Minorities
Vietnam Draft
The 1969 lottery drawing for the Vietnam War was
demonstrated not to be random. A barrel with 366
plastic capsules was used, where each capsule had a
birth date on it (month and day); one capsule was for
those who were born on leap day. One at a time, the
capsules were drawn by hand. The first to be drawn was
ranked first. The second to be drawn ranked second.
Thus, if September 21 was drawn first, then all men
aged 18–26 with a birthday on September 21 would be
the first group called to service.
The procedure that was followed to order the men
with the shared birthday depended on each man’s initials. A separate lottery was held in which the 26 letters
of the alphabet were ranked. This followed the same
process as the birthdays, in that 26 letters were placed
in a barrel and one by one were drawn. Using the resulting ranking, each man within a shared birthday was
ranked according to the permutation of the first letter of his last name, the first letter of his middle name,
and the first letter of his first name. Overall, this should
have been a fair method for selection, as it was based
on randomized birthdays and letter permutations.
Why It Was Not Random
The above-mentioned method would be random if
implemented properly. However, it turned out that
men with birthdays later in the year (for example,
December birthdays) were much more likely to be
drafted than those with birthdays in the beginning of
the year. What happened is quite simple. The capsules
were placed in the barrel month-by-month beginning
with January, and the barrel was not well mixed. The
December capsules were on top and they had a higher
probability of being pulled out first, resulting in lower
draft numbers for those men.
Further Reading
Friedman, Lauri S. Military Draft (Writing the Critical
Essay: An Opposing Viewpoints Guide). Farmington
Hills, MI: Greenhaven Press, 2007.
Hay, Jack. Military Draft (History of Issues). Farmington
Hills, MI: Greenhaven Press, 2007.
Carmen M. Latterell
See Also: Lotteries; Probability; Randomness;
Vietnam War.
667
Minorities
Category: Mathematics Culture and Identity.
Fields of Study: Communication; Connections.
Summary: Minorities are historically
underrepresented in American mathematics and
efforts have been made to rectify this.
Mathematics is a vital tool in modern life and mastery of mathematical subjects is a requirement to enter
many professions, including medicine, engineering,
and the sciences. For this reason, observed trends in
mathematical achievement in school and representation in mathematics-oriented professions, both dominated by whites and Asians with other minorities lagging behind, give cause for concern. At the end of the
twentieth century and into the twenty-first century, the
media publicized information about the performance
and underrepresentation of minorities in mathematics, many authors published works about minority
individuals in mathematics, and mathematicians and
mathematics educators designed and implemented
successful educational initiatives and programs.
The United States is a racially and ethnically diverse
country with a history of reporting extensive statistics
about school and professional accomplishment by race
and ethnicity. Few in the twenty-first century would
argue that observed differences are because of inherited differences in ability; instead, several other explanations have been offered.
One is that minority students have fewer opportunities to master mathematics because they may be more
likely to attend low-achieving schools, which may have
more inexperienced and uncertified teachers and fewer
teachers with graduate degrees. A second explanation
is the lack of role models, since many mathematics faculty and prize winners are white or Asian, so students
of color (or their teachers) may incorrectly believe that
mathematics ability is somehow linked to race or ethnicity. In addition, students may not feel comfortable
taking advanced mathematics classes in which they are
the only person of color. A third factor is that some
minority students report being actively discouraged
from pursuing careers in mathematics and science.
Racial and ethnic categories used for collecting data
are not consistent across all organizations and some
have changed over time, somewhat complicating comparisons. The terms “minority” and “person of color”
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Minorities
Eighteenth-Century
Minority Mathematicians
I
n the eighteenth century, Benjamin Banneker created astronomical almanacs,
solved mathematical puzzles, and wrote to
Thomas Jefferson to plead against slavery.
Other eighteenth-century individuals include
ex-slave Thomas Fuller, who was known for
his calculating abilities, and Muhammad ibn
Muhammad al-Fullani al-Kishnawi, a mathematician, astronomer,
astrologer, and mystic who constructed
magic squares.
Mathematicians
and historians have
also written ethnomathematics works
on African mathematics, Native American
mathematics,
and
Incan and Mayan
mathematics.
are themselves controversial; for instance in the United
States, persons of Asian descent would qualify on both
scores and yet are not usually classified as such. A better formulation in this case might be “members of ethnic groups with traditionally lower representation in
mathematics,” but the terms “minority” and “person
of color” will be retained, since those terms are commonly used and understood.
Minority Mathematicians in History
In part because of research that suggested the importance of role models, the known benefits of humanizing
mathematics, and a desire to provide counterexamples
to noted racist comments, historians and mathematicians have detailed the lives and work of many outstanding mathematically talented minority individuals.
Minority mathematicians in the nineteenth and
twentieth centuries faced many barriers, including
restricted educational, employment, and publishing
opportunities; derogatory comments and intimidation; and Jim Crow treatment that barred minorities
from attending conferences. Despite these conditions,
many minority mathematicians succeeded in making
great contributions to the mathematics community.
Elbert Cox was the first minority American to obtain
a Ph.D. in mathematics. He attended a segregated primary school with what has been noted as inadequate
educational resources. In high school he became a
talented violinist, and he also enjoyed and excelled in
mathematics and physics. He graduated from Indiana
University with a degree in mathematics and his transcript listed “COLORED” across it. His 1925 Cornell
University Ph.D. thesis was “Polynomial Solutions of
Difference Equations.” He was recognized as an outstanding teacher and effective master’s thesis adviser
during his career at Howard University, a historically
black institution.
Other early minority Ph.D.s in mathematics include
dozens of mathematicians whose contributions to
mathematics and mathematics education have been
broad and varied. One name that often appears on
lists of prominent minority mathematicians is that of
David Blackwell, a noted statistician and game theorist who earned his Ph.D. in 1941. He stated, “[Racial
discrimination] never bothered me. I’ll put it that way.
It surely shaped my expectations from the very beginning. It never occurred to me to think about teaching in a major university since it wasn’t in my horizon
at all.” Joaquin Diaz is noted as the first Hispanic to
obtain his Ph.D. in mathematics from an American
institution. His 1945 thesis at Brown University was
titled “On a Class of Partial Differential Equations of
Even Order.” He worked at a number of different institutions, including as a research associate at the Institute for Fluid Dynamics and Applied Mathematics at
the University of Maryland and as a professor at Rensselaer Polytechnic Institute.
Until the twenty-first century, it was thought that
Evelyn Boyd Granville, who received her Ph.D. in
1949 from Yale University in functional analysis, and
Marjorie Lee Browne, who received her Ph.D. in 1950
from the University of Michigan in topological and
matrix groups, were the first minority women Ph.D.s
in mathematics. They both remained active in the
mathematical community. Earlier in the 1940s Martha Euphemia Lofton Haynes obtained her Ph.D. from
Minorities
Catholic University of America by writing a thesis on
the “Determination of Sets of Independent Conditions
Characterizing Certain Special Cases of Symmetric
Correspondences.” While she had a very distinguished
teaching career in the Washington, D.C. public school
system, her divergence from the research community
may explain why mathematicians were not aware that
she was the first woman minority Ph.D. in mathematics. In addition, histories and statistics on minority
mathematicians were not common until later in the
twentieth century, so it is difficult to identify some of
the early mathematicians.
In 1964, when Thomas Storer graduated from the
University of Southern California with a thesis on “A
Family of Generalized Difference Sets,” he may have
been the first Native American to obtain a Ph.D. in
mathematics, although some historians refer to the
possibility of an earlier Ph.D. in mathematics education. Storer’s research was primarily in combinatorics,
although he was also known for his teaching, advising of honors students, and as a leading authority on
string tricks and figures. Another notable minority
mathematician who obtained his Ph.D. before 1970 is
Hispanic mathematician Richard Tapia, who graduated from the University of California, Los Angeles, in
1967. He has received many honors and awards and
his research in computational mathematics and educational outreach programs are known nationwide.
He explained:
Some of my job duties include teaching mathematics and science to college students, writing books,
doing research, and working with the community.
When I made my career choice, I knew I wanted to
reach out to underrepresented groups, especially
Hispanics. I wanted to show minority students
that if they really want to do something, they can.
I believe I can improve minorities’ participation in
science and mathematics. However, in order to do
this, I have to serve as a role model by first being an
excellent scientist.
Recent Developments
Despite the climbing cumulative numbers of minority
mathematicians and improving conditions and opportunities for minority students, during the latter part of
the twentieth century authors noted that the traditional
stereotypes of mathematicians conflicted with the cul-
669
tural identities of minority groups. In 1997, mathematician Scott Williams created the Mathematicians
of the African Diaspora Web site, “to suggest modern
mathematicians and scientists as images of success to
present to the African American community.” The site
grew to thousands of Web pages filled with history,
statistics, articles, and reference lists. The Society for
Advancement of Chicanos and Native Americans in
Science and the Mathematical Association of America
program on Strengthening Underrepresented Minority Mathematics Achievement also host biography Web
pages. In addition, there are a number of published
articles and books on minorities in mathematics.
Many researchers have conducted studies exploring factors relating to the continued underrepresentation of minorities in mathematics. For example, some
researchers noted that differences in mathematics
achievement may begin at the elementary school level.
The Early Childhood Longitudinal Survey (ECLS),
which followed a cohort of children from kindergarten in fall 1998 to grade 5 in spring 2004, found that
in kindergarten there were already noticeable gaps in
achievement by race and ethnicity. At the high school
level, the National Assessment of Educational Progress reported that 12th graders in all racial and ethnic
groups showed similar improvement in mathematics
achievement scores from 1990 to 2000, but that minority groups still had lower achievement. Scores on the
Scholastic Aptitude Test (SAT), a nationally administered exam often taken by college-bound students, over
the period 1990–2008 show a similar pattern with most
racial and ethnic groups showing improvement but
Asian and white students consistently having the highest scores. Recently the numbers of African-American
and Hispanic students taking Advanced Placement
(AP) exams, specialized subject exams offered in some
high schools and which may gain students college
credit, has increased.
According to the National Center for Education
Statistics, mathematics teaching staff tended to be
primarily white in U.S. public schools. Data from the
National Center for Education Statistics also gives
credence to the argument that some of the achievement gap may be because of minority students being
more likely to have been taught by teachers with inferior qualifications. In 2007–2008, 12% of high school
mathematics teachers had neither a college major nor
standard certification in mathematics, but in schools
670
Minorities
with at least 50% African-American enrollment this
was true of 25% of people teaching mathematics.
Schools with a majority of African-American students
were also likely to have less experienced teachers.
The millennial mathematics major consists of
diverse students pursuing diverse careers and yet
there are concerns about the percentages of minorities, including Asians/Pacific Islanders, African
Americans, Hispanics, and American Indians/Alaskan Natives. For instance, in the late twentieth century and early twenty-first century, the percentage of
undergraduate degrees in mathematics and statistics
awarded to such minorities was approximately 20%,
which was below the percentages of the resident college population. Historically, in the United States,
Asian and white students have comprised the bulk of
enrollment in graduate programs in mathematics and
have received a disproportionate share of advanced
mathematics degrees.
Minorities are also underrepresented among scientists and engineers in the United States. For instance
African Americans, Hispanics, and American Indians
as a group constituted about 24% of the U.S. population in 1999 but only 7% of the science and engineering workforce, while Asians constituted about 4% of
the population but 11% of the science and engineering workforce. Some evidence suggested that choice
of career fields also differed by race. Salaries in science
and engineering fields also differed by race.
Researchers continue to study factors related to
the underrepresentation of minorities in mathematics. There have been many successful programs that
increased the participation of minorities in mathematics, including the Meyerhoff Scholars Program,
the Tensor-SUMMA Grants, and the Enhancing
Diversity in Graduate Education Program. Organizations, and conferences, such as the National Association of Mathematicians, the Society for the Advancement of Chicanos and Native Americans in Science,
the Conference for African American Researchers in
the Mathematical Sciences, and the Mathematical
Association of America through its Strengthening
Underrepresented Minority Mathematics Achievement (SUMMA) program, have been dedicated to
supporting and promoting minorities in the mathematical sciences.
The International Study Group on Ethnomathematics has focused on the cultural diversity in math-
ematics and its applications to mathematics education. The Benjamin Banneker Association has been
dedicated to the mathematics education of minority
children. These professional associations have sponsored mathematics talks, sessions, and awards, published newsletters, and provided opportunities for
social interaction and support.
Further Reading
Burke, Ronald, and Mary Mattis. Women and Minorities
in Science, Technology, Engineering and Mathematics:
Upping the Numbers. Northampton, MA: Edward
Elgar, 2007.
D’mbrosio, Ubiratan. Ethnomathematics: Link between
Traditions and Modernity. Rotterdam, Netherlands:
Sense Publishers, 2006.
Donaldson, James, and Richard Fleming. “Elbert F. Cox:
An Early Pioneer.” American Mathematical Monthly
107, no. 2 (2000).
Hawkins, William. Constructing a Secure Mathematics
Pipeline for Minority Students. Storrs, CT: The
National Research Center on the Gifted and
Talented, 1995.
———. “Mathematical Association of America
Strengthening Underrepresented Minority
Mathematics Achievement.” http://www.maa.org/
summa/archive/summa_wl.htm.
Kenschaft, Patricia. Change Is Possible: Stories of Women
and Minorities in Mathematics. Providence, RI:
American Mathematical Society, 2005.
Lorch, Lee. “The Painful Path Toward Inclusiveness.”
In A Century of Mathematical Meetings. Edited
by Bettye Anne Case. Providence, RI: American
Mathematical Society, 1996.
Moses, Robert P., and Charles E. Cobb, Jr. Radical
Equations: Civil Rights from Mississippi to the Algebra
Project. Boston: Beacon Press, 2001.
National Science Foundation. “Women, Minorities and
Persons with Disabilities in Science and Engineering.”
http://www.nsf.gov/statistics/wmpd/start.htm.
Sarah Boslaugh
See Also: African Mathematics; Castillo-Chávez,
Carlos; Hunt, Fern; Incan and Mayan Mathematics;
Jackson, Shirley Ann; Mathematics Literacy and Civil
Rights; Native American Mathematics; Ross, Mary G.;
Succeeding In Mathematics.