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The Illusion of 'Rigor' in Math


Mark Schneider, the former chief of the U.S. Department of Education's statistical office, lays bare the discrepancy between American high schoolers' enrollment in tougher math classes, their alleged success in those courses, and their continuing mediocre academic performance in that subject.

Policymakers have long been flummoxed by U.S. students' failure to make gains in high school math, during the same period when math scores among younger students have risen. Schneider, writing for the American Enterprise Institute, suggests that American states and schools are fixated on putting students in the kinds of math courses that are supposed to be "rigorous," but in truth are anything but.

On the one hand, more students than ever are taking tougher math high school math classes—Algebra 1, Algebra 2, and calculus—and taking them earlier in school, he explains. On paper, Schneider explains, it seems like a "remarkable change." They're also getting better grades in those classes: The average math GPA has risen from 2.2 to 2.6 since 1990.

But here comes the rub. Schneider, the former commissioner of the National Center for Education Statistics, notes that students who take various high school math classes are actually doing worse than they did 30 years ago, as judged by the National Assessment of Educational Progress. (Check out Figure 5.) He also looks at data from international tests.

"Students who stopped at Algebra I, geometry, and Algebra II all scored lower on NAEP in 2008 than the students enrolled in the same courses in 1978," Schneider writes. "The only bright spot is that students completing calculus now do about as well as their peers from thirty years ago."

Schneider also knocks down a couple possible explanations for these unsettling trends. One of them is that the flat scores are primarily due to a decline in the U.S. population of higher-scoring white students at the high school level. That trend is indeed occurring, he says, but so what? It hasn't prevented an increase in the math scores among 9- and 13-year-olds.

Many of the math courses with impressive-sounding titles, Schneider concludes, are simply not what they seem. The responsibility to ensure that math courses are top-notch rests largely on states, which have not shown an inclination to make sure that curricula and tests are holding students to high standards. (Some say that under No Child Left Behind, states haven't had much incentive to do so.)

"If policymakers decide that a mark of a successful high school career is completion of Algebra II, then schools enroll more students into a course called Algebra II," he says. "But not all math courses are equal—and it is easier to rebrand courses and still teach low-level math than it is to increase the rigor of math instruction."


I studied high school math about 50 years ago, observed 3 children and 5 stepchildren during their education, and now am guardian of my grandsons - bringing me, once more, into the education arena - only now my involvement is intense.

What I observed is that educators, and the educational materials that feed off them, have year by year come up with a new NEW math and with each new and improved methodology our youth has suffered and fallen further behind. Sells a lot of textbooks tho!

You can't teach advanced mathematics when you don't instill and reinforce the basics. Our kids enter high school without a functional ability in 4 function math. My youngest grandson (now 11) had algebra introduced in 3rd grade. Now in 6th, he can't recite his multiplication tables, do long division, or understand basic math concepts.

However, we have new math jargon and paradigms coming out our ears which has fallen on our students' deaf ears.

If we were really serious about increasing math knowledge then we need to spend time in elementary grades (up to 6th grade) reinforcing the basics over and over again - by rote. I can still quickly recite the multiplication tables and I challenge a high schooler to do the same.

Without that foundation you can't move on to advanced math and instill the ability to move on to abstract concepts.

As a teacher, I've seen the same issues as A Natoli. I wonder if there's a correlation between the popularity of math programs such as Everyday Math (with their lessened homework load and new approaches) and falling math scores.

How can we blame Everyday Math when elementary and middle school students are doing better? I would guess the reason for the NAEP decline is the much higher percentage of students enrolled in Algebra II these days. I would venture to say that at least half of the students enrolled in the course at the high school where I teach would never have considered taking Algebra II in the 70's. NONE of my close friends were in math class with me back in those days.

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