questions,

Thanks for the link � I had not seen the article.

I generally agree with the points mentioned in the Times� article. In fact, many of the quotes from the panel�s report sound as if they could almost have been lifted from the book I mentioned above, Liping Ma's �Knowing and Teaching Elementary Mathematics." Specifically, Dr. Ma mentioned the point about fractions, and she has some very concrete and very useful suggestions for how to teach division of fractions, which is the sticking point for so many children (and teachers).

My one reservation is that I fear that the panel�s recommendations, as quoted in the Times, solid as they are, will be twisted and misused by the time they work their way into the nation�s elementary classrooms.

For example, the Times says:
> The report tries to put to rest the long, heated debate over math teaching methods. Parents and teachers have fought passionately in school districts around the country over the relative merits of traditional, or teacher-directed, instruction, in which students are told how to do problems and then drilled on them, versus reform or child-centered instruction, emphasizing student exploration and conceptual understanding. It said both methods had a role.

Indeed. The problem, though, is that some of the �child-centered� (AKA �constructivist�) programs out there have avoided making sure that students master the traditional algorithms in favor of letting the kids develop their own algorithms.

That is not a good idea.

The traditional algorithms have been worked out over centuries by some very bright people. Those algorithms always work, and they are fairly easy to understand and very efficient for paper-and-pencil calculation.

I�m good enough at math that, when I am doing math in my head, I often invent a new algorithm on the fly. But I already know the traditional algorithms. To encourage kids who do not already know the traditional algorithms to do this is unwise. Also, the traditional algorithms transfer nicely into more advanced math: for example, �synthetic division� of polynomials is basically a generalization of the traditional long-division algorithm learned in grade-school arithmetic. If you do not understand the traditional long-division algorithm, you are going to have trouble understanding synthetic division.

I�m also concerned about the point that:
> The report, adopted unanimously by the panel on Thursday and presented to Education Secretary Margaret Spellings, said that prekindergarten-to-eighth-grade math curriculums should be streamlined and put focused attention on skills like the handling of whole numbers and fractions and certain aspects of geometry and measurement.

There has indeed been a lot of silly topics in the �fuzzy math� curricula that should just be abandoned, and, yes, the first priority in grade-school math has to be mastery of whole numbers and fractions (the latter including decimals and percents).

But, especially for bright kids, there can also be exposure to real ideas in math that give a sense of what real math is about beyond grade-school arithmetic � everything from prime numbers to a peek at what has been done with infinity. Infinity, incidentally, was central to twentieth-century mathematics: as a physicist, I routinely work in infinite-dimensional spaces (so-called �Hilbert space�), but I doubt that very many adults, aside from mathematicians or physicists, even know that infinity is not a vague philosophical idea but an integral part of modern mathematics.

So, I�m a bit afraid that, if the panel�s recommendations are followed, the best we can hope for is a return to the way our parents were taught math. That would be a real improvement on what now prevails in many grade schools. But it�s not optimal, especially for the brighter children.

On the other hand, the report�s points about committing elementary facts to long-term memory so that you can focus on higher-level activities, about intellectual achievement being based on extensive knowledge of facts, and about mastering math being a result not simply of talent but primarily of hard work are, in my experience, quite true, and, as the Times suggests, are now backed up by a good deal of research in cognitive science (and, of course, common sense).

All the best,

Dave