Across the nation, the reconsideration of what should be taught and how has been accelerated by a report in September by the National Council of Teachers of Mathematics, the nation’s leading group of math teachers.Maybe if told for the umpteenth time that it did, NCTM will come to believe that it did.
It was a report from this same group in 1989 that influenced a generation of teachers to let children explore their own solutions to problems, write and draw pictures about math, and use tools like the calculator at the same time they learn algorithms.
But this fall, the group changed course, recommending a tighter focus on basic math skills and an end to “mile wide, inch deep” state standards that force schools to teach dozens of math topics in each grade. In fourth grade, for example, the report recommends that the curriculum should center on the “quick recall” of multiplication and division, the area of two-dimensional shapes and an understanding of decimals.
For those interested in a lot of conceptual math there is a series of teacher training videos funded by the Annenberg project. (Simple registration required). You won't get computational fluency and procedural knowledge out of them but they can certainly stretch your mind. Nevertheless, these conceptual exercises ultimately meant for pupils shouldn't displace computational fluency and procedural knowledge. They also can make simple procedures extraordinarily complicated. This is the impression I got when watching Video 8. Rational Numbers and Proportional Reasoning in which operations with fractions are modeled with Cuisenaire rods. It left me confused. If I were a child, I would conclude that operations with fractions are enormously complicated and intimidating. I would develop a phobia toward fractions and wait for the spiral to come around in a year or two.