Gaps and Redundancies

There is some irony to be found in the title of Tamar Levin's excellent article in Friday's edition of The New York Times, "Report Urges Changes in Teaching Math." To do anything other than what the report recommends would hardly qualify as teaching math. Here's the crux of the matter:

Closely tracking an influential 2006 report by the National Council of Teachers of Mathematics, the panel recommended that math curriculum should include fewer topics, spending enough time to make sure each is learned in enough depth that it need not be revisited in later grades. That is the approach used in most top-performing nations, and since the 2006 report, many states have been revising their standards to cover fewer topics in greater depth.

It was the frequent revisiting of earlier topics in later grades, with little increase in the sophistication of the approach, that drove me crazy in primary and secondary school. And it wasn't just math--it was virtually every subject. And despite this revisiting in later grades, students' achievements lag those in other countries. So much redundancy in instruction, and yet so many gaps in knowledge. That's strong evidence of the possibility of making gains in outcomes without additional resources.

There is more of interest in the article, particularly in this passage:

After hearing testimony and comments from hundreds of organizations and individuals, and sifting through a broad array of 16,000 research publications, the panelists shaped their report around recent research on how children learn.

For example, the report found it is important for students to master their basic math facts well enough that their recall becomes automatic, stored in their long-term memory, leaving room in their working memory to take in new math processes.

“For all content areas, practice allows students to achieve automaticity of basic skills — the fast, accurate and effortless processing of content information — which frees up working memory for more complex aspects of problem solving,” the report said.

Dr. Faulkner, a former president of the University of Texas at Austin, said the panel “buys the notion from cognitive science that kids have to know the facts.”

We needed cognitive science to figure that out? There was some competing notion, masquerading as an educational philosophy, that suggested that kids did not have to know the facts? The recommended approach all sounds very familiar, if not widely utilized.

Read the whole thing.

Don't Blame this on Math

In yesterday's New York Times, we are told "Math Suggests College Frenzy Will Soon Ease." Actually, I don't get the math in a couple of places. Let's start here:

Projections show that by next year or the year after, the annual number of high school graduates in the United States will peak at about 2.9 million after a 15-year climb. The number is then expected to decline until about 2015. Most universities expect this to translate into fewer applications and less selectivity, with most students probably finding it easier to get into college.

The article cites projections from the Western Interstate Commission for Higher Education. How can there only be 2.9 million high school graduates per year?

We know from the American Community Survey that in 2006, there were 17.5 million students enrolled in high school and that enrollment rates for those under age 17 are 95% or higher. We also know that only 7% of teens 16-19 are classified as high school dropouts. So we are looking at a graduation number that's in the neighborhood of 17.5*(1/4)*(0.93) = 4.1 million.

So I don't trust the WICHE projections, but it is worth considering the simple population movements. Here is a graph of the number of 18-year olds by year, based on Census projections:

So there is a dip coming up in the population of 18-year olds that will turn back the clock by about 10 years.

Is that a lot or a little? As one example, for the Class of 2010 at Dartmouth, there were 13,938 applicants, of whom 2,186 or 15.7% were admitted. If this were the peak, and we applied the changes in the projections (a drop to 90.7% of the peak), that would boost the admit rate to 15.7/0.907 = 16.9% before it began to fall again. I don't think we'll notice any easing in the frenzy here in Hanover.

Good Jobs at Good Wages

I know, the employment report has no good news in it, but this front page story in The New York Times is sure to get some attention. The concept:

Would six-figure salaries attract better teachers?

A New York City charter school set to open in 2009 in Washington Heights will test one of the most fundamental questions in education: Whether significantly higher pay for teachers is the key to improving schools.

The school, which will run from fifth to eighth grades, is promising to pay teachers $125,000, plus a potential bonus based on schoolwide performance. That is nearly twice as much as the average New York City public school teacher earns, roughly two and a half times the national average teacher salary and higher than the base salary of all but the most senior teachers in the most generous districts nationwide.

The school’s creator and first principal, Zeke M. Vanderhoek, contends that high salaries will lure the best teachers. He says he wants to put into practice the conclusion reached by a growing body of research: that teacher quality — not star principals, laptop computers or abundant electives — is the crucial ingredient for success.

“I would much rather put a phenomenal, great teacher in a field with 30 kids and nothing else than take the mediocre teacher and give them half the number of students and give them all the technology in the world,” said Mr. Vanderhoek, 31, a Yale graduate and former middle school teacher who built a test preparation company that pays its tutors far more than the competition.

I would much rather see that, too. At this school, teachers will be paid so well that they'll make more than the principal, an inversion which generated this:

Ernest A. Logan, president of the city principals’ union, called the notion of paying the principal less than the teachers “the craziest thing I’ve ever heard.”

“It’s nice to have a first violinist, a first tuba, but you’ve got to have someone who brings them all together,” Mr. Logan said. “If you cheapen the role of the school leader, you’re going to have anarchy and chaos.”

Randi Weingarten, president of the United Federation of Teachers, called the hefty salaries “a good experiment.” But she said that when teachers were not unionized, and most charter school teachers are not, their performance can be hampered by a lack of power in dealing with the principal. “What happens the first time a teacher says something like, ‘I don’t agree with you?’ ”

Presumably, the principal listens to what the teacher has to say and then makes a decision, which may or may not accommodate the teacher's disagreement. Millions of businesses, and even some educational institutions, operate on this principle. Those that operate in competitive markets don't prosper by ignoring good advice or treating talented employees as if they are inconsequential. And the teacher is not an indentured servant here--"nothing" prevents a teacher dissatisfied with a principal from starting a rival school with better policies.

The Age of Friedman is not dead yet.

The Play's the Thing

Why am I not surprised by this?

Harry Potter, James Patterson and Oprah Winfrey’s book club aside, Americans — particularly young Americans — appear to be reading less for fun, and as that happens, their reading test scores are declining. At the same time, performance in other academic disciplines like math and science is dipping for students whose access to books is limited, and employers are rating workers deficient in basic writing skills.

That is the message of a new report being released today by the National Endowment for the Arts, based on an analysis of data from about two dozen studies from the federal Education and Labor Departments and the Census Bureau as well as other academic, foundation and business surveys. After its 2004 report, “Reading at Risk,” which found that fewer than half of Americans over 18 read novels, short stories, plays or poetry, the endowment sought to collect more comprehensive data to build a picture of the role of all reading, including nonfiction.

Despite the problem of establishing the direction of causation, I am inclined to believe that it is the reduction in reading for pleasure that has caused the deterioration in reading and writing competency. It is so much easier to teach young people to do something when they get to take some ownership of and responsibility for what they are learning. Within some loose constraints regarding length and degree of difficulty, students should simply be encouraged and expected to read, with adults leading by example. As I've blogged before, force-feeding students a steady diet of stuff that doesn't interest them is a losing strategy. And, sadly, there can be a vicious cycle here: loss of interest leads to more regimentation; more regimentation further erodes interest; and on it goes.

I came across the article linked above shortly after reading this story in the Sunday paper, from which the following is an excerpt:

As Richard [Louv] notes in "Last Child in the Woods," the obesity epidemic coincides with a record-high increase in organized sports for kids. How does that correlate with the need for more outdoor play?

[Martha] Erickson: Obesity relates not only to activity level but also to the type and quantity of food we eat. That said, in organized sports, kids often have little actual playtime. But watch a group of children in a wooded area, and you'll see them running, climbing over things, then dashing over to whatever captures their attention next.

[Tedd] Mitchell: Last summer, my sons built a fort out of storage pallets and hay at our ranch. That project took them all weekend. They were like beavers, constantly moving back and forth between our barn and the woods. Sports are more about following directions to the letter. They're great for discipline -- and can have mental and physical benefits -- but they don't leave room for the imagination. Kids get bored so easily because they don't have the amount of time we did, when we were young, to just play.

Again, there could be reverse causality, but I am inclined to think that the organized sports, when they come at the expense of disorganized play, are the critical factor here. If there is no imagination involved, we don't get the full body and mind involved, and we don't get the long-term benefits.

Narrowing, Widening, and Polarizing

This new NBER working paper by Claudia Goldin and Larry Katz just made it to the top of the must-read pile. The title and abstract (with my emphasis added):

Long-Run Changes in the U.S. Wage Structure: Narrowing, Widening, Polarizing

The U.S. wage structure evolved across the last century: narrowing from 1910 to 1950, fairly stable in the 1950s and 1960s, widening rapidly during the 1980s, and “polarizing” since the late 1980s. We document the spectacular rise of U.S. wage inequality after 1980 and place recent changes into a century-long historical perspective to understand the sources of change. The majority of the increase in wage inequality since 1980 can be accounted for by rising educational wage differentials, just as a substantial part of the decrease in wage inequality in the earlier era can be accounted for by decreasing educational wage differentials.

Although skill-biased technological change has generated rapid growth in the relative demand for more-educated workers for at least the past century, increases in the supply of skills, from rising educational attainment of the U.S. work force, more than kept pace for most of the twentieth century. Since 1980, however, a sharp decline in skill supply growth driven by a slowdown in the rise of educational attainment of successive U.S. born cohorts has been a major factor in the surge in educational wage differentials. Polarization set in during the late 1980s with employment shifts into high- and low-wage jobs at the expense of the middle leading to rapidly rising upper tail wage inequality but modestly falling lower tail wage inequality.

The sentences that I have highlighted seem directly relevant to this earlier discussion in August 2006 about whether Paul Krugman was right to accuse Treasury Secretary Paulson of "falsely implying that rising inequality is mainly a story about rising wages for the highly educated." (See follow up posts here and here.)

I'll look forward to reading the paper and revisiting the broader issue.

Public Education Reform in the Presence of Monopolies

Via Ezra Klein and Mark Thoma, I am directed to a very good post by Kevin Carey at The Quick and the Ed on the relevance of teacher's unions to fixing the problems in public schools. I'll first take issue with a theme that emerges in the commentary, expressed by Mark as:

Public schools in higher ranked socio-economic areas do very well, even with unions present, so I don't think unions are the major issue.

The statement is worded so loosely that I can't really falsify it. However, the issue is not whether a union is present but whether the union's presence is a binding constraint on improvements to the educational system. In higher socio-economic areas, there are far fewer underlying challenges to the educational system and thus fewer opportunities for the union's pursuit of its own interests to interfere with addressing those challenges. The appropriate counterfactual to consider is whether the public schools--whether in higher or lower ranked socio-economic areas--would do even better in the absence of unions. The answer can certainly be "yes" if the unions were using their monopoly power to constrain the behavior of other stakeholders in the system.

But the monopoly that's relevant is not primarily the teacher's union, it is the monopoly of the school board over the educational choices of the families in the area (which itself may facilitate the unionization of the labor force). Of the several elements that characterize the public schools in my town:

I do not object to the generally progressive manner in which educational funds are raised within the district. We have a local property tax. In this community, the value of the house is a pretty close analogue of permanent income. (I don't necessarily advocate property tax funding more generally given the disparities across districts, but that's a different matter.)

I do not object to the use of some of those monies to run our highly regarded public schools that my children could attend without additional payments from K-12.

However, I strongly object to the constraint that all of these monies go into just these three schools (covering K-5, 6-8, 9-12). I have no choice of provider if my views of the best educational program for my children are at odds with those of the school board, acting on behalf (hopefully) of the other members of my community. I don't begrudge them their views, but I simply may not share them. I don't see why I should have to forfeit all of the tax monies that would be spent on my children's behalf to put them in private schools.

The money that is allocated to my children's education--not the tax money I pay--should follow the children rather than being constrained to be spent only at the government-run schools. That's the key monopoly problem, whether in high-ranked socio-economic areas like mine where additional expenditures are a desirable luxury good or in more disadvantaged areas where the consigning of low-income students to poorly performing schools is catastrophic. If the money followed the children, then multiple providers would compete, and members of the community could be better served by that diversity.

I may post more on implementation of such a system at a later date.

The Knowledge Deficit

I read with some dismay the article, "Failing Schools See a Solution in Longer Day," in today's New York Times. The opening paragraph:

States and school districts nationwide are moving to lengthen the day at struggling schools, spurred by grim test results suggesting that more than 10,000 schools are likely to be declared failing under federal law next year.

It was some consolation that the various states are paying some attention to areas in greatest need and evaluation of the initial efforts. It was also some relief that one of the reasons for lengthening the day was to restore some balance to the curriculum:

Pressed by the demands of the law [No Child Left Behind], school officials who support longer days say that much of the regular day must concentrate on test preparation. With extra hours, they say, they can devote more time to test readiness, if needed, and teach subjects that have increasingly been dropped from the curriculum, like history, art, drama.

I think that dropping subjects like history, art, and drama is the way to worsen, not improve, reading skills. I was very persuaded by the ideas set forth by E.D. Hirsch in The Knowledge Deficit. In the very earliest grades, reading skills consist primarily of decoding words. Our schools do a decent job of that. In later grades, though, reading skills consist primarily of comprehension--understanding the meaning of what is read--on a wide range of topics. Our schools don't do a particularly good job of that. The review of the book in Publishers Weekly summarizes Hirsch's thesis very well:

Education theorist Hirsch decries a dominant "Romantic" pedagogy that disparages factual knowledge and emphasizes reading comprehension "strategies"—summarizing, identifying themes, drawing inferences—that children can deploy on any text. Such formal skills, he argues, are easily acquired; what kids really need is a broad background knowledge of history, science and culture to help them assimilate new vocabulary and understand more advanced readings. "Process-oriented" methods that apply reading comprehension drills to "vapid" texts waste time and slow kids' progress, Hirsch contends, and should be replaced with a more traditional, "knowledge-oriented" academic approach with a rich factual content.

In one part of the book, Hirsch describes the reading comprehension problem as follows. Suppose that you are confronted with a new paragraph in which you know the meaning of 90 percent of the words. You can reasonably be expected to guess the meaning of the other 10 percent from the context, and then it is possible for you to evaluate what's being presented in the whole paragraph. Suppose now that you are confronted with a new paragraph in which you know the meaning of only 70 percent of the words. It is much less likely that you will be able to guess the meaning of a full 30 percent of the words in the paragraph well enough to understand the ideas being presented. So, according to this theory, you make kids better readers if you expand their vocabularies, so that they are more likely to be in the 90/10 position than the 70/30 position (or worse).

Doing process-oriented reading drills on third-rate fiction is a less effective tool for teaching reading than listening to a good piece of non-fiction. Where do kids get that good non-fiction? History class. Art class. Science class. Even music class and drama class. Schools are not lacking for time--they are lacking for content.

Writing as Communication

Katie at A Constrained Vision is one of the most thoughtful bloggers about education. In this post, she discusses the perception of poor writing skills by college students. One element of the problem is that students aren't widely read, and so they don't become particularly good writers.

There is an element of truth in that, but I think the largest part of the problem is that students in college are writing with the wrong emphasis. There is no denying that many of the college students that I teach are extremely bright. As such, they have been encouraged from a very early age to "express" themselves. Writing for them is a very self-oriented process, as if it is a reply to the admonition, "Show us how smart you are."

This is acceptable for a student in grade school, but as a student matures, writing needs to become more about communication and less about expression per se. (This is true even if the purpose of writing is still for students to show us how smart they are.) Communication is oriented toward the needs of the audience, particularly the audience's need to be persuaded of something in order to change its mind. This is certainly the case every time I read a student's term paper, an article in a professional journal, or an opinion piece.

I think that if this transition were stressed earlier in a student's education, we would see better communicators in college. What to do about the poor communication skills of college students is a bit of a problem. No college administration wants to have to devote large amounts of resources to teaching a skill (as opposed to content) that should have been developed before the student arrived. In our current system, it ought to be taken care of with the 1-3 courses on writing in the first-year curriculum.

The Right Way to Do Unpaid Internships

I'm going to guess if college students shunned unpaid summer internships, somebody who wrote this book would take them to task for imitating the Baby Boomers' alleged self-centeredness. I cannot but shake my head in disbelief at (and naturally blog about) yesterday's op-ed about unpaid internships by Anya Kamenetz in The New York Times.

Her thesis is to question whether the encouragement of unpaid internships is a good thing for the interns and for society at large. In her own words:

Let's look at the risks to the lowly intern. First there are opportunity costs. Lost wages and living expenses are significant considerations for the two-thirds of students who need loans to get through college. Since many internships are done for credit and some even cost money for the privilege of placement overseas or on Capitol Hill, those students who must borrow to pay tuition are going further into debt for internships.

Second, though their duties range from the menial to quasi-professional, unpaid internships are not jobs, only simulations. And fake jobs are not the best preparation for real jobs.

It is true that there are opportunity costs. (Shall I ask her to identify the activity for which ther are no opportunity costs, or should I just refer her to a discussion of revealed preference?) At Dartmouth, students may apply to the Rockefeller Center for a stipend to cover living expenses when they take an unpaid internship in the public or non-profit sectors. Several of the roughly 40 internships awarded each year are supported financially by alumni or alumni classes who specifically value the opportunities gained through working in an unpaid capacity in the public or non-profit sector.

Just as importantly, when students receiving financial aid apply for a grant, the Center contributes to or covers the financial aid contribution expected from the students' summer work activities, enabling them to focus on their internships without necessarily picking up a part-time job. So Ms. Kamanetz is overstating her case, at least where institutions like Dartmouth are concerned. If her younger sister at Yale, whose internship in New Orleans motivated her op-ed, did not have this opportunity, then her sister (like many others) should have tried to come to Dartmouth rather than Yale.

No one would deny the simple fact that students who come from well off families have more opportunities than those who come from less well off families. That point is irrelevant here, as long as we make sure that the internship is not relatively more expensive for the students from less well off families.

Her second point is sheer lunacy. I supervised a few interns while at CEA. I wouldn't call their experiences "simulations" or "fake." They were assigned projects commensurate with their abilities and academic preparation. Their contributions were generally quite good, and some were downright impressive. One of my regrets after my year at CEA was that I did not go work there as an intern or research assistant 15 years earlier while I was in college. It would have made me a better economist. I think the 10 students being sponsored by the Rockefeller Center this spring (on the page linked above) all have interesting opportunities ahead of them as well. Take a look at the full list from last year, along with a few in-depth profiles, in the Center's annual report.

At the Center, we have taken our support of internships further with the advent of our Civic Skills Training program, in which the Center's staff spends 5 days in Washington with a group of students before their internships to educate them about the public and non-profit sectors and to train them in the skills they will need to succeed in their internships. The Rockefeller Center picks up the entire cost of the training.

I would never presume to disparage a student's choice to work to earn money over the summer rather than work in an unpaid public or non-profit internship. But the suggestion that unpaid internships are not contributing substantially to students' development as young adults is preposterous and flies in the face of what thoughtful colleges are doing to support those internships.

UPDATE: Tony Vallencourt comments below and posts to his blog about the other parts of the Kamenetz op-ed, dealing with societal issues of a perceived lack of access to internships. I actually thought those were the weak points of the op-ed and so left them out of my post. Will Wilkinson takes Kamenetz to task for them on his blog in "The Baffling Mind of Anya Kamenetz."

That's a Feature, Not a Bug

Yesterday's New York Times ran a front-page story with the headline, "Schools Cut Back Subjects to Push Reading and Math." Like many discussions of the impact of the No Child Left Behind Act, it seems to miss the central element that this was the inevitable consequence of the legislation. Here's an excerpt of interest:

The historian David McCullough told a Senate Committee last June that because of the law, "history is being put on the back burner or taken off the stove altogether in many or most schools, in favor of math and reading."

Some may disagree with this as an objective, but one should not be surprised at the result. The logic runs as follows:

• Reading and math are deemed to be more fundamental skills than other subjects to which class time is devoted in public schools; and
• Some schools can be demonstrated to be inadequate in the outcomes they generate in reading and math; and
• Schools that are so demonstrated are unlikely to have additional financial capacity to expand their programs; so
• Those schools should be devoting more time to reading and math, with other subjects crowded out in whole or in part.

I think we should have been surprised if the law were not having the effect of narrowing the curriculum, but I was surprised that the law was having as pronounced an effect as it is. In general, my view is well summarized by this quote:

"When you only have so many hours per day and you're behind in some area that's being hammered on, you have to work on that," said Henry Lind, the schools superintendent. "It's like basketball. If you can't make layups, then you've got to work on layups."

I'd like to be able to say that every school district should offer a broad curriculum of liberal arts courses including history and music and languages and lab sciences, but some school districts aren't able to do all of that successfully. So given that they won't be at the ideal, where should they be? I think of reading and math as foundational. There's very little use in trying to build on a weak foundation. That doesn't mean I support this sort of federal involvement in primary and secondary education, but it does mean that I don't think the consequences of the law, as they are described in this article, are a source of concern.

The article is well written and of interest. I recommend the whole thing.

A Setback for School Vouchers in Florida

From yesterday's New York Times:

In a ruling expected to reverberate through battles over school choice in many states, the Florida Supreme Court struck down a voucher program yesterday for students attending failing schools, saying the State Constitution bars Florida from using taxpayer money to finance a private alternative to the public system.

The 5-to-2 ruling orders state officials to end, at the close of this school year, a program that Gov. Jeb Bush has considered one of his chief accomplishments.

Known as the Opportunity Scholarship Program, it uses public money to pay tuition for 730 students who have left failing public schools and enrolled in private schools.

Quoting from the opinion, the article continues:

In its ruling, the Florida court cited an article in the State Constitution that says, "Adequate provision shall be made by law for a uniform, efficient, safe, secure and high quality system of free public schools."

The Opportunity Scholarships Program "violates this language," the court said.

"It diverts public dollars into separate private systems parallel to and in competition with the free public schools that are the sole means set out in the Constitution for the state to provide for the education of Florida's children," the ruling said. "This diversion not only reduces money available to the free schools, but also funds private schools that are not 'uniform' when compared with each other or the public system."

Hard to argue with the reasoning there. The problem is in the language in the state Constitution. I am a graduate of the public schools in Palm Beach County, Florida. The notion that the system is "uniform," even within the same school district, is preposterous. Schools located in neighborhoods with higher income residents were better schools. And the disparities were not small. I do not see how the Court could uphold a challenge against the current system, even without vouchers.

I do not know the facts of this case, but I suspect that the 730 students in question went from schools where they couldn't get a good education to schools where they could. In the process of getting an education more like the typical student's, they violated this principle of uniformity. Fascinating.

Reform of the public system remains the priority. Over at a Constrained Vision, Katie Newmark lines it up just right: find some philanthropic organization to help get these kids into private schools and work to change the state constitution.