Are they starting to get it?

SOURCE: Seattle Times, 16 April 2006
WEBSITE: http://seattletimes.nwsource.com/
TITLE: “Math comes with its own problems”

“The biggest problem we have with mathematics in the U.S. is there isn’t a clear mathematics program,” said Mike Riley, district superintendent, Bellevue, Washington. “If it is not clearly organized, and you don’t have agreement on what kids need to learn in second grade so the third-grade teacher can count on it, you get what we have: weak performance in mathematics.”

The key is to order topics over the grades such that they follow the inherent structure and logic of mathematics, and to ensure that kids reach a deep understanding of each mathematical concept before moving on, said William Schmidt, a math expert at Michigan State University. “The idea is to build ideas on each other in an increasingly complex way,” he said.

It sounds like educators are beginning to discover what teachers long ago knew and mathematicians have been desparately trying to tell them for years. Yet, they still haven't got it quite right. Deep understanding doesn't come in chunks, but is a continuous process that comes from review and integration. You don't stop where you are until everybody has a deep understanding, then move on. You wouldn't get very far that way. But you move on, and you come back. You integrate, refresh, and expand. You constantly check for understanding and look for those powerful "aha" moments when students suddenly comprehend what they learned about months before--you capitalize on the psychological rewards of mathematics.