At the end he talks about this:

” You talked about math books as a symbol for educational failure in America. Explain that.
A: We have huge textbooks?300-page math books. Because they?re designed by committee and everybody wants things to be in them, they are very intimidating. I thought, maybe the Asian textbooks are [going to be] twice as big because they do so much better than us and our kids are going to have to do some weight exercises to carry these books around so we can be in their league. In fact, the Asian textbooks are half as big. Their textbooks are little but they are really drilling in concepts in particular grades and then they don?t go over that again. We do all of it again and again and again.”

Much like other subjects, over and over again.

Gates has very good points, now if only the teachers’ unions are listening, along with the rest of the education bureaucracy.

This is a reference to “spiralling”, a wasteful and ineffective method of teaching, most prevalent in math instruction.  It’s a killer for math, as is semestering.

Next in line of usual suspects is the literally endless re-invention of math texts, whose proliferation is matched only by their worthlessness.  And they are getting bigger as more razmataz is added with Sesame-street enthusiasm.

“Delay long and never come to a conclusion” —instructions of the pope to his emissary in the court of king Henry viii when the latter was suing for a divorce from Catherine of Aragon.

I never heard or read of the use of spiralling, and so I look it up.

“?Recycling or spiralling: Sometimes called the cyclical approach; the purpose is to repeat language items throughout the syllabus; each time a language item is encountered more detail about it is added; this allows students to build on prior knowledge.”
http://en.wikipedia.org/wiki/Glossary_of_language_teaching_terms_and_ideas

I would call it, bits and pieces teaching approach, where the whole means less than the bits and pieces. My child, and I suspect many other children, concerning math,  need to understand the whole concept rather then spending most of their time on the bits and pieces of the concept. With my child it brought confusion, rather than a deep understanding of the concept, and unlikely the bits and pieces would be remember from one year to the next.

Here is a timely article from Education Week, on:

Panel Calls for Systematic, Basic Approach to Math
Federal advisory group?s proposals may reignite debate on ?broken? content and instruction

http://www.edweek.org/ew/articles/2008/03/19/28math_ep.h27.html

As usual, there is plenty coming from the other side why it cannot be done, or it should not be done, or as one will read it, plenty of other reasons given.

“Nearly two years in the making, the report went through 90 drafts, with its members wrestling over major recommendations and individual words and phrases. It was approved unanimously at the panel?s final meeting, held March 13 at Longfellow Middle School here in a suburb of the nation?s capital.

The 90-page document calls for the math curriculum to be streamlined in pre-K-8, a strategy it calls putting ?first things first.? Students need to be grounded in both the effortless, automatic recall of simple procedures and in the acquisition of broader problem-solving skills. Too often, those skills are wrongly presented as incompatible, the report says.

At various points, the authors also allude to the enduring philosophical battles over how to teach the subject?commonly referred to as ?the math wars.? Those disputes tend to pit those who argue that students should be grounded more firmly in simple math procedures against others who advocate a more conceptual approach to teaching and learning. “

The comments are interesting. I like this comment from an ex-solider, now a teacher, who is still not considered a teacher by his colleagues.

” By Mathman: I totally agree with this finding. I retired form the United States Air Force and became a teacher seven years ago. I was placed in a resource room and asked to work with students (4th and 5th grade) who just don?t get math. What I discovered was that they didn?t get math because they were not grounded in the basics. They could not add, subtract, multiply or divide and worse they depended on wall charts and calculators to do their math work. I was told that the use of these is acceptable because they are allowed on our states test. The students use copy sheets and workbooks so most could not even line up numbers properly. I went to work by starting over and gone from the room are charts, workbooks, and calculators. We worked hard and the students found they could get math and the more they understood the faster they learned. Twenty-two students finished the year back in class and working right along with the other students…..........”

Of course teachers’ unions and math textbook publishers are not at all thrilled about the report, and have applied their own spin,

“But Steven Rasmussen, the publisher of Key Curriculum Press, a producer of math textbooks and software based in Emeryville, Calif., said the report?s heavy emphasis on basic arithmetic and fractions?which he regards as important?left out other topics that help prepare students for high school math.

Exposure to basic elements of data analysis, statistics, and applied math, engage students and allow them to relate math to workforce skills, he said.

?This report is biased in favor of teaching arithmetic and not [modern] mathematics,? Mr. Rasmussen said, ?and it?s biased in favor of procedures and not applied skill.?

Post-secondary institutions are finding out that many of their first-year students need remedial help in basic arithmetic, but according to Mr. Rasmussen, basic arithmetic and fractions should not be stress in   modern mathematics. Today modern mathematics instructions = do it again and again and again. Healthy for the profits of math textbook publishers.