As a society, we reward people for making predictions about things that we find interesting to contemplate: Colts or Saints? Will the stock market go up or down tomorrow? Not surprisingly, we don't much punish people for being wrong about their predictions in these nearly random situations that so intrigue us.

Unf0rtunately, that lack of accountability extends to systems that aren't at all as smooth-operating as the NFL playoffs, the systems that we find boring and depressing to think about. So, we allow magical thinking to run amok. For example, a few years ago the Gates Foundation pressured the gigantic Los Angeles Unified School District into making it a requirement for graduating from high school that students pass Algebra I, Geometry, and Algebra II, a course so far over the cognitive capabilities and needs of a large fraction of perfectly nice kids who deserve to go through life as high school graduates that they might as well get a letter from Bill Gates telling them to drop out now and beat the rush.

The notion that students who haven't mastered fractions yet should be taking algebra is the kind of idea that can flourish only in areas of society that are deeply crippled by taboos.

From Education Week:

"Algebra-for-All" Push Found to Yield Poor Results Spurred by a succession of reports pointing to the importance of algebra as a gateway to college, educators and policymakers embraced â€?algebra for allâ€? policies in the 1990s and began working to ensure that students take the subject by 9th grade or earlier.Can't have that! What elite groups of students who get better advising ever contributed to humanity?A trickle of studies suggests that in practice, though, getting all students past the algebra hump has proved difficult and has failed, some of the time, to yield the kinds of payoffs educators seek.

Among the newer findings:

â€? An analysis using longitudinal statewide data on students in Arkansas and Texas found that, for the lowest-scoring 8th graders, even making it one course past Algebra 2 might not be enough to help them become â€?college and career readyâ€? by the end of high school.

â€? An evaluation of the Chicago public schoolsâ€™ efforts to boost algebra coursetaking found that, although more students completed the course by 9th grade as a result of the policy, failure rates increased, grades dropped slightly, test scores did not improve, and students were no more likely to attend college when they left the system.

â€? A 2008 paper by the Brookings Institution suggested that as many as 120,000 students nationwide were â€?misplacedâ€? in algebra programs, meaning they had test scores on national exams that put them about seven grades below their peers in algebra classes. Further, it said, states with a high proportion of students taking algebra in 8th grade didnâ€™t necessarily outperform other states on national math assessments.

â€?Simply sticking students in courses without preparing them ahead of time for the class does not seem to work as an intervention,â€? said Chrys Dougherty, the author of the Arkansas and Texas analysis, published last month by the National Center for Educational Achievement, in Austin, which is owned by the test publisher ACT Inc. â€?It seems to work with adequately prepared students, but not for the most challenged students.â€? ...

What Mr. Schmidt found was that the learning gains were greatest for students who moved from either a general math class or a prealgebra class into a full-blown algebra class.

His findings are in keeping with a larger body of studies from the 1990s and early 2000s that suggested algebra was, for many students, the primary gateway to advanced-level mathematics and college. The problem was that too many studentsâ€”particularly those who were poor or members of disadvantaged minority groupsâ€”were turned away at the gate, screened out by ability-grouping practices at their schools. ...

â€?For the high-achieving kids, there was a big change in the classroom composition, so that changes the quality of classes,â€? said study co-author Elaine M. Allensworth, the interim co-executive director at the consortium, an independent research group based at the University of Chicago. â€?That means you have to have teachers who can teach to all classes, and it also means you donâ€™t have an elite group of students who may be getting better advising in smaller classes.â€?

â€?Meanwhile, the kids who werenâ€™t taking advanced classes before are taking them now,â€? she said, â€?but theyâ€™re not very engaged in them. They have high absence rates and low levels of learning.â€?Because it's hard to do. It's easier to teach tracked classes, but that's out of fashion ... unless you call them AP classes. Then they are the height of fashion.As the trends became evident, the school system in 2003 began requiring 9th graders who scored below the national median on standardized math tests in 8th grade to take an algebra â€?supportâ€? class in addition to a regular algebra class. Students who scored higher continued to take a single period of algebra.

For the Chicago consortiumâ€™s study, the researchers compared outcomes for students just above and below the cutoff for the â€?double doseâ€? classes.

Worried about the potential for reintroducing tracking, the district also provided professional-development workshops and other resources to the teachers of the support classes, according to Ms. Allensworth.

â€?Because teachers had more time and resources, the instructional quality in those classes improved quite a bit,â€? she said. â€?But the classes ended up concentrating more students with attendance and behavioral problems.â€?

In the end, the study found, failure rates increased for both the targeted students and for their peers in single-period algebra classes. On the other hand, algebra test scores rose substantially for the students in the double-dose classes.

â€?The district thought [the double-dose initiative] was a failure because it did not improve pass rates, but our analysis showed that test scores improved a lot,â€? Ms. Allensworth said.

Part of the problem, the Chicago researcher said, is that schools have little guidance on how to structure algebra programs to serve all students.

Tom Loveless, the author of the report from the Washington-based Brookings Institution on â€?misplacedâ€? math students in algebra, said the issue is even more complex.â€?No one has figured out how to teach algebra to kids who are seven or eight years behind before they get to algebra, and teach it all in one year,â€? said Mr. Loveless, who favors interventions for struggling students at even earlier ages.Giving the dumb kids more time to learn the times tables by rote would be a good idea for a start.

Nationwide, research findings may diverge because testing content variesâ€”the TIMSS test has more algebra content than many state exams taken by 8th gradersâ€”and because course content varies from classroom to classroom.As well they should.â€?If you take whatâ€™s called algebra class, and you look at the actual distribution of allocated time, you find that many of those teachers spend a very large portion of that year on basic arithmetic,â€? said Mr. Schmidt, who is a distinguished university professor of education at Michigan Stateâ€™s East Lansing campus. His research on U.S. classrooms has found, in fact, that nearly a third of students studying algebra are using arithmetic books in their classes.