Wednesday, July 18, 2018

Legacy of Coleman study


EdWeek 2006 Article on the Coleman Report and its legacy

Race Report’s Influence Felt 40 Years Later
Legacy of Coleman study was new view of equity
By Debra Viadero
Just before the Fourth of July weekend in 1966, the U.S. Office of Education quietly released a report that would shake the beliefs upon which many educators and social reformers had staked their work.
Titled “Equality of Educational Opportunity,” the mammoth, 737-page study reached the unsettling conclusion that school might not be society’s great equalizer after all.
On the eve of the 40th anniversary of that study, now better known as the Coleman Report, researchers continue to grapple with many of the same questions about how family background contributes to disparities in children’s school performance.
The report found that black children started out school trailing behind their white counterparts and essentially never caught up—even when their schools were as well equipped as those with predominantly white enrollments.
What mattered more in determining children’s academic success, concluded the authors, was their family backgrounds.
“This was the 1960s,” the policy expert Marc S. Tucker recalled. “The idea that who one’s parents were and what happened in the home is a far greater determinant of one’s future than what schools could do was a pretty grim commentary and one that was very hard for people to accept.”
Mr. Tucker, today the president of the Washington-based National Center on Education and the Economy, was among a group of scholars convened by Harvard University later the same year to make sense of the findings.
Four decades later, scholars say that much has changed in American education and much has not. While social science has found more sophisticated ways to chart disparities in children’s schooling and achievement, it has failed to make them go away.
“The Coleman Report basically opened up that question, and nobody’s been able to answer it satisfactorily since,” said David J. Armor, a researcher who worked on the original study and subsequent reanalysis. “No one has found a way, on a large-scale basis, to overcome the influence of family,” added Mr. Armor, currently a professor of public policy at George Mason University in Fairfax, Va.
The project was historic for more than its provocative conclusions, though, says David K. Cohen, a professor of education and public policy at the University of Michigan in Ann Arbor.
“I think it really marked the beginning of a new era for both research on education and a more general understanding of schooling and how schools work,” he said.
Breaking New Ground
The study was ordered by Congress as part of the Civil Rights Act of 1964. In Section 402 of the legislation, federal lawmakers directed the U.S. commissioner of education to “conduct a survey … within two years of the enactment of this title, concerning the lack of availability of equal educational opportunities for individuals by reason of race, color, religion, or national origin.”
Lasting Impact
Following the release of "Equality of Educational Opportunity" in July 1966, Harvard University convened a yearlong seminar on that controversial federal study from a research team led by James S. Coleman. The Harvard University Faculty Seminar on the Coleman Report drew some 75 participants from along the Eastern Seaboard and helped shape a generation of education policy experts whose influence continues to be felt. Below are 10 profiles of some of those participants.

To carry out that task, Alex M. Mood, then assistant commissioner for educational statistics, chose two researchers: James S. Coleman, the Johns Hopkins University sociologist whose name has become indelibly associated with the study, and Ernest Q. Campbell, a sociology researcher from Vanderbilt University.
The report they produced was, and some say, remains, among the most extensive and best-known studies of American education. At a cost of $1.5 million in 1966 dollars, the project drew on data for 570,000 students, 60,000 teachers, and 4,000 elementary and secondary schools across the country. When completed, it weighed as much as the Manhattan telephone directory and was only slightly more readable.
What was revolutionary about the report, though, was its use of testing data to measure educational disparities, which was an innovation that went beyond the project’s congressional mandate. Rather than provide a checklist of physical resources, Mr. Coleman and Mr. Mood wanted the study to find out what children actually learned.
“Up until that time, very little attention was paid to student outcomes,” said Eric A. Hanushek, a Stanford University economist who participated in the post- report analyses at Harvard. “It was all about inputs—whether the schools had books, libraries, or computer labs. The importance of the Coleman Report was that it changed the perspective to concentrating on student performance, and that has endured.”
Mr. Coleman, an unassuming football-player-turned-academician, and his research team worked under intense pressure to complete the massive project within the two-year time frame. James McPartland, one of the young researchers whom Mr. Coleman recruited to work on the study, recalled that the sociologist even rented an apartment near Capitol Hill to cut down on commuting time from Johns Hopkins in Baltimore.
“The frenzy was all about, ‘What do we have here?’ ” said Mr. McPartland, who is now a co-director of the Center for Social Organization of Schools, based at Johns Hopkins. “And Jim was the one making sense of it all.”
Mr. Coleman, who later moved to the University of Chicago, died in 1995.
Greeted With Silence
When the report was done, it met with deafening silence. The lack of response was due in part to its release right before the July 4 weekend.
In addition, the advisory committee that had been appointed for the project refused to sign off on it, citing methodological concerns, recalled Edmund W. Gordon, a member of that committee.
“We weren’t sure that Jim had drawn his conclusions from a sample that was sufficiently representative,” said Mr. Gordon, who is now an emeritus professor of psychology at both Yale University and Teachers College, Columbia University. “And we were not comfortable with the finding that the effects of schools were so small. Only after a year or a year and a half of study in the Harvard seminar did we become comfortable with it.”
Gradually, though, news of the findings spread. Christopher S. Jencks, a journalist-turned-policy expert, writing in The New Republic in October 1966, called attention to the report as the “most important piece of education research in years.” And he noted that its “diagnosis of what makes students learn is at odds with almost everything legislators, school board members, and school administrators have believed in recent decades.”
The findings, in fact, came less than a year after President Lyndon B. Johnson had signed into law the Elementary and Secondary Education Act, with its Title I—a Great Society program aimed at providing compensatory educational services to disadvantaged students.
The news also reached Daniel Patrick Moynihan, a sociologist, former Johnson administration official and future U.S. senator, at Harvard University.
Mr. Moynihan had just written a controversial report, “The Negro Family: The Case for Action,”which argued for federal attention to problems of disorganization in black families. With other Harvard academic stars, such as Thomas F. Pettigrew, a social psychologist, Mr. Moynihan obtained funding from the Carnegie Corporation of New York to launch a yearlong seminar to dissect the Coleman Report’s findings.
“Because the results were so earthshaking, everybody wanted to reanalyze the data and make sure nothing was amiss,” said Mr. Armor.
Gordon M. Ambach, who later became New York’s state education commissioner and headed the Washington-based Council of Chief State School Officers, served as the executive secretary to the newly formed cross-disciplinary group, called the Harvard Faculty Seminar on the Coleman Report. Originally, he said, the plan was to involve 10 to 15 scholars from a variety of disciplines.
In the end, 75 scholars became regular attendees, traveling to Harvard at their own expense once every two weeks for the dinner-to-late-night sessions. Their ranks included some of the most prominent academics in the social sciences—people such as Frederick Mosteller, a widely admired statistician; the reading expert Jeanne Chall; and Theodore R. Sizer, then the dean of Harvard’s graduate school of education. Seven professors came from the law school. The sessions also drew a crop of young graduate students and junior professors who would later go on to make their own names in the field of education.
“Many people cut their teeth at that seminar,” said Ellen Condliffe Lagemann, an education historian at Harvard. “I don’t think there’s been a Coleman seminar since, or anything equivalent to it.”
Findings Wide-Ranging
The Coleman Report’s conclusion on schools’ relative ineffectiveness at overcoming the academic disparities that children bring with them was just one of many findings in the study.
It found, for instance, that the next-most important determinant of academic achievement after family characteristics was a student’s sense of control over his or her own destiny.
The report also found that, more than a decade after the U.S. Supreme Court’s 1954 decision in the Brown v. Board of Education school desegregation case, most American students still attended schools populated mainly with students from the same racial group. More surprisingly, though, the study found that school segregation was just as pervasive in the North as it was in the South.
And the achievement disparities the report documented were troublingly large. In 6th grade, the authors found, the average African-American 6th grader lagged 1.9 years behind his or her white counterpart. By 12th grade, the statistics suggested, the average gap had widened to nearly four years.
As expected, the report also showed that black children typically attended schools that were more poorly equipped than those attended by whites. They had less access to physics, chemistry, and language laboratories, for instance, and fewer books per pupil. But the differences were much smaller than expected, and particularly so for white and black schools in the same geographic regions.
“Congress really expected to see the South shortchanging black schools, and we didn’t have much evidence of that at the time,” Mr. McPartland said.
In retrospect, though, some scholars suggest that the disparities may have failed to emerge because of limitations in the survey.
“One person’s science lab may be another person’s closet,” said Marshall S. Smith, who was the research director for the Harvard seminar as a young faculty member there. “Some of that was also partly due to the fact that the South had been gearing up since Brown to provide better resources to black schools in the hope that they could convince courts not to desegregate,” said Mr. Smith, who later became Stanford University’s education dean and served as the deputy secretary and undersecretary of the U.S. Department of Education under President Clinton.
In any event, the study found that few school-related “inputs” seemed to matter much in terms of improving student achievement. Only teachers’ verbal ability seemed to be linked to higher student test scores.
Schools where teachers scored high on a 10-item verbal test embedded in the survey tended also to have students who scored high on academic tests. And having those so-called “good” teachers seemed to be more important for black students than for white students—a finding that subsequent studies have echoed.
The Coleman team also found that whom students went to school with was almost as important as family background in predicting academic success.
Black students did better in schools that were predominantly middle-class than they did in lower-class schools, even though the improvements were not large enough to make up for achievement differences due to family background. Since students in majority-minority schools also tended to be poorer than average, that finding was later seen as a plus for the desegregation movement as it began to switch into high gear.
Schools’ Effect Muted
What most people took away from the report, however, was the notion that “schools don’t matter.”
Some politicians, in fact, later used that argument in opposing increased funding for education. But the scholars who were involved in the report and its subsequent reanalysis say that the “schools don’t matter” interpretation was greatly oversimplified.
“This is absurd,” Mr. Moynihan and Mr. Mosteller wrote later. “Children don’t think up algebra on their own.”
What the study found, specifically, was that differences in achievement varied as much within schools as they did from school to school.
What that means, Mr. McPartland says, is that schools tend to have a uniform effect on everyone: Students come to school with academic differences and learn, more or less, at the same rate.
“I had to think through the next two or three years on why I still thought schools could make a difference,” said Mr. Tucker. “What the study was showing, though, was what happened in average, ordinary schools. But it could never look at the effects of a particular intervention.”
The findings related to schools’ demographic composition were less in dispute, according to Mr. Cohen of the University of Michigan, who led a study for the U.S. Commission on Civil Rights that confirmed and amplified the Coleman Report’s conclusions.
Called “Racial Isolation in the Public Schools,”the 1967 report took the next step and concluded that, at least at the 9th grade level, black students learned more in majority-white classrooms.
Later characterized by the education historian Diane Ravitch as the “bible of integrationist forces,” the racial-isolationstudy provided fodder for the desegregation movement for years to come.
Mr. Coleman himself was labeled a traitor to that cause years later, after he published a different study that concluded the mandatory-busing movement was contributing to “white flight” from urban neighborhoods.
Data Flaws Cited
In the end, the scholars who participated in the Harvard seminar identified some methodological flaws in the Coleman study but, in the main, affirmed its conclusions.
With additional foundation support, Mr. Moynihan and Mr. Mosteller gathered the reanalysis in a book, On Equality of Educational Opportunity, which was published in 1972, putting the Coleman Report back in the public eye again.
“In retrospect, it’s fair to say there are some pretty serious weaknesses in the data,” said Karl L. Alexander, a Johns Hopkins sociologist who now teaches an upper-level undergraduate course on Mr. Coleman’s work.
Weaknesses that he and other experts cite include the use of per-pupil-spending data for districts rather than individual schools, an insufficient response rate to the surveys, improper sampling procedures, and flawed testing instruments.
“By today’s standards, that kind of analysis would not have passed muster, but it was in the vanguard then,” Mr. Alexander said. “I think we are getting better at asking the questions and understanding how to do analyses that are more compelling.”
He said the report also reframed many scholars’ thinking in the field.
“If the resource differences were not that pronounced,” he said, “people thought then perhaps we needed to start looking inside schools.”
Other researchers, most notably the late Ron Edmonds of Harvard University, built careers on challenging the belief that schools don’t matter. Those experts studied schools where minority children were succeeding, and distilled lessons for other schools.
Gaps Persist
Mr. Jencks said the Harvard seminar experience led him to make permanent his switch from journalism to academia and to undertake quantitative research in public policy.
“Just the idea that you could take social-science evidence and bring it to bear on policy issues was really inspiring,” he said. “I had been in Washington, and the way people got things done there was to tell a story about your Aunt Matilda.”
With Mr. Smith and Mr. Cohen, Mr. Jencks went from the seminar to found the Center for Education Policy Research at Harvard.
As for the black-white achievement gap that the Coleman Report documented, the organizers of the Harvard seminar, at least, appeared to be confident that the U.S. education community could overcome it.
“It may be hoped that before the century is out the great gaps will have disappeared,” Mr. Moynihan and Mr. Mosteller predicted in On Equality of Educational Opportunity.
“It may also happen that in the process a general theory of education will have evolved, been tested, replicated, and accepted,” they concluded.
On both counts, scholars agree, the nation is not there yet.


Friday, November 24, 2017

Anne of Green Gables

https://www.nytimes.com/2017/04/27/magazine/the-other-side-of-anne-of-green-gables.html


If you know only one thing about Anne Shirley, it is most likely that she has red hair. Maybe you can even picture it, braided into pigtails, sticking out from underneath an unfortunate straw hat, as when Matthew first sets eyes on her. In the 1890s, red hair was a symbol of witchiness, ugliness, passion. Anne’s hair immediately establishes her as an outsider, even as it intimates a kinship between her and Avonlea, with its startling red roads. Anne wants nothing so much as to be rid of it. “I can’t be perfectly happy,” she tells Matthew with characteristic drama on their first ride to Green Gables. “Nobody could who has red hair. ... It will be my lifelong sorrow.”
Anne longs to be beautiful. Not only does she wish for her hair to turn a more dignified auburn, she also tells her best friend, Diana Barry, “I’d rather be pretty than clever.” Praying at Marilla’s behest, she asks God to let her stay at Green Gables and to “please let me be good-looking when I grow up.” She loves pretty things, because she has had none, and swoons over cherry blossoms, an amethyst brooch and the possibility of one day having a stylish dress with puffed sleeves, which sensible Marilla refuses to make for her.
If “Anne of Green Gables” were written today, it is easy to imagine that over the course of the book, Anne would come to learn that none of these externalities matter: not the color of her hair, not the sleeves of her dress. Instead, in the novel, her hair mellows to the coveted auburn, and Matthew, in a moment of tremendous fatherly kindness, gives her a dress with puffed sleeves. Rather than dispense the message that it’s only what’s on the inside that counts, “Anne of Green Gables” conveys something more nuanced, that beauty can be a pleasure, that costumes can provide succor, that the right dress can improve your life — all things that adults know to be true, sometimes, but that we try to simplify for our children.
“Green Gables” is rife with complications like these; it’s an artifact from a different time that, instead of being outdated, speaks to ours in an uncanned, unpredictable voice. Anne has survived for so long because she is more sophisticated than she initially seems.
The book, in a manner that is rare for young-adult novels even now, is a celebration of Anne’s intelligence, which is ultimately cherished by her adoptive parents, her community and her future partner, Gilbert — who is also her closest academic rival and who instead of being threatened by Anne’s brain admires her for it. And yet at the end of “Anne of Green Gables,” Anne quits college and returns to the farm to care for an ailing Marilla, never becoming the writer she wanted to be as a child. This is, perhaps, a disappointing ending (and one that presages a string of follow-up novels in which Anne eventually becomes muted by family life), but it is an honest one: We still live in a world where a woman’s intellect does not preclude her from accruing vast domestic responsibilities.
“Anne of Green Gables” is also a romance, but a slow-burning one. Anne can’t stand Gilbert until the final pages of the first novel, her attentions turned less to love than her friendship with Diana. In the middle of the third novel in the series, “Anne of the Island,” Anne is still putting Gilbert off, rejecting his proposal of marriage. It is not until the beginning of the fifth book, “Anne’s House of Dreams,” by which point Anne has had other suitors and other proposals, that the two are finally married, going on to have seven children.
For all her curiosity, imagination and education, Anne eventually arrives at the traditional ending: a husband, a family and all the attendant duties, the nonconforming woman who conforms. But the novels do not present this as either a great tragedy or a great victory. Instead, these choices look a lot like the fraught and difficult compromises of adulthood, in which you might put aside personal desires to care for your mother or modify your career goals to accommodate children. We would flatter ourselves to think that there is anything particularly old-fashioned about Anne’s trajectory. She is a thoroughly modern girl.

Saturday, October 21, 2017

propositional logic

Some notes for the Stanford class "Introduction to Mathematical Thinking".

Propositional logic is the branch of logic concerned with the study of propositions (whether they are true or false) that are formed by other propositions with the use of logical connectives, and how their value depends on the truth value of their components.

The following is an example of a very simple inference within the scope of propositional logic:
Premise 1: If it's raining then it's cloudy.
Premise 2: It's raining.
Conclusion: It's cloudy.
Both premises and the conclusion are propositions. 

This inference can be restated replacing those atomic statements with statement letters, which are interpreted as variables representing statements:


Premise 1: 
Premise 2: 
Conclusion: 

Mathematicians sometimes distinguish between propositional constants, propositional variables, and schemata. Propositional constants represent some particular proposition, while propositional variables range over the set of all atomic propositions. Schemata range over all propositions and are commonly represented with Greek letters, most often Ï†Ïˆ, and Ï‡.

Conjunction is a truth-functional connective which forms a proposition out of two simpler propositions, for example, P and Q. The conjunction of P and Q is written P ∧ Q, and expresses that each are true.

Disjunction resembles conjunction in that it forms a proposition out of two simpler propositions. We write it P ∨ Q, and it is read "P or Q". It expresses that either P or Q is true.

Implication (also known as material conditional) also joins two simpler propositions, and we write P → Q, which is read "if P then Q". The proposition to the left of the arrow is called the antecedent and the proposition to the right is called the consequent. (There is no such designation for conjunction or disjunction, since they are commutative operations.) It expresses that Q is true whenever P is true. 

The material conditional can yield some unexpected truths when expressed in natural language. For example, any material conditional statement with a false antecedent is true (see vacuous truth). So the statement "if 2 is odd then 2 is even" is true. Similarly, any material conditional with a true consequent is true. So the statement "if I have a penny in my pocket then Paris is in France" is always true, regardless of whether or not there is a penny in my pocket.

In the statement "it is necessary that Q in order for P", P is the antecedent and Q the consequent.

Sunday, September 24, 2017

math books


"How the Brain Learns Mathematics" by Sousa


"What is the name of this book?" by Raymond Smullyan for logic puzzles.

https://www.amazon.ca/Parrots-Theorem-Novel-Denis-Guedj/dp/0312303025
https://www.maa.org/external_archive/devlin/LockhartsLament.pdf

Journey Through Genius by William Dunham

John Mighton's books "The Myth of Ability" and "The End of ignorance"
The Talent Code, by Daniel Coyle
Daniel Willingham's "Why Don't Students Like School?"

Sunday, September 17, 2017

a: the sum of odd numbers

Three solutions:


Solution 1 is geometric


square divided into odd numbers




Solution 2 uses pairwise addition:


Add the 1st and last number in the sequence, then the 2nd and next to last, etc. 


For example, if you have 4 numbers
1 + 3 + 5 + 7, 
then you add 1 + 7 = 8 and 3 + 5 = 8.

Each pair adds to 8, twice the value of the number of numbers (4).

On average, each member of the pair is 4 and you have 4 members so the answer is 4^2.

This can be done for any length of a sequence of odd numbers starting from 1.


Here is the proof:
The number of terms is "n".

When n is even, there are n/2 pairs.

Each pair's value is the same as the sum of the first and last term. The first term is 1, the last term is 2n - 1

The sum of the terms is the number of pairs times the value of the pairs.

The total is then n/2 * (1 + (2n - 1)) = n/2 * 2n = n^2

When n is odd, there are (n-1)/2 pairs plus the middle term whose value is n.

Each pair's value is the same as the sum of the first and last term. The first term is 1, the last term is 2n - 1

The sum of the terms is the number of pairs times the value of the pairs plus the middle term.

The total is then (n-1)/2 * ( 1+ (2n - 1)) + n =
(n-1)/2 * 2n + n =

(n-1)*n + n = n^2



Solution 3 uses induction:



  ie,


squaring the next number adds the corresponding odd number.



q: the sum of odd numbers

The sum of sequential odd numbers starting from 1 is a square number.
Examples:

1+3=4 (or 2 squared)
1+3+5=9 (or 3 squared)
1+3+5+7=16 (or 4 squared)
1+3+5+7+9=25 (or 5 squared)
1+3+5+7+9+11=36 (or 6 squared)

Question 1:
Is this always true?

Question 2:
Why?

Friday, August 18, 2017

mathematical education

Mark Taylor Nice summary. As an educational psychologist, I have a strong interest in this topic. Since the 1990s we have known definitively what causes dyslexia and we know clearly how to treat it (not that it is easy), but we still know little about math disabilities. 

I used to organize the major annual training institute for the Montana Association of School Psychologists. Our institutes last for two-and-a-half days, all on a single topic, and all presented by just one speaker. I tried to get David Geary to come to present to us, having had a chance to visit with him at a major conference in Chicago in the late 1990s, but he declined, on the grounds that no one in the entire world knew enough about math disabilities to present for that much time. Finally, in 2011, after calling a bunch of top researchers, I was able to bring Michele Mazzocco from Johns Hopkins to talk to us. We still do not know much, but we are finally getting some good research. 


David Geary was lead author on the National Panel report on math learning processes in - I think - 2009, and that is available for free on line. A book that I like a lot is Dehaene, S. The Number Sense: How the Mind Creates Mathematics. (OUP - not sure what the current edition is). He is working in France but writes brilliantly in English and for a geek like me the book is laugh-out-loud funny in parts. He also had a terrific article in Science on sources of mathematical thinking. It is a little bit older information but it is solid. If you are a member of AAAS you can find it on line.



http://www.newyorker.com/magazine/2008/03/03/numbers-guy