The Headmistress/Zookeeper at The Common Room wrote this.
Beth Clarkson sent this link to "A Mathematician's Lament". The author's credential should command respect. His enthusiasm for Math probably inspires students. Still... his dismissive position on notation and symbolic manipulation gives me pause. Some problems are hard without notation and easy with notation. See postscript, below.
My bottom line? "What works?" is an empirical question which only a competitive market in education services can answer.
In related news, Georgia and Louisiana recently enacted school vouchers. Georgia, statewide, and Louisiana, limited. More, please.
P.S. A Sam Lloyd puzzle: A milkman has two 10-gallon dairy cans of fresh milk. Two cooks want to buy milk. One cook has a 5-gallon pail and one cook has a 3-gallon pail. Each cook wants two gallons of milk. The milkman has no way to mark the containers. There are no spare containers available. He does not want to pour milk away. How does he make the sale?
Just try this without notation.