Now, let us accept that there are different approaches to teaching mathematics, with a major divide between the "reform, discovery approaches" and the more "traditional, direct instruction" approaches. Reform/discovery approaches became the rage among the educational community in the 1990s and I believe it is a major, but not sole, reason that math performance has lagged.
As a scientist, it would seem to me that the next step is clear: test a variety of curriculum approaches in the classroom, insuring the class demographics are similar, and find out what works best. In short, do a carefully controlled experiment with proper statistics and find the truth in an empirical way. But what frustrates me is that such experimentation is virtually never done by the educational bureaucracy. They seem to go from fad to fad and student progress suffers. Reform math, Integrated Math, Teach for America, Whole Language, and many more.
Last Friday I and some other interested parties met with the head of curriculum and head of science/math for the Seattle Public Schools. I do appreciate the fact that there were willing to hear us out. But when we asked them about what plan they had for testing various math curricula and then proceeding with the most effective approaches, you would think we were from a different planet. No plans to do such testing and a dedication to the "system approach", which appears to be arranging lots of tutoring and alternative classes when students run into trouble. I would suggest it is better to stop them from getting into trouble in the first place.
Just maddening! But the interesting thing is that some unofficial experiments with the use of more traditional approaches to teaching, ones based on direct instruction, learning of foundational concepts, and practice to mastery ARE occurring and the results are stunning.
The Seattle Public Schools use reform/discovery math at all levels (my opinion...a disaster). Schmitz Park Elementary got permission to try Singapore Math textbooks in 2007 (traditional direct instruction). Its students’ math scores soared; in 2010 the 5th graders had the third highest passing rate in the state on the state test, even though the school has no gifted magnet program. North Beach Elementary began using Saxon Math in 2001. Their scores rose dramatically and stayed high for years, until a new principal, who opposed Saxon, took over; then the scores plummeted. That principal was replaced, and the scores are back up. At Ballard High, teacher Ted Nutting's students' scores on the AP calculus test have for several years averaged far higher than those of any other school in the district--guess what he and the Ballard precalculus teacher doesn't use? Discovery/reform math.
Or how about Seattle high schools? Here are the scores from the Algebra I end of course (EOC) assessments in order of % of students getting free lunch (a proxy for economic status of students). Now you might expect student scores to scale with the socioeconomic status of the students, assuming everyone got the same curricula right? And that is generally true except for two schools: Franklin and Cleveland. Franklin is the largest anomaly. Well folks, a little research has found that teachers at Franklin have generally put the district-provided reform math books away and have taught the students using more traditional/direct instruction approaches...and the results are obvious. Cleveland has double-length math classes. Can you imagine if we had double-length math classes plus good curricula in all Seattle schools?
What about in other districts? Consider Gildo Ray Elementary in Auburn, which switched to Singapore Math -- Math in Focus (traditional texts) for the last two years from Everyday Math (which Seattle uses). The pass rates on the MSP Math Exam in 2011 for grade 5 jumped to astounding levels:
Low Income : Black : Limited English Pass Rates in the 3 Columns
47.2% : 39.3% : 23.2% : State
44.8% : 33.8% : 26.0% : Seattle
88.5% : ..n/a… : 85.0% : Gildo Rey elementary in Auburn
I could give you many more examples. But the bottom line is clear: a large number of informal experiments have shown that direct instruction approaches with an emphasis on mastering basic facts and practice to mastery produce widely better outcomes for our students, and the educational bureaucracy doesn't seem to care. Why? Because the educational business is far more interested in theoretical ideas and "social justice" than empirical proof. And Schools of Education are more a part of the problem than the solution.
It is really so sad. Replacing the curriculum and books is relatively inexpensive and easy compared to most other changes and could be done quickly. Don't get me wrong, poor student performance has a multiplicity of causes, from too large classes, overworked teachers, teachers without sufficient subject mastery, student poverty, lack of home support, and many more. But curriculum improvement is a low-hanging fruit that we should grab. The money could be found for new books. How many parents would be willing to contribute for a new textbook to insure their child had a chance for a future? Or might the Gates Foundation contribute to textbooks instead of the valueless Teach for American boondoggle? God knows the huge sums wasted by the Gates Foundation and Microsoft on ill-considered experiments that have generally done more harm than good.
In short, there is very strong evidence that a change of curriculum from reform/discovery/fuzzy math to direct instruction approaches with an emphasis on basic facts/mastery could greatly improve the math performance of all students. I challenge the educational establishment to do the robust experiments that will prove or disprove this statement. Sadly, I suspect they won't. That is why we need new school board members in Seattle and in other districts that will ask for a more rational approach to curriculum acquisition.