kitchen table math, the sequel: the one that got away

Friday, May 23, 2008

the one that got away

Major find.

A 1991 Atlantic Monthly article on The Other Crisis in American Education.

the 16-year decline and the 1995 "recentering"

By way of background: SAT scores declined from 1964 to 1980. Math scores rose most of the way back up to where they'd been but verbal scores did not, and in 1995 the College Board recentered the scores.

My district's scores, which are significantly higher than those for other schools in our demographic, assuming I've read the charts correctly (chart correlating income and scores here; chart for determining significance here) are:

V-540 M-568 W-540 total: 1648

Prior to 1995 those scores would have been:

V-460 M-560

1108 today; 1020 before 1995. Big difference.

decline at the top

Over the years I've seen various rebuttals of the claim that the decline was due to an expansion of the pool of test takers. See here and here.

What I had not seen was the data showing that the decline was concentrated at the top:

[N]orm-referenced tests .... were able to tell us not just about the existence of the decline but something about its magnitude--half a standard deviation on the SAT--and something about its source--the decline on all norm-referenced tests was much greater among students at the top of the score distribution than among those at the bottom.

The decline at the top was so steep that the absolute number of students scoring over 650 on the verbal half of the SAT declined 45 percent between 1972 and 1982. That means the pool of top talent available for scholarship and research, for business and industry, and for the military has actually shrunk. We need to enlarge it again as quickly as we can by encouraging excellence in our schools, and we need tests that will let us gauge our progress at that vital task. The best-calibrated gauge for these purposes is a norm-referenced test. That is why a national census of educational quality should include not just a test of V and M, but a norm-referenced test of those essential, all-purpose abilities.
p. 49


The importance of these periodic checks on test constancy is well illustrated by data on the SAT. They show that efforts to hold the difficulty level of the test constant over the years were quite successful from 1941 to 1963; less so from 1963 to 1973, when some downward drift occurred, making it a bit easier to get higher scores after 1963 than before.[23] The SAT was also easier to read in the 1960s and the 1970s than it was in the 1940s and the 1950s; the difficulty level of reading passages on the test declined, as measured by the Dale-Chall formula, from a corrected grade level of 13 to 15 to only 11 to 12.24

All in all, SAT scores in recent decades probably underestimate the great American score decline by about 8 to 12 points, roughly one-tenth of a standard deviation.

A National Census of Educational Quality—What Is Needed by Barbara Lerner NASSP Bulletin / March 1987 p. 56

the one that got away

While the rest of the country was falling apart, SAT-wise, some schools sailed through those years unscathed. Daniel Singal's 1991 article summarizes a study of the ones that got away:

What has caused this great decline in our schools? The multitude of reports that now fill the library shelves tend to designate “social factors” as the prime culprit. Television usually heads the list, followed by rock music, the influence of adolescent peer groups, the increase in both single-parent families and households where both parents work, and even faulty nutrition.
Those who attribute the loss of academic performance to social factors don't take account of the small number of high schools around the country that have managed to escape the downturn. Some are posh private academies; a few are located in blue-collar neighborhoods. What they have in common is a pattern of stable or even rising test scores at a time when virtually all the schools around them experienced sharp declines. There is no indication that the children attending these exceptional schools watched significantly fewer hours of television, listened to less heavy-metal music, were less likely to have working mothers, or ate fewer Big Macs than other children. Rather, they appear to have had the good fortune to go to schools that were intent on steering a steady course in a time of rapid change, thus countering the potentially negative impact of various social factors.

It would seem obvious good sense to look closely at this select group of schools to determine what they have been doing right, but as far as I can determine this has been done in only two national studies. The better one was issued by the National Association of Secondary School Principals (NASSP) in 1978, under the somewhat pedestrian title Guidelines for Improving SAT Scores. Now out of print and hard to find, it contains one of the most perceptive diagnoses available of the underlying malady in our schools.


The report identifies one main characteristic that successful schools have shared—the belief that academics must invariably receive priority over every other activity. “The difference comes,” we are told, “from a singular commitment to academic achievement for the college-bound student.” These schools did not ignore the other dimensions of student life. By and large, the NASSP found, schools that maintained excellence in academics sought to be excellent in everything else they did, they “proved to be apt jugglers, keeping all important balls in the air.” But academic work came first.

Two other factors help account for the prowess of these schools in holding the line against deterioration. The first is a dogged reliance on a traditional liberal-arts curriculum. In an era of mini-courses and electives, the tiny group of high schools that kept test scores and achievement high continued to require year-long courses in literature and to encourage enrollment in rigorous math classes, including geometry and advanced algebra. Though the learning environment in those schools was often “broad and imaginative,” in the words of the NASSP, fundamentals such as English grammar and vocabulary received heavy stress. The other key factor in preserving academic quality was the practice of grouping students by ability in as many subjects as possible. The contrast was stark: schools that had “severely declining test scores” had “moved determinedly toward heterogeneous grouping” (that is, mixed students of differing ability levels in the same classes), while the “schools who have maintained good SAT scores” tended “to prefer homogeneous grouping.”

If attaining educational excellence is this simple, why have these high-quality schools become so rare? The answer lies in the cultural ferment of the 1960s.

So there you have it.

The hardy little band of schools where student achievement did not decline shared three characteristics:
  • academics first and foremost, with a commitment to excellence in all endeavors
  • “dogged reliance on a traditional liberal-arts curriculum”
  • homogeneous grouping; schools with heterogeneous grouping had “severely declining scores”

My own district is doggedly moving in exactly the opposite direction. Character education and the whole child over academics, the fragmenting and blurring of the curriculum via "Exploratory" courses and interdisciplinary teaming thanks to the middle school model, and an "identified need" for "balanced classes." Balanced classes being the new term of art for heterogeneous grouping in these parts.

Oh, and more more technology.

Most school districts are headed in this direction, and the kids at the top will be hurt.

I think kids at all levels will be hurt, but if I had to guess I'd say the kids at the top and at the bottom will be worst off. More on them anon.

Nobody cares. The kids at the top are assumed to be bulletproof; as our middle school principal told a well-attended school board meeting, "I'm not concerned about the kids at the top."

The kids at the bottom can flounder and sink until they qualify for special ed. Then they'll get some "pull-out."

stagnation at the top - Fordham report
Tracking: Can It Benefit Low Achieving Children?
Linda Valli on tracking in 5 Catholic high schools, 1
Linda Valli on tracking in 5 Catholic high schools, 2
"school commitment" in Valli's study of tracking in Catholic high schools

7th grade depression starts in 1st grade

ability grouping in Singapore
characteristics of schools where SAT scores did not decline
The Other Crisis in American Education by Daniel Singal
Hiding in Plain Sight: grouping & the achievement gap
tracking: first random-assignment study

SAT equivalence tables
SAT I Individual Score Equivalents
SAT I Mean Score Equivalents

chickens have come home to roost
the deathless meme of the high performing school
Allison on the naturals


Anonymous said...

The practice of putting everyone in the same room, regardless of ability, to achieve some social goal is probably more destructive than the math wars.

It's one of those things that sounds good in a meeting and fails miserably in the real world. When you get a real population spread out over 4-5 years of ability
this is what happens.

Linda Seebach said...

Charles Murray and Richard Herrnstein wrote about the decline at the top:
Murray, C. & Herrnstein, R.(1992). What's really behind the SAT-score decline? The Public Interest, 106, 32-56.

I can't find a copy of the article online, and the photocopy I'd saved since 1992 disappeared in last year's cross-country move.

Catherine Johnson said...

Linda - thank you!!!

I'm looking for anything on this subject.

I think they've got their archives posted still.

Catherine Johnson said...

I found it fascinating that homogeneous grouping popped up in that study.

I believe it -- but I'm still amazed that the effect of grouping like with like is so powerful.

I'll have to find Loveless' great passage about tracking in a Catholic school. The whole goal was to get the kids in the bottom track up out of it -- and they did.

But they didn't do it by putting those kids in over their heads and declaring the bottom track gone.

They did it by accelerating their work and learning.

Anonymous said...

Is there a list somewhere of those schools that have *not* experienced the "drop at the top"?

I'm curious, wondering if the school I attended might be one of them (I told Catherine where, but don't wish to name it. Name would only be familiar to people who knew about schools in that area anyway.) We had several kids in my class with 800's on the SAT-V (and M too). And someone with a 799, which made me wonder what was the difference between a 799 and an 800? Maybe 1 item? This was pre-recentering.

The school was very traditional in academic focus and accelerated curricula.

On the other hand, at a recent reunion (actually an anti-reunion, organized by classmates, not the school, and well attended) many had rather negative memories of their academic preparation, although all conceded that they were unbelievably well prepared for college and never had to work so hard again even in medical school/PhD/whatever. Many thought they were low average students and their SAT scores were a surprise. They were quite high. Many of these people went to prestige colleges (Oberlin, Vassar, Reed, Cornell, Princeton, McGill, Oxford).

Just worth remembering that grades are not the whole story. Maybe we had grade deflation in my day also. Obviously it did not hurt the B and C students I went to school with who scored well on SATs and attended their choice of college and went on from glory to glory.

I was amazed that the top achievers almost all came from the middle of the pack -- good students but not on the honor roll or anything. They ended up being the doctors, lawyers, veterinarians, medical researchers, college professors, media moguls, environmental activists and whatnot. Some back-to-the-land types too.

Every single person said they never, ever had to work so hard at academics again.

When my mother moved out of the family home about 10 years ago I found a whole stash of my school work she had saved from the distant past (my siblings found the same). Looking over the corpus from the vantage point of recent teaching in middle school, I was astounded by the assignments given. Analyzing imagery of light and dark in D.H. Lawrence's short stories (8th grade), comparing aspects of Beowulf and Macbeth (something about characterization and use of techniques like foreshadowing and dramatic irony). Analyzing plot structure in the historical novels of Rosemary Sutliffe (6th grade), finding examples of anachronism as a humor technique in contemporary popular works (I used Asterix, en francais) and explaining the anachronism.

We were also assigned to research and write about historical topics, using original documents. No internet then, so that meant going to a major library and using microfiche (or very old books) I remember researching settlements in 17th-18th century Louisiana and elsewhere and plowing through very musty leatherbound volumes of the Jesuit Relations. Whew! I didn't get great grades but I sure learned a lot of history, not to mention research skills.

I didn't find any masterpieces of literary criticism in my mom's filing drawer, but I was bowled over at the level of the assignments. I have worked with G-T students who could not begin to do that kind of writing. They lack experience in any kind of formal analytic writing after a surfeit of "reading response" journaling.

So maybe we are selling the young way too short.

Anonymous said...


I think we do sell students short, particularly in middle school. In my public California middle school, in 8th grade, we had a sub come in most of the year. She hated our textbook and loved drama, so we read Oedipus Rex, Romeo and Juliet, and a couple of modern dramas I remember less clearly. The other teachers were shocked at what we were reading (the 12th grade Honors teacher strongly disapproved), but we absolutely loved it.

This was an honors class, and we certainly were responding to her enthusiasm. But I also think we stepped up to what was expected of us.

SteveH said...

When I was in Junior High, our school had two groups of "accelerated students". Although there were real issues of who got in and who were left out, it consisted of a good percentage of students. ALL of our classes were accelerated.

In my son's middle schools, they seem to not like smart kids. That's not really true, but they do want to hide it. After years of full-inclusion through 8th grade, they are finally relenting (in 7th and 8th grades) and offering advanced classes for some kids. This is only for math and a foreign language.

They also have a problem with deciding who gets in and who doesn't, but few get in. In my old Junior High, it was open and very clear (visible tracking). In my son's school, it's hidden and not available unless a parent figures it out and pushes.

On top of all that, the expectations are lower for the advanced students. After K-6 of low expectations and bad enrichment, these kids are shocked by the extra work. I see it as across-the-board low expectations because they want to treat all kids as equals.

Me said...

I was just thinking back to when I taught regular and advanced placement high school chemistry 40 odd years ago.

In the first place, I knew a lot more than the students because I had a master's degree, because chemistry was a new subject for most of them, and because it was before the Information Age.

In the second place, I was as academically talented as almost all of the students and was enough smarter than most of them that it's not something that I even thought about at the time.

I'm not trying to brag -- there's lots of things I'm not good at. I'm just trying to imagine what it's like for teachers who are confronted with a class where the majority of students are smarter than they are. I don't think I'd do a good job in those circumstances.

Catherine Johnson said...

In my son's middle schools, they seem to not like smart kids.

The middle school philosophy is actively hostile to bright kids.

As far as I can tell, Carol Tomlinson invented "differentiated instruction" to create a way to give gifted kids a slightly accelerated curriculum while grouping them heterogeneously.

A few months ago the head of the science department for 6-12, a middle school science teacher, told Ed and me angrily, "If it were up to me I wouldn't teach any accelerated courses to any middle school students at all. But this community demands it.

Her face was a study. Equal part contempt and fury.

Our middle school offers accelerated math and Earth science in the 8th grade. That's it.

Both courses are "taught to the top" -- the naturals can do them & the other kids get tutors and grades of B or C to put on their high school transcripts.

That's the price kids & their parents pay for belonging to the part of the community that "demands" accelerated courses.

Kids like C., whose natural talents lie in the language-based disciplines, have no opportunities for any form of acceleration in those areas at all. Zero.

None will be forthcoming, either.

We're going to the middle school model, so all bets are off. The school will be meeting the needs of young adolescents through Exploratories, Advisories, Interdisciplinary Teaming, and lots and lots of teacher release time.

Catherine Johnson said...

Historically, tension has existed between gifted education and middle school education (Tomlinson, 1992), leaving some advocates of each educational practice suspicious of the other, and leaving middle school students who are advanced in one or more dimensions of learning in a sort of educational no-man's-land.

Gifted Learners and the Middle School: Problem or Promise?

VickyS said...

In addressing the supposed conflict between equity and excellence, Tomlinson asserts that both gifted educators and middle school educators "continue to struggle with mechanisms for balancing the belief that all people should have equal opportunity with the belief that each individual should be assisted in developing his or her maximum capacity."

Seems to me "equity vs. excellence" is a false dichotomy. Equality of opportunity promotes both equity and excellence. Given equal opportunity some children, due to natural ability or hard work or a combination of both*, will move faster, or reach higher levels, than others (thereby achieving excellence). The important thing (for equity) is to provide each child with continuous opportunity to advance.

What the system currently lacks is support for each child at his or her particular point on the learning trajectory. This works against both equity and excellence.

A conflict between excellence and equity arises, I believe, only when we define "equity" in terms of equality of outcome (not opportunity). Equality of outcome seems to be the hidden goal of most middle schools. Means of ranking students are abolished or downplayed; group work exerts an averaging influence of the performance of the group members; and authentic assessments are individualized and subjective. When equity is viewed as equality of outcome, any call for academic excellence definitely sets up a conflict. The recognition that excellence can exist implies that non-excellence also exists, i.e., that outcomes will not be equal.

*Some might say an argument based on equal opportunity assumes kids start at the same point, which they certainly don't. But I think we can provide equal opportunity by asking the schools to meet each child at whatever point they are at on their own trajectory, then to continue to advance that student--every student--along their trajectory as far and as fast as that child can or wants to go.

SteveH said...

"... Carol Tomlinson invented 'differentiated instruction' to create a way to give gifted kids a slightly accelerated curriculum while grouping them heterogeneously."

Her philosophy is the guiding light for our schools. It doesn't work. It's not even slightly accelerated. At best, it allows for something like Everyday Math, which doesn't stop you from learning the material the first time you see it. But then again, you have to get to the material. Our schools don't allow kids to go ahead in the workbooks. So the question is how do you do acceleration in mixed-ability, child-centered groups? You don't. At best, it's differentiated homework and differentiated rubric. For EM, the teachers don't have to do anything. Everyday Math differentiates on mastery. It's not acceleration for some, it's self-deceleration for any.

We have absolutely no acceleration until you get to 7th and 8th grades, and that is done homogeneously. This is only for math and a foreign language. This has to be done not because parents demand it, but because these advanced courses are prerequisites for high school courses.

SteveH said...

"Equality of outcome seems to be the hidden goal of most middle schools."

Our schools seem to think they can have it both ways; treat all kids as equals and then throw in a couple of accelerated courses in 7th and 8th grades. Enough kids do well that they don't have to worry about the details.

Tracy W said...

Gifted Learners and the Middle School: Problem or Promise?

This article makes for interesting reading. What impresses me is how flimsy and how disconnected from details the recommendations are. For example, the author writes:
it is not surprising that both groups continue to struggle with mechanisms for balancing the belief that all people should have equal opportunity with the belief that each individual should be assisted in developing his or her maximum capacity. The tension is heightened in the face of scarce resources for education.

Okay, this is indeed a serious problem. But what's the author's solution?
Understand the advantages of emphasizing both equity and excellence. And a series of more of the same. The solution to the problems of scarce resources and balancing values is simply to do both. There, easy! Why didn't anyone think of it before? While we're at it, let's solve the world's transport problems by "Using a form of transport that doesn't harm the environment, and doesn't cause any congestion problems". Okay, I have no details to offer about how to develop this magic form of transport, but hey, it sounds good.
And, I love the emphasise on emphasizing both: "emphasizing both equity and excellence". The question that springs to mind is, what is not emphasised? Let us note the other things that are to be emphasised:
- appropriately-differentiated instruction
- use of gifted/talented resource specialists
- student differences and student similiarities
- problem-based cooperative strategies (oh, we do have something that is not to be emphasised - skill-focused cooperative strategies)
- special emphasis (not merely emphasis, but special emphasis) on females and culturally-diverse learners (okay, which learners are not culturally diverse?).

Now, that's by my count 9 things that are to be emphasised. That's at the very upper end of 7+/-2. And remember, this is only about differentiated instruction. Where teachers are meant to fit in details like the curriculum, or classroom discipline, or fire drills, or special-ed is not mentioned.

Furthermore, it's like Steve says, no details. The conversation is all about generalities, never details.

Anonymous said...

The most recent comments are all probing a common theme, that grouping is mired in a 19th century instructional model. In order to group in this model you have to have: classroom, available teacher (with advanced content knowledge), different curriculum, placement mechanism (that identifies kids to be advanced), and a reporting system that doesn't disadvantage advanced kids.

Let me provoke you.

Kids don't come in 'advanced', 'basic', and 'economy' groups. They come in a continuum.

Secondly there should not be a notion of 'advanced' curriculum. Curriculum is also a continuum, especially in math.

So what is required given these two continuums? The instructional model you need is one that says every kid gets the stuff they need, today, i.e. it's in their ZPD, regardless of grade level, classroom, teacher availability, etc. When you assess in this model you don't report a grade, you report progress along the continuum.

Today's instructional model is inept and incapable of addressing the continuous nature of content and student. Think about what a good homeschooler does. They don't have an 'advanced' class. If their child is blowing through grade 4 stuff they just go faster. Parents are acutely aware of their child's ZPD, naturally.

We need to uproot the 19th century model and apply technology in ways that empower kids and teachers to seek out the sweet spots, every day.

Anonymous said...

"Think about what a good homeschooler does. They don't have an 'advanced' class. If their child is blowing through grade 4 stuff they just go faster. Parents are acutely aware of their child's ZPD, naturally."

This is one advantage of having, say, three kids to teach. Consider an average California classroom with 25 kids and a school day that is 300 minutes long. Each kid gets a bit more than 10 minutes of the teacher's time. This is why roughly-binned ability grouping makes sense for a classroom environment. If the group of 10-25 kids is all mostly working on the same stuff, you might get 100-200 minutes of teacher time per student per day that is actually relevant to each student. Not as good as 1-on-1, but much better than 10-12 minutes per day.

-Mark Roulo

Tracy W said...

We need to uproot the 19th century model and apply technology in ways that empower kids and teachers to seek out the sweet spots, every day.

And we need to build a transport system that doesn't harm the environment, and doesn't cause any congestion problems. Those transporters on Star Trek sound good. Let's use those.

Look, I think these are lovely goals and dreams to have. But just because every kid comes in a continuum doens't mean that every kid can be taught according to a continuum. I don't know if people can be taught that way or not - in the engineering field there are always surprises about what can and can't be done. On one hand, guys figure out a way to communicate using a Signal-to-Noise ratio of less than 1, on the other hand, artificial intelligence has developed far slower than most people were expecting. It strikes me as quite possible that, despite children coming in a continuum, teaching many need to be done using a discontinuous model.

SteveH said...

Given that my son spends little time being directly taught by a teacher, I can perhaps see some advantage to having a self-learning system that allows him to progress at his own pace. Is such a system possible? Perhaps it is for my son (with my supervision), but I think it would be difficult for many kids.

I don't think there is much lost with Mark's "roughly-binned ability grouping". The problem is that most K-8 schools won't consider this at all. A technology approach that allows kids to progress at their own speed in a mixed ability classroom might appeal to schools, but Tracy is right about artificial intelligence. I haven't seen any computer education program/system that I like.

Besides, what our school does now is really a 21st century model. It's one that places social issues before academic ones. They make trade-offs that I disagree with. They think they can do both, but they can't. So I wouldn't say that it's about changing from a 19th century model. I would say that it's about deciding what is a proper education. What schools have to change is that they get to decide on basic assumptions, not parents.

I would like a good curriculum, reasonable academic grouping, and teachers who makes me not look for a technological solution.

It really seems backwards to me. I think that teachers with content knowledge using direct instruction are very important. Modern educators seem to believe that teachers are superfluous; just guides on the side.

Catherine Johnson said...

Ed has a great line about the 19th century re: knowledge & skills.

He says since the schools are teaching 21st century skills, parents have to teach the 19th century skills.

Catherine Johnson said...

I'm just trying to imagine what it's like for teachers who are confronted with a class where the majority of students are smarter than they are. I don't think I'd do a good job in those circumstances.

I had a fascinating conversation with a guy on a plane once who happened to have been head of the JPL for a time (I think he was head...)

He also Cal Tech?

(Yes, I should have written all this down. I think I did write it all down, but where? toujours le question)

In any case, he talked about having students who were much smarter than he was. He kicked them out of his class! He told them they were too smart for him and for the class & they had to move up.

In some cases, they didn't want to move; they didn't think they could handle the more advanced class. He forced them to move, anyway.

They came back later & told him he was right.

This happened to Ed when he was in high school - I've told that story many times. It happened to my neighbor. I think teachers kicking the smart kids upstairs must have been a common event back in the day.

Does it happen now?

It doesn't happen here. The focus is always on keeping kids out of Honors courses. (A mom told me the other day that one of her friends' kids loved the high school -- loved every second of his high school experience. Then she added, "He took himself out of the Honors track."

took himself out

The school has no problem -- none -- with kids taking themselves out of the Honors track. Good enough is good enough.

AP is open enrollment.

Not sure whether the school encourages kids to take AP; what I've heard is that there's huge pent-up demand for the courses because so many kids are barred from Honors.

The high school did, a year or so ago, establish a policy that Honors English sophomore year would be open enrollment, but the price of admission was that all students enrolling in Honors English would have to enroll in AP global studies, too.

I took that to be a means of outsourcing the rejection process to students and their parents. Students who could manage one Honors class but no more would be forced to self-select out of the pool, sparing the school the burden of having to explain why the student was rejected. (One of the letters sent home from the high school included a line from the principal referring to parents besieging the school with demands that their kids be allowed into Honors classes.)

Crimson Wife said...

A "decline at the top" doesn't make sense to me as admissions to elite universities have gotten WAY more competitive in recent decades. My dad had solid but not super-high grades & test scores when he got into Harvard in 1967. By the time I got accepted to Stanford in 1995, the bar had been raised significantly higher. But when I look at the kids I know these days who are getting *REJECTED*, their credentials absolutely put mine to shame.

How can there be a decline in the absolute number of high achievers at the same time as such an incredible increase in competition for admission to the top universities?