso, and then cut arm holes. And then she cut slashes at the front of the 'hood' so that it would push back off her head. Next she used some of the cuttings to make a pocket which she safety-pinned and taped to the "jacket." She talked about wearing "my own-made jacket" to town if it was raining. Thankfully it was not, so she just wore it around home for a while.
Next she cut a cottage cheese container apart and made a visor which fit to her head. She wore this for a while as a sun-shade, and then decided it was a belt. Then she made a spring from some long strips of paper she taped together and folded. And another spring. And a little 3D house with peaked roof.
And then she built a 'box' out of three sheets of origami paper. First she diagonally half-folded two of the papers, then folded in the points. She taped these folded triangles together. Then she noticed that the gap between them needed a folded square to complete it, so she cut, folded and taped that on. (I highlighted the diagonal square in the image since it didn't photograph well.) And then she fussed around for a while with a scrap of red paper to make a slot for the coins to drop through.
And then there was plenty more taping involved to seal up the holes so the coins wouldn't drop out. Her adhesive medium and technique could probably use a little work, but the geometric sophistication of these things she invents out of her little brain just blows me away sometimes.
Pattern blocks were next. Sophie is the queen of complex pattern block creations in 3D but Fiona is doing some pretty neat things too. That's one of her snowflakes up top.
Fiona does pretty well with numerical and symbolic math too (she's the kid who will blurt out things like "half of six plus half of twelve is nine" for no particular reason). But even though she'd love a workbook program I don't want to hurry her into formal math study, as I see so much richness and value in the intuitive, creative, exploratory work she's doing on her own these days.
Noah was similarly intuitive with visual-spatial and numerical relationships at a young age. He didn't really delve into formal math until last fall around his tenth birthday. It's been necessary for him to do a certain amount of gap-filling in terms of arithmetical fluency, but I can now see what all that intuitive, informal mathematical experience has given him. He's almost ready to jump into a high school program after a mere 8 months of diligent work in the Singapore Primary Math curriculum.
I doubt Fiona will wait until 10 to start formal math study, but I'm hoping I can hold her off a while yet. This self-motivated, exploratory learning that is part of her play is a priceless part of her learning foundation.