Math Versus English

This is a very provocative scholarly paper on charter schools. It's a working paper that just got posted on the MIT website.

It's by economists Parag Pathak, Josh Angrist, and Christopher Walters. They are top notch. I've known Josh for many years, and his kid -- an MIT undergrad -- has volunteered with our school.

They find:

1. Suburban charter schools are "uniformly ineffective" at generating gains in student achievement.

2. Among urban charter schools: No Excuses charters work, other kinds don't.

Sure to stir up some controversy!

On a related note, I've contended previously on this blog that the test score gains associated with No Excuses schools are consistently bigger in math than in reading. This squares with findings in Pathak's paper.

Why? MTR grad Lauren Latto blogged about this from her point of view. She's a young teacher at a Brooklyn No Excuses school (and wonderful writer).

The achievement gap is a lot more nuanced, though, than mainstream media gives it credit. My school got its state test scores back this week, and we’re feeling pretty damn good. 100% of our seventh and eight graders scored proficient or advanced on the math exam, outperforming Brooklyn students by a scary margin and keeping pace with white students across the state. Take that, achievement gap: You can close yourself right up.

Except not quite.

The data isn’t nearly so tidy where English/Language Arts is concerned. Though twice as many of my seventh graders scored proficient than did Brooklyn seventh graders at large, the scores are a far cry from 100%. Breakdown: math gives us bragging/drinking rights, but there’s still a gaping gap in more literary pursuits.

She wonders why. I've blogged before about one component, the ED Hirsch/Robert Pondiscio/Dan Willingham argument of "knowledge gap." That's true. There's a related gap, though. Lauren writes:

Why is it that inner city kids can lap white kids in fractions and division but still trail far behind in reading and writing? There are lots of theories, but I find one particularly compelling: the vocabulary gap.

Studies show that by the time a disadvantaged, inner city kid enters elementary school, she knows something like 10,000 fewer words than her wealthy white counterpart. If nothing is done to counteract these numbers, the cavern widens until we’re talking Grand Canyon. This is absolutely staggering.

Yes. One of the huge challenges here is that kids in well-educated families are partially amassing this vocabulary "organically" -- simply by being present for 5,000 waking hours a year where more vocabulary flies around. A 1995 study (Hart & Risley) found "children living in advantage homes hear three times as many words spoken as children living in disadvantaged homes."

The gap has to be somehow made up in a non-organic way -- i.e., a school has a kid for 1,000 waking hours a year, and can't just flood the zone with spoken words.

So what's a teacher (or team of teachers -- i.e., a school) to do? Lauren writes about a recent training she attended in Tarrytown (probably with Doug Lemov):

Close to 20% of our instructional time as reading teachers should be devoted to word study. We started the session by reading a chapter from Animal Farm and identifying the words with which our students would struggle. Overall comprehension of the text relies on these words, and the list was close to 30.

Do you teach these words before the reading or during? Do you skip over some and focus on others? In the vocabulary hierarchy, which words are tops? If you pause to explicitly teach every difficult word, you’re losing out on Socialist allegories and narrative tone, but without the words, are those things even possible? For a teacher, the task at hand is daunting; for a student who’s been vocabulary gapped, the task is near-impossible. But if we give up, it gets worse.

Yup. This is a very difficult strategy for the individual teacher. Imagine you explicitly teach 10 new words a week, such that they stick. That's 300 or so per year. Still such a small dent. Lauren's right, though. That's (to my knowledge) the only empirically proven method to cut gap.

How big is that vocab gap exactly? Here's a 2007 research summary.

How many words are normally acquired?

Various sources now suggest that by the end of grade two, an average child knows about 6000 root word meanings (Anglin, 1993; Biemiller, 2005; Nagy and Scott, 2001). This count of root words includes word forms with different meanings, e.g. lean (slant to the side) and, lean (without fat); but does not include "derived forms", e.g. leans, leaner, etc.). Many “words” have several meanings. Consequently, I usually refer to “word meanings” or “meanings”, rather than “words”. There are more “meanings” than there are “words”. Before grade three, children add an average of 860 root word meanings per year, starting at about age 1. During grades three to six, children acquire about 1000 root word meanings per year. Thus by the end of grade six, average children understand about 10,000 root words (Biemiller, 2005).

These findings are based on a combination of recent empirical research (Anglin, 1993; Biemiller & Slonim, 2001), and data in Dale and O'Rourke's Living Word Vocabulary (1981). Dale and O'Rourke empirically assessed knowledge of some 30,000 root and derived word meanings known between grades four and twelve.

How much variation is there in vocabulary acquired?

By the end of grade two, children's vocabulary already differs a great deal.

a. English-speaking children whose vocabulary is in the lowest 25 percent know an average of 4000 root word meanings.

b. Children with average vocabulary know about 6000 root word meanings.

c. Children in the highest 25 percent vocabulary group know an average of 8000 root word meanings (Biemiller, 2005).

Thus very large differences in vocabulary have developed in the preliterate period before children have had much opportunity to acquire vocabulary from reading.

Even if children with low vocabularies add 1000 meanings per year after grade two (as many do), by the time they begin grade six they will have about the same size vocabulary as children from the top 25 percent had at the end of grade two.

I've often thought we should wage an all-out effort to generate pleasure reading habits among older kids. In our early years at MATCH High, we took kids to the bookstore each month, to buy whatever book they wanted. Somehow our tradition faded away.