What if math education used no writing for the first few years? What if all sorting, arithmetic, geometry and algebra problems were done with movement and objects? Chocolate-bar fractions and M&M probability. Area and perimeter using square tiles and real rulers. Graphing using footsteps and string. "Solving equations" using a scale and bags of goodies.
I wonder how much of people's math difficulties and fears stem from premature writing, and too few hands-on activities. "Manipulatives" is a current buzz-word, but if they're only tossed in as an extra now and then, are they enough? When I tutor math students and they're struggling with a particular concept, I always try to show them in a hands-on manner what is going on. But why should I wait until they're struggling? Why can't math be kinesthetic all along?
My kids are (almost) 6 and 4 1/2 and they've both been doing kindergarten this year. I have done no worksheets about numbers and counting, but we talk about numbers all the time. We spent all Fall doing math activities concentrating on classifying, directions, and quantities. Numbers were something I brought up every now and then. Now my kids bring up numbers themselves and are continually telling me things like, "Mom, 2 and 3 make 5!" My older child has tried writing equations on her own because she's becoming enamored with writing in general. But I wonder if I wouldn't be better off saving the writing for later.
I think I would have more fun teaching and I know the kids would have more fun learning, if math were taught this way. And maybe, as a small side benefit, our next generation would not be so math illiterate.