The new curriculum in British Columbia suggests that mathematical skills are best learned in a problem-solving context. First, concretely through the use of manipulatives, then pictorially to represent concepts, and finally symbolically, making the full leap to abstract representations.
I'm still trying to wrap my head around what this would look like in a classroom. I had thought to use summer school as an opportunity to try out some new strategies and methods. But that hasn't happened as much as I would like. Although I have spent most of the summer pondering the implications of this approach.
It seems to me that this is exactly how children learn best. Children play with stuff. My one year-old puts everything in her mouth. She shakes it. She drops it from her high chair... over and over again. She passes it to me... then takes it back, She rolls it on the floor. She tries everything she can think of. Then discards it for something else.
My three year-old is the same. Just less drool. She pokes and prods and swings and shakes and rolls and throws and hides. She tries stuff. She loves soap as a play thing. She paints it, keeps it in her purse and uses it as money. Old store fliers are perfect for her projects. She demonstrates unique and creative ways to use common household items.
I think teenagers are the same. Watch them skateboard... or play video games. They explore and experiment. They try to break things until they figure out its limits and how it works. They are engaged and they persevere through failure.
I think our classrooms ought to give them the same opportunities.