The *New York Times* is reporting that President Bush has chosen Larry Faulkner, a chemist and a former President of the University of Texas at Austin to head the National Math Panel:

The former president, Larry R. Faulkner, who led the university from 1998 until early this year, will be chairman of the National Math Panel, which President Bush created by executive order in mid-April.

The panel is modeled on the National Reading Panel, which has been highly influential in promoting phonics and a back-to-basics approach to reading in classrooms around the nation. Though that panel has been criticized by English teachers and other educators, its report has become the guide by which $5 billion in federal grants to promote reading proficiency are being awarded.

The new panel reflects a growing concern by the Bush administration that the United States risks losing its competitive edge as other nations outpace its performance in math and science. Citing figures from a report by the National Academies in his State of the Union address in January, President Bush unveiled an American Competitiveness Initiative to pump hundreds of millions of dollars into research in the physical sciences, and some $250 million into improving math instruction in elementary and secondary schools.

The article goes on to mention some difficult issues in mathematics education:

The conflict over how to teach reading — whether by teaching children to recognize words in the context of stories or through more explicit instruction in letters and sounds — has its parallels in the fight over how to teach math, and the conflicts share many of the same political and philosophical disputes.

In traditional math, children learn multiplication tables and specific techniques for calculating 25 x 25, for example. In so-called constructivist math, the process by which students explore the question can be more important than getting the right answer, and the early use of calculators is welcomed.

I’m much closer to the traditionalists on this one.

I haven’t always felt this way, but the specatcle of college students having to think about 8×7, or being unable to add 1/2 and 1/3 in their head, is pretty persuasive evidence that the constructivists have the wrong emphasis. To have any hope of being successful in higher levels of mathematics, it is essential first to be comfortable with arithmetic. Multiplication tables have to be automatic, as does an ability to find common denominators for fractions with small denominators. Likewise for basic skills such as converting between fractions, decimals and percentages.

The way you develop that comfort is by doing it. Over and over again. Lot’s of drill. It’s boring and tedious and stressful for many kids. Sorry, but it’s the only way. And, yes, getting the right answer is important.

On top of that, there is a limit to how much abstraction young children can handle. A typical bright eight-year old can learn his multiplication tables without too much difficulty, but abstract set theory is probably beyond him. That is one of the lessons we learned from the “New Math” fiasco in the 1960′s (in which children were introduced to abstract mathematics at a very young age.)

As for calculators, I believe there are probably innovative ways to integrate them into the early math curriculum. For example, one teacher suggested to me that calculators can facilitate things like “counting by fives.” The idea is that a child types 5+5 and then the equal sign over and over again, watching the sums go 5, 10, 15, 20 and so forth. This can help develop a certain number sense in small children. That’s fine, but it is essential that the calculator not become a crutch for replacing pencil and paper algorithms.

None of this is to say that the reasoning behind the algorithms, or the general approach to solving a given problem is unimportant. Clearly both items are important: Getting the right answer, and understanding the means by which the answer is obtained. The issue is finding the appropriate balance between these concerns at each grade level. The way I see it, as a student gets older there should be a gradual shift away from algorithms and towards nore abstract approaches.

In other words, first master your basic skills then worry about proofs and abstract reasoning.