The Washington Post's Michael Alison Chandler has been doing some good work this month on math education. She's had pieces on math scores that are relatively weak compared to literacy marks, the challenges related to teaching algebra in the eighth grade, and what math lessons should look like beginning in pre-kindergarten. [She is also retaking high school algebra herself, to get grounded in it! What a great idea.]

The folks she talks to about the early math lessons, I must say, don't do much more than repeat the standard progressive line. You know the one: "relevant," "hands on," "concrete," math is "abstract." That's all fine. But, as another expert she quotes says, the activities need to contain some math that's talked about in explicit ways. Key math concepts such as place value and one-to-one correspondence between units and numerals need to be taught and spoken about using mathematical terms.

The other point is that the Virginia state standards she excerpts are not focused. As Michigan State University professor Bill Schmidt says, countries where math achievement exceeds that in the U.S. focus on only two or three key concepts in each of the early grades. But they do so with rigor so that students don't have to come back and relearn them in every grade up until they take algebra.

A good source on early math education is Herbert Ginsburg here at Teachers College.