Author Archives: stern

Mathematica at StackExchange

There is a proposal to create a Mathematica section at the popular programming Q&A site StackExchange. I think it’s probably a good idea; the mathgroup mailing list has been a great resource for years but the web is easier and quicker than e-mail sometimes.

Sign up to support it here:
Stack Exchange Q&A site proposal: Mathematica

(Or, if the link above is busted, just visit

The dark secret behind the ignorance of college students (1943 edition)

Following up on my summary of the New York Times‘s 1943 survey of American college freshman, and their ignorance of American history and geography— I didn’t do so well on that test, scoring under 50%. I’m embarrassed to admit that my mother, whom I quizzed over the phone, did better than I did.

It’s scant comfort that the students of the day also got most of the questions wrong, and their guesses were typically far from the mark. As Benjamin Fine put it, “More impressive than the lack of knowledge is the amount of mis information that the survey disclosed. A large majority of the college freshmen showed that they had virtually no knowledge of elementary aspects of American history.” Much of his article about the survey is devoted to the wrong answers produced by the students. For example, when asked who had been president during the U.S. Civil War, wrong answers including George Washington, Woodrow Wilson, Ulysses S. Grant, Theodore Roosevelt, William Taft, Herbert Hoover, Andrew Jackson, and Warren G. Harding.

The public response fell into two broad categories:

1. Some proclaimed the survey results to be shocking, and commended the Times for bringing them to public attention. Numerous politicians and professors of history took this view, but the jewel in the crown was that the Times won a Pulitzer Prize for Public Service, only their second, for this work. The Times‘s nomination letter for the prize argued that the piece had already inspired changes in American education, that a number of colleges introduced American history after the article ran, and that the states of Illinois and Pennsylvania passed their first requirements for U.S. history to be taught. Other responses included formal endorsement of the teaching of history by the War Department (they wanted this to take place in “Victory” courses for high school students). Congress debated federal aid for history instruction, and the entire Times survey was read into the Congressional Record. Senator Homer Bone (D-WA) called the Times survey: “an indictment of our system of teaching.” Fiorello LaGuardia, mayor of New York City, took the results as a call for the teaching of U.S. history. Eleanor Roosevelt commented on the survey as well, though mostly to suggest that people should have better access to libraries.

2. Others argued that the survey was absurd and revealed nothing but the risks of lousy methodology.

Reading the responses that the Times got on its survey, one must suspect that students weren’t taking it entirely seriously. Remember the question about “who was president during the civil war”? Over 150 student, mostly at southern colleges and universities, answered “Jefferson Davis.” Harvard did not participate in the survey, but the Crimson came to the defense of the students who had done so, printing an editorial arguing that students had thought the survey was a “farce,” and that the results had no meaning at all.

The Times waved away this concern, saying “Although it is likely that some of the students were not serious in answering the questions, it is evident, even after discounting that possibility, that the students simply do not know American history.”

But common sense says that the Crimson had a pretty good case — students were given half an hour to answer dozens of questions, some of them perposterously hard, and the results were anonymous and would not count towards their grades. Why would any of them go to the effort of trying to answer well?

Many students included Franklin Roosevelt [president at the time the survey was given] on their lists of assassinated presidents. Some called Walt Whitman a popular band leader. [they may have been riffing on the name of popular band leader of the 1920s and ’30s, Paul Whiteman]

As mentioned in my first discussion of the Times survey, one student wrote that Teddy’s Roosevelt’s greatest contribution to the United States was that “he collected a large quantitiy of animal heads.”

How could anybody think these students were serious? And yet, the Times claimed that these answers reflected honest ignorance, and that they had removed all joking responses from consideration.

Something not discussed at the time, even by those who thought the test was absurd, was the fact, fully revealed only years later, that the test was designed to produce failure.

At the time the survey was administered, there was a national debate on whether students should be studying history or social studies and civics. The Times had sided with the history camp, perhaps because Iphigene Ochs Sulzberger, wife of New York Times publisher Arthur Hays Sulzberger, had studied history herself and feared that standards had fallen since her days as a student. The start of World War II gave the issue some urgency, and the paper had raised the issue even before 1943. For example, in May 1942, Allan Nevins wrote in the New York Times Magazine that “No nation can be patriotic in the best sense, so people can feel a proud comradeship without a knowledge of the past.”

The process by which the survey was designed is dissected in a recent article from the Teachers College Record [““Don’t Know Much About History”: The New York Times 1943 Survey of U.S. History and the Controversy It Generated,” Anne-Lise Halvorsen, 2012], which relates how opponents of the social studies curriculum designed the survey specifically to generate New York Times headlines in favor of the teaching of history.

Mrs. Sulzberger imagined that publicizing the results of a survey showing ignorance of history in college students would help push back the tide of social studies in high schools. The historians hired to write and grade the survey understood precisely how the results would be used, and they constructed the survey to minimize the number of correct answers received. For example, the survey asked students to name all the states on the eastern seaboard of the United States. This requires a fourteen part answer, and students would get no points if they made even a single error. Many of the questions had ambiguous answers, yet the Times accepted only a short list of responses as correct. See for instance the question about America’s policy towards China — many of the responses mocked by the Times seem just as valid as the desired answer of “The Open Door Policy.”

For some of the questions, especially some of the geography questions, the Times answers are arguably wrong. To quote the Crimson article above, for example, “the Times was greatly distressed because only 15 per cent placed Portland. Ore, on the Columbia River as the Times expected them to. The current Rand-McNally Atlas places it squarely on the contributory Willamette, with the city limits stopping noticeably short of the Columbia. “Close, but no cigar.”

Possibly hurting scores, elite schools of higher education (Harvard, Yale, Princeton, et al) were not included.

And some of the questions asked were almost comically hard, and asked students to display knowledge of no likely interest to anybody. The minimum cost of an acre of federal land before the passing of the Homestead Act — Who could possibly care? Questions of this sort probably worked against the broader mission the Times was pursuing in advancing history over social studies. It is impossible to imagine requiring students to learn such minutia would advance the republic.

Erling Hunt, head of the Teaching of Social Science at Teachers College, Columbia University, and thus very much in the crosshairs in this survey, thought the survey had been arranged by isolationists who wanted the U.S. to withdraw from WWII, and that Mrs. Sulzberger “seems to have a kind of D.A.R. interest in patriotic history, together with an extreme aversion to progressive education, resulting from a very unhappy experience of one of her children in a progressive school.”

This wasn’t the first study to lead to the conclusion that Americans don’t know their own history, nor the last. The first study of the subject seems to have been by J. Carleton Bell and David McCollum’s and was published in the Journal of Educational Psychology in 1917. (“It was particularly troubling that many of these [students] could not state the significance of the year 1846, the beginning of the Mexican-American War”). There has been a more or less continuous series of similar studies since. It’s amusing to think what would have qualified as ignorance about history in 1917, given that from our point of view even their present was fairly ancient history.

The shocking ignorance of college students (in 1943)

In 1943, the New York Times ran a series of articles about the woeful state of knowledge of American history among college freshmen. The articles were informed by a survey the Times had commissioned in which 7000 students at 36 colleges and universities were asked to respond to questions about American history and geography. The results were given to Times education reporter Benjamin Fine, who found them to be appalling, and who then wrote the first in what would prove to be a series of articles, titled “Ignorance of U.S. History Shown by College Freshmen: Survey of 7,000 Students in 36 Institutions Discloses Vast Fund of Misinformation On Many Basic Facts.”

Learning of the survey and the subsequent controversy during a recent visit to the New York Times offices, I found myself curious as to how my own knowledge of U.S. history would measure up against the scandalous ignoramuses of 1943.

Fine’s article lists many of the questions from the survey. You may want to read these as I did, as a quiz. I’ve presented Wikipedia links so you can check your answers. The students taking the test did poorly, and I have indicated the percentage that got a correct answer for a number of the questions, where the Times provided that detail.

    1. Carter Glass
    2. James F. Byrnes
    3. Jesse Jones
    4. Norman Thomas
    5. Sam Rayburn
    6. Sumner Welles
    7. John D. Rockefeller
    8. Alexander Hamilton
    9. Charles W. Eliot
    10. Jay Cooke
    11. William James
    12. Carl Schurz
    13. Walt Whitman
    14. John Burroughs
    15. Nicholas Biddle
    16. Roger Taney
    17. Jay Gould
    18. Henry Ward Beecher, and
    19. Roger Williams.
    1. Thomas Hart Benton
    2. Mark Hanna
    3. John C. Calhoun
    4. Henry Clay
    5. Andrew Jackson
    6. Samuel Adams
    7. Daniel Webster

Students were given only 30 minutes to complete the test, and there were only a handful of questions that more than 50 percent of students answered correctly.

The colleges participating included Boston University, Brooklyn College, Bucknell, City College, University of Cincinnati, Colgate, College of Good Counsel, Dartmouth, George Washington University, Hunter, Illinois Institute of Technology, Indiana University, Kansas University, Kentucky University, Maequette, Maryland University, Massachusetts State College, Mount Holyoke, New York University, North Carolina University, Pennsylvania State College, Pennsylvania Univeristy, Pittsburgh University, Rensselaer Polytechnic Institute, Rhode Island State College, Smith College, Texas University, Tulane, Virginia University, Washington University, State College of Washington, Central Washington College of Education, Eastern Washington College of Education, Western Reserve, William and Mary, and Yeshiva College.

To follow soon: the aftermath of the article’s publication, and the survey’s terrible secret revealed.

Amusing Youth With A Computable Document Format

A few months ago, Wolfram proposed the Computable Document Format, a standard format for files with computable content. If you have a CDF reader, you can execute the computations on your own machine. At this point, only Wolfram itself makes software for producing or reading CDFs, and I see no signs of rapid adoption, though it may be taking off in educational communities or others to which I have little exposure.

If you have Wolfram’s Computable Document Player, or Plugin installed on your computer, you should be able to use the following bit of code, which I created to amuse my daughter after the “day of the week your birthday falls on” code failed to do so.

colorList = ColorData["Indexed", "ColorList"][[1]];

Rotate[Style[Text["CHILD'S NAME HERE"], FontSize -> size,
FontColor -> colorList[[Round[color]]]], rotation], {{size, 40},
30, 120}, {rotation, 0, 2*Pi}, {color, 1, Length[colorList]}]

[WolframCDF source=”” CDFwidth=”600″ CDFheight=”600″ altimage=””]

I actually modified it for the CDF, combining the two lines into a single Module[], which the CDF player seems to prefer, and giving a choice of three names. You might think it would be best to include a text entry field so that the program can display any name you like, but the CDF player is Mathematica at heart, if you feed it a solvable math problem as the name, it will try to solve it. Wolfram therefore disallows free-form text entry.

Trivial birthday code

My daughter asked yesterday what an “application” was, which led to a discussion of computer programming. I demonstrated by writing a one-line program in Mathematica that computed the day of the week her birthday landed on every year since she was born. She was not impressed.

Code below; birthday changed for privacy protection.

  Table[{i, bday = DatePlus["August 1, 2005", {i, "Year"}];
    DateString[bday, {"MonthName", " ", "DayShort", ", ", "Year"}],
    DateString[bday, "DayName"]}, {i, 0, 7}],
  TableHeadings -> {None, {"Birthday", "Date", "Day of Week"}}]]

table of birthdays

For extra credit, it’s not hard to generate a histogram showing the distribution of days of the week.

daysOfTheWeek = {"Sunday", "Monday", "Tuesday", "Wednesday", "Thursday",  "Friday", "Saturday"};

numboHits[dayOfWeek_] :=
  holder =
       DateString[DatePlus["August 1, 2005", {i, "Year"}], "DayName"], {i, 0,
        25(*years to check*)}]]], #[[1]] == dayOfWeek &];
  If[Length[holder] == 1, Length[holder[[1]]], 0]]

BarChart[Map[numboHits[#] &, daysOfTheWeek], ChartLabels -> daysOfTheWeek]

birthday histogram