Math Versus English
Posted: August 17th, 2011 | Author: Michael Goldstein | | 10 Comments »
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.
One problem with our testing regime is that it makes math look like half of the goal of a school. Math as a discipline is constructed and taught differently than all others. If your school is constructed to optimize math instruction, you’re not half way there; you’re more like 1/5th of the way.
Yes, that’s a good point.
One note–Lauren calculates the achievement gap incorrectly. When calculating the gap, proficiency scores provide an incorrect assessment of the gap. Only scale scores can be used to assess the achievement gap. I suspect her “zapping” of the achievement gap may not be a zapping at all when the scale scores are used to examine the gap rather than just proficiency scores. See Daniel Koretz’ book “Measuring Up’ for an easy-to-read explanation of why this is.
Ohh–as a former high school math teacher and someone who has also taught grad students how to write, I can tell you that math is much more amenable to test prep that focuses on memorization of facts and certain skills. I never met a regular ed student who I could not teach to pass a state standardized math test. Now, teaching them to understand the math is a different story, but passing the test is easy.
I think Lauren is confronting issues of “scoreboard.” The NYS math tests are (or at least were) easier than the ELA tests in that kids do better on them across the board. Part of that was that questions were recycled so frequently in the past – thought that’s less of an issue now from what I hear.
The reverse trend happens in MA. Across the state, ELA scores are higher in general. For example, in 2010 Brooke 7th graders had 100% A + P in both ELA and math. That outperformed the state average by 28 points in ELA but a whopping 47 points in math. Clearly the proficiency bar is lower in ELA. However, the reverse is true when we zero in on advanced numbers. In general, across all tests (except it seems, 7th grade), there is a wide gap between state advanced averages in math and ELA, with it being much harder to score advanced on ELA tests.
All this to say, that I agree with your post on vocab; it’s becoming a bigger and bigger focus across our school, K-8, every year.
I hate to pour oil on the fire, but I believe the achievement gap is more than a word gap. It’s an EXPLANATION gap. I’ve written an entire essay on this issue and have been looking for the right place to publish it (besides in the book I’m writing). This seems like an opportune moment, so here it is…
To Close the Achievement Gap, We Need to Close the EXPLANATION Gap
By Sarah Tantillo, Ed.D.
In recent years, it has become increasingly accepted that the Achievement Gap between historically disadvantaged children and children from high socioeconomic backgrounds is a literacy gap. Because all subjects require comprehension skills, students who can’t read or write as well as their peers fall behind not just in language arts, but in science, social studies, math, etc.. A recent study by the Annie E. Casey Foundation found that one in six children who are not reading proficiently in third grade do not graduate from high school on time, a rate four times greater than that for proficient readers.
Some educators attribute this literacy gap to a “Word Gap.” As Betty Hart and Todd R. Risley discovered, some children—from an early age—are exposed to many words while others are exposed to few. In a study of 42 families from three different socioeconomic categories (professional, working-class, welfare), they observed and tape-recorded family interactions for an hour a month for 30 months. They found that children from the wealthiest families heard more than 1,500 more words each hour, on average, than children from the poorest families (2,153 vs. 616). Over a four-year period, this amounts to an estimated 32-million-word gap.
They also found that children mirrored their parents’ vocabulary resources, use of language, and interaction styles. In fact, about 9 out of every 10 words in each child’s vocabulary consisted of words also recorded in their parents’ vocabularies.
Vocabulary knowledge is clearly a key component of the background knowledge that enables comprehension. In order to paraphrase text, we must recognize words and decipher unfamiliar vocabulary. Few would dispute the correlation between vocabulary and comprehension. Indeed, Dale Walker’s follow-up to Hart and Risley’s study of 29 of the original 42 children found that children’s rate of vocabulary growth and vocabulary use at age 3 was strongly associated with their grade 3 standardized test scores in receptive vocabulary, listening, speaking, semantics, syntax, and reading comprehension. In short, those with a smaller vocabulary at age 3 were still struggling with reading five years later, in grade 3.
The problem is not merely a word gap. It’s also an explanation gap.
Exposure to fewer words means that one hears fewer examples of complex thinking: fewer sentences, fewer questions, and fewer explanations of ideas or arguments. Hart and Risley noted that a family’s language style affected the amount of language spoken because “explaining alternatives takes many more words than straightforward directives.” They found that parents who explained more also asked more questions and encouraged their children to ask more questions that the parents then had to answer.
In other words, children exposed to more words are also exposed to more examples of logical thinking. The reverse is also true. Children who communicate with others who speak less have fewer opportunities to 1) build fluency, 2) express and react to ideas, and 3) ask questions and figure things out. In short, they have fewer opportunities to practice comprehension and logical thinking.
What are the implications for closing the literacy gap and ultimately, the Achievement Gap?
For parents: it means being aware of how important parent-child verbal interactions are and paying more attention to how much you speak with your child. It means being more patient: taking the time to answer the question “Why?” no matter how many times it’s raised, listening with care and respect to beginning thinkers, and giving children ample time to articulate their often inchoate ideas. Providing children with more opportunities for self-expression may also require some lifestyle changes, such as reinforcing the value of active family discussion over passive TV viewing. Family meal time could help children become stronger readers and writers as a result of the discussions that transpire.
For teachers: it means that we can’t simply stuff students with vocabulary lists to boost comprehension. They need more than synonyms and definitions; they need extensive practice in inferring and explaining. Closing the literacy gap isn’t just the job of language arts teachers. Although the word gaps are real and cannot be bridged overnight, there are three simple things that all teachers can do immediately which, over time, will improve student fluency and comprehension: 1) Ask “Why?” frequently to elicit inferences and explanations. 2) Use “Think-Pair-Share” to maximize student engagement and give students more experience in explaining ideas—asking them to report what their partners said, so they can practice listening carefully (instead of merely waiting for the other person to stop talking so they can talk). 3) Require complete-sentence responses to ensure that students express complete thoughts and their peers hear these complete models of thinking. Doug Lemov refers to complete sentences as “the battering ram that knocks down the door to college,” and I wholeheartedly agree. More complete explanations—from parents, teachers, and students—could begin to close the Explanation Gap, and ultimately, the Achievement Gap.
Sarah Tantillo, Ed.D.
505 13th Ave.
Belmar, NJ 07719
sarahtantillo@literacycookbook.com
http://www.literacycookbook.com
312-933-8593 (cell)
Sarah Tantillo, Ed.D., consults in NJ and nationally with schools seeking to close the Achievement Gap. She is the creator of The Literacy Cookbook, a Website that provides resources for literacy instruction across the curriculum. She also recently launched a blog called ONLY GOOD BOOKS.
Check out this recent post about Word Generation, a program that focuses on the teaching of academic vocabulary words to improve students’ reading ability.
http://blogs.edweek.org/edweek/learning-the-language/2011/08/create_brief.html
Michael,
You won’t agree with much of this, but you inspired a lot of it.
http://www.huffingtonpost.com/john-thompson/it-iss-time-for-charter-a_b_972549.html
Here’s an article from the Atlantic that describes some ideas for teaching writing that seemed to work at New Dorp HS in NYC. It synthesizes some of the ideas in this thread.
http://www.theatlantic.com/magazine/archive/2012/10/the-writing-revolution/309090/
Hi Jon,
Yep, an exceedingly handsome devil blogged about those Atlantic essays right here.
http://www.startinganedschool.org/2012/10/08/send-this-one-to-your-english-teacher-friends/