A double dose of algebra

An interesting article by Kalena Cortes, Joshua Goodman and Takako Nomi appeared recently in EducationNexta right-wing magazine that comes out of Stanford’s Hoover Institute. They claim to be fair and balanced. Sound familiar? Those aren’t their words, actually, but that’s definitely their gist:

This journal will steer a steady course, presenting the facts as best they can be determined, giving voice (without fear or favor) to worthy research, sound ideas, and responsible arguments. Bold change is needed in American K–12 education, but Education Next partakes of no program, campaign, or ideology. It goes where the evidence points.

Anyhow, the article in question is titled “A Double Dose of Algebra.” Although it starts off with a rather unfortunate photo (see educationnext.org/files/ednext_20131_EN_Cortes_img01.jpg), it gets better after that. The essential question is how to help high-school students who are unsuccessful in math (and often in reading as well). The proposed remedy — as the title indicates — is to give mathematically weak Algebra I students two classes of algebra a day instead of just one. The conclusion of the study needs a bit of untangling, but here it what it says [bold italics and red color added by me]:

Our study provides the first evidence of positive and substantial long-run impacts of intensive math instruction on college entrance exam scores, high school graduation rates, and college enrollment rates. We also show that the intervention was most successful for students with relatively high math skills but relatively low reading skills. Although the intervention was not particularly effective for the average affected student, the fact that it improved high school graduation and college enrollment rates for even a subset of low-performing and at-risk students is extraordinarily promising when targeted at the appropriate students. In this case, those were students with only moderately low math skills but below-average reading skills.

This double-dose strategy has become an increasingly popular way to aid students struggling in mathematics. Today, nearly half of large urban districts in the United States report double math instruction as the most common form of support for students with lower skills. The central concern of urban school districts is that algebra may be a gateway for later academic success, so early high-school failure in math may have large effects on subsequent academic achievement and graduation rates. With the current policy environment calling for “algebra for all” in 9th grade or earlier, effective and proactive intervention is particularly critical for those who lack foundational mathematical skills. A successful early intervention may be the best way to boost students’ long-term academic success.

Note the qualifiers of “successful” and “may be” in the last sentence. Do they equate to double algebra? Also, since the intervention was intended for students with weak math skills, what’s going on with the conclusion that it “was most successful for students with relatively high math skills”? Let’s first look at who was admitted to the study described in the article:

Students scoring below the national median on the 8th-grade math exam were required to take two periods of algebra a day during 9th grade instead of one, with the second class providing support and extra practice.

“Below the national median” is of course a huge group — 50% in general, 55% in the Chicago Public Schools, where the study was conducted (only 55%? I’m surprised) — so we’re not really identifying the weakest students, who indeed turned out to be the ones who were helped the least. Some of the other specifics were even more interesting:

CPS also strongly advised schools to schedule their algebra support courses in three specific ways. First, double-dose algebra students should have the same teacher for their two periods of algebra. Second, the two algebra periods should be offered consecutively. Third, double-dose students should take the algebra support class with the same students who are in their regular algebra class. Most schools followed these recommendations in the initial year. In the second year, schools began to object to the scheduling difficulties of assigning the same teacher to both periods, so CPS removed that recommendation… The recommendation that students take the two classes with the same set of peers increased tracking by skill level. All of these factors were likely to, if anything, improve student outcomes. We will also show, however, that the increased tracking by skill placed double-dose students among substantially lower-skilled classmates than non-double-dose students, which could have hurt student outcomes.

Indeed, even if greater tracking is deemed “likely to, if anything, improve student outcomes,” it is not at all surprising that it places these students “among substantially lower-skilled classmates.” That’s exactly why we don’t do it that way in Weston. Now Weston is not Chicago, of course. We’re such a very different school system in so many ways that I wouldn’t even dream of suggesting a comparison. But it’s still instructive to see what we do. First of all, in our case it’s Algebra II, not Algebra I, since our students have all already taken Algebra I before entering the high school. Ninth-graders take geometry, where we provide two different courses (honors and college-prep) and two levels of difficulty within the college-prep course. Tenth-graders take Algebra II, which is again offered as a choice of two courses, but with a different solution for the weakest students: they’re the ones who have close to a “double dose of algebra.” All our Algebra II students start with slightly more than a “single dose,” since their class meets for five 76-minute blocks every eight school days, averaging 48 minutes a day, just barely over the national median of 46 minutes. Then the weakest 25% or so take an additional course, called “Topics in Algebra II,” which meets for two and a half 76-minute blocks every eight school days, averaging 24 minutes a day. So we end up with an average of 72 minutes of math a day for those students. Unfortunately, for the same reasons cited by the Chicago schools, we can’t have the same teacher teaching both courses; this causes some difficulties, but may also have the advantage of a fresh point of view for students who are struggling and might need such a change. Also, for most students, Algebra II and Topics are not back-to-back. The biggest difference is that we avoid the problem cited: that of placing “double-dose students among substantially lower-skilled classmates.” Since all our non-honors Algebra II students are commingled heterogeneously, they have plenty of successful classmates as role models. It’s not perfect, but it clearly works.

Finally, let’s look at a dissenting voice, the pseudonymous “Educationrealist,” who describes herself or himself as a math teacher in the fourth year of teaching (and as a registered Republican, though I don’t know why that matters). In an annoying but fascinating essay, s/he writes about the double dose of algebra, starting with some personal feelings on the subject:

In retrospect, my second year of teaching was my most brutal, thanks to my schedule of all algebra I, all the time. I learned a lot. I never want to go back. Oh, sure, I’d like to teach one class of Algebra I, particularly to see if my data modeling lessons they work as well in algebra I as algebra II. But I do not want to be an “algebra I specialist”, and never, ever, EVER want to devote anything more than a class a year to algebra I. I’ve said it many times, but I’m always ready to bore folks: high school algebra I classes should convince anyone—from loopy liberal progressive to anti-teacher union tenure hating eduformer—that our educational policy is twisted and broken beyond all recovery.

So why bring it up now? Because until I saw this article, I’d forgotten the very worst part: A Double Dose of Algebra.

That certainly grabbed my attention. But I was a bit put off by the description of “A Double Dose of Algebra” [caps in the original]:

it’s this brilliant strategy of identifying kids who are really weak in math and increasing their hours of torture.

Anyway, despite the rhetoric, Educationrealist noticed some upsetting conclusions and statistical flaws in the original study. Quoting from the original article, “Nomi and Allensworth reported no improvement in 9th-grade algebra failure rates as a result of this intervention, a disappointing result for CPS.” Hmmm… And then s/he observes that the Chicago study did eventually show some improvement, because of the two groups they compared: they “checked the kids just below and just above the threshold? So you only compared the strongest intervention students with the weakest regular students? Well, golly. Did you, perchance, check how the weakest regular students did compared to the weakest intervention students? Was it substantially different from the gap between the strongest intervention and weakest intervention?”

Then the rant continues. The teachers of “A Double Dose of Algebra” were given eight days of professional development to learn what to do. Are you listening, Weston? But wait…“the PD was utterly useless.” Oh, well. And what happened as a result of keeping all these kids together? Let’s see:

For every intervention class, some 20–30 underachieving, low-incentive kids are moving through their entire day together, in non-remedial and remedial classes both. Of course, since most intervention kids are weak in all their subjects, this means that their classes have a disproportionately high number of low achievers — all of whom spend their entire day together, socializing. Or planning ways to wreak havoc. The troublemakers in my class arranged signals that they would use to disrupt classes — all their classes. They’d pick a code word, and whenever the teacher said that word, they’d all start laughing loudly, or squeaking their shoes, or sneezing.


Anyway, the article goes on and on. You might find it tedious, or it might be the sort of thing you like, if you like that sort of thing.

Categories: Math, Teaching & Learning, Weston