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This paper was written as an assignment for Ian Walton's Math G - Math for liberal Arts Students - at Mission College. If you use material please acknowledge it.

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It was a hot June afternoon in 1969, and I was sitting with my fellow classmates through an unbearably long academic awards ceremony. I remember being quite surprised to learn that my name had just been announced as the winner of my Jr. High Schoolâs eighth grade "Outstanding Mathematics Student" award. Although quite proud of my achievement, I remember experiencing an overwhelming feeling of bewilderment. I had assumed that one of the boys in my class would be the recipient of this award. As I glanced over at my mathematics teacher I could tell that he was quite pleased with his choice. I remember his wink of approval, and the slight twinkle in his eye. I felt sure then that it was not a mistake, he had actually chosen me for this award.

What I didnât know on that day was that the award would mark the end of my exposure to higher mathematics, rather than beginning it. My parents firmly believed (having grown up in the 1930âs and â40âs) that my role as a female was to take high school courses that would help me land me a great job as a secretary. Possible college plans were reserved for the boys in my family. The boys, after all, would need to support a family. My future was determined. I was to work for a few years in the clerical profession, and then find a nice man to settle down with. I would then presumably live happily ever after. After one year of freshman high school algebra I switched to accounting and bookkeeping courses. By the time I reached my senior year, due to my lack of exposure and my familyâs beliefs and attitudes, I had indeed concluded that I was "just no good at math."

With this belief system firmly intact, it has taken me over thirty years to finally find the courage to attempt a college mathematics course, forced by my desire to attain a graduate degree. I have come to realize that my success in mathematics classes is not necessarily influenced by my lack of ability, but rather by my lack of exposure to the subject area.

I have also come to realize that I am not alone. There has been an internationally held belief for the majority of the nineteenth and twentieth centuries that fundamentally women lack the biological make-up or necessary talent to succeed in higher mathematics. "First it was argued that their (womenâs) brains were too small, later that it would compromise their reproductive capacities, still later that their hormones were not compatible with mathematical development." (Henrion, 1997).

For centuries, women who exhibited a gift in the mathematical field have faced many societal prejudices and obstacles in pursuing their mathematical goals. Before the early 20^th century women were banned from formal entrance to universities and had to devise a variety of strategies to further their education. Indeed, access to higher education has proven to be one of the main barriers that women have faced not only in the field of mathematics, but in other subject areas as well.

A notable case is that of Sofia Kovalesvskaya, (1850-1891), a native of Russia whose ground-breaking work in mathematics made her male counterparts reconsider their archaic notions of womenâs inferiority to men in the scientific arena. Sofiaâs work is considered one of the catalysts that allowed future discoveries in mathematics to occur. During her career, she published ten papers in mathematics and mathematical physics. In 1888 she achieved her greatest personal triumph by winning a competition sponsored by the French Academy of Science. Her winning entry titled "On the Rotation of a Solid Body about a Fixed Point" developed the theory for an unsymmetrical body where the center of its mass is not on an axis in the body.

Sofiaâs mathematical accomplishments were not easily come by. In Russia, she was not allowed to study mathematics, and subsequently traveled to Switzerland in order to try to gain entrance to a University there. However, young girls were not allowed to travel alone, so she entered into a marriage of convenience in order to travel to Switzerland to study mathematics. Sofiaâs goal was to seek the tutelage of Karl Weierstrass at the University of Berlin. Weierstrass was considered one of the most renowned mathematicians of his time, and at first did not take Sofia seriously. After realizing her potential, he assisted her by privately tutoring her for four years. By the time she was finished, she had written three doctoral dissertations in order to be awarded her Ph.D. (Henrion, 1997).

Another revolutionary female mathematician was Sophie Germain (1776-1831), who was also denied access to formal education. She studied mathematics on her own in her fatherâs library, until she was caught studying her fatherâs mathematics books and reprimanded by her parents about it. She eventually made friends with several students at Ecole Polytechnique (a leading institution designed to train mathematicians and scientists for the country of France, which women could not attend), and obtained their lecture notes. Subsequently, she submitted a memoir to the mathematician J. L. Lagrange under a male studentâs name. Lagrange saw talent in the work, sought out the author, and was quite surprised to find that it had been written by a woman. Sophieâs early work began in number theory, but later shifted to applied mathematics. She became very curious about a phenomenon of "patterns produced on small glass plates covered with sand and played, as though the plates were violins, by using a bow. The sand moved until it reached the nodes, and the array of patterns resulting from the "playing" of different notes caused great excitement among the Parisian polymaths. It was the first "scientific visualization" of two-dimensional harmonic motion. Napoleon authorized an extraordinary prize for the best mathematical explanation of the phenomenon, and a contest was announced." (Sophie Germain Website, 11/00). After three attempts at solving the problem, Sophia finally won the prize on her third attempt in 1816.

These two women are representative of many women through out history who have shown an aptitude for mathematics, and who were discouraged from attempts to pursue this field of study. Eventually, however, by the late 1800âs and early 1900âs women were gaining access to formal college education, and the mathematical field became more available for women. However, other obstacles stood in the way of womenâs complete acceptance into mathematics. "The ante continued to rise; no longer was a college education, or even a doctorate, sufficient credentials for membership in the mathematical elite·women were often formally or informally excluded from the inner circle·progress for women in mathematics, even in the last century was not necessarily linear."(Henrion, l997).

By the l970âs the conversation had begun to change. Instead of centering on access to mathematical education, women were focusing on attainment of equity in the mathematical field. Membership and recognition in the mathematical professional organizations still belonged mostly to men. In addition, men dominated college professorships, with a few exceptions. As the womenâs cultural movement became increasingly more powerful in the 1970âs many questions were being raised. Why werenât women holding an equal number of professorships in mathematics across the country? Was it that men wouldnât give them the opportunity? Why werenât women equally represented in the national mathematical associationâs conferences?

Lenore Blum, a well known mathematician and one of the founders of The Mathematical Association of Americaâs (MAA) Committee on the Participation of Women, spent some time researching the various mathematical societiesâ conferences that occurred in 1971. She found that of the major mathematical conferences scheduled that year, none of the conferencesâ invited speakers were women. In addition, of the more than 300 ten minute talks, about fifteen were given by women (5%). Additionally, many of the published programs from the mathematical conferences listed individualsâ professional activities and achievements as well as job promotions and appointments. She found that of the thirty-one promotions listed, only three were female. As she went down the list, she found that as the positions became less prestigious, the percentage of women increased. (A Brief History of the Association of Women in Mathematics Website, accessed 11/25/00).

Violet H. Larney, in her article titled Female Mathematicians, Where Are You? (1994) examined the hiring practices of women in higher mathematical education during the same time period that Lenore Blum had investigated. Her study revealed some interesting facts. She defined a qualified female mathematician as a female who possessed an earned doctorate in mathematics. She assumed age 25 was the minimum age at which a woman earned her Ph.D., and that retirement was at age 65. "Then the female mathematicians qualified to hold academic appointments in 1970-71 would have earned their doctorates some time during the preceding forty years. A few reference books and a desk calculator yield the figure of 816 as the total number of women who received doctorates in mathematics from the academic year 1930-31 through 1969-70·Hence, the number of available women Ph.D.âs is too small to average even one woman at each institution·One might safely conjecture that in 1970 there was available only one female with a Ph.D. in mathematics for every two degree-granting institutions in the United States."

(Reprinted from A Century of Mathematics, John Ewing (Editor), page 282)
 
 

So, what has happened over the last thirty years? Has access and equity for women in mathematics increased, and, are more women finding success in the field? Henrion (1997) reports that as of 1997:

• 44% of the math majors at the bachelorâs degree level were women.
• At the top thirty-nine math institutions in the U.S., 37% of the bachelorâs

• Women held 24% of the Ph.D.âs., 17.4% of this 24% were from the top thirty-nine math institutions in the U. S.

• Women make up 19% of full-time mathematics faculty across the U.S.
• Less than 10% of the 19% of full-time mathematics faculty that are women are tenured.
• Women represent less than 5% of the mathematical faculty across the U.S. who hold positions in doctoral granting departments.

According to Henrion (1997), it is clear "that obstacles continue to exist to womenâs complete acceptance in mathematics. Though these obstacles are rarely the blatant or formal barriers of the past, they continue to exist in more subtle forms, embedded in attitudes, beliefs, and expectations about women, mathematicians and mathematics."

The Mathematical Association of Americaâs Committee on the Participation of Women agrees. In an article by Patricia Clark Kenschaft (1991), they support the argument that subtle barriers still exist. Ms. Kenschaft classifies five categories as the cultural reasons that too few women succeed at mathematics. These include:

• Societal Customs
• Family Customs
• Customs in our Educational System
• Customs Specific to Mathematics, and
• The Effects of these Customs on Individuals.

Studies have also shown that many girls become uninterested in mathematics at the start of puberty. It is at this stage in their lives that the social pressures of seeking popularity and the ability to "fit in" take precedence over academic endeavors. In contrast, boys seem to thrive in an individually competitive environment during this period, while girls thrive in a cooperative environment. Several articles on the Weaving Gender Equity into Math Reform Website (accessed 11/16/00) suggest solutions to losing girls in mathematics at this stage in their development. The suggestions include:

• Teach mathematics in a cooperative learning style.
• Integrate mathematics into other curriculum areas that girls feel competent with.
• Write about the thinking process in mathematics.
• A connection of math to real-life experiences helps to make it accessible.
• Alternative assessment to test taking improves elementary and middle school girlâs involvement in math classrooms.
• Girls do better in math when grouped together rather than focusing on individualized instruction.
• Girls donât realize as young teens which careers require math. It is important to include this as part of mathematical education.
• Girls have lower expectations than boys do because they believe they lack ability. It is important to assist them in believing they have mathematical ability.

• Research shows that teachers give less attention and praise to girls in all subject areas. It is important for educators to become acutely aware of this and to continually examine and evaluate their behavior for bias in the classroom setting. (See attachment: Equity Checklist for the Standards-Based Classroom by Christina Perez).

• Responding to a sonâs inadequate performance in mathematics with "he must work harder," and responding to a daughterâs performance with "I was never good at math either."
• Regarding the father as better at mathematics than the mother, and allowing the father to be the authority on math.

An important book on how the use of mathematics is used in careers chosen by women is titled She Does Math(1995) by Marla Parker. Ms. Parker examines real-life problems contributed from women on the job in the many careers that use mathematics. She includes women in careers such as Environmental Psychology, Software Engineering, Archaeology, Computer Science, Civil Engineering, Astronaut Training, Real Estate Investment, and even Foodservice Management and Nutrition. Her reasoning is simple. "I created this book for two reasons: to motivate students to take math every year in high school, and to encourage high school and college students-especially women and minorities-to consider technical fields while planning their careers·Here is a collection of concrete answers to the question, "Why should I take math?"

All in all, in retrospect, it must be said that opportunities available for women in the mathematical field have taken an incredible leap in the last fifty years as compared to the last several centuries. Many associations for the support of women in mathematics have been created and credited with milestones and creative solutions in helping women to gain the access and recognition they deserve in the field of mathematics. These include the Association for Women in Mathematics, Women in Mathematics Education, and the International Organization for Women in Mathematics. Considering these milestones, it is quite likely that over the next century biases regarding women and mathematics will disappear and equality will result, thereby giving women and other minorities equal access to careers (and the high salaries that accompany those careers) in science, medicine and technology. As for me, I think Iâll stick with the arts·

BOOKS

Ewing, John, H., Editor, A Century of Mathematics, Through the Eyes of the Monthly,

Washington, DC: Mathematical Association of America, 1994.

Henrion, Claudia, Women in Mathematics

Bloomington, Indiana: University Press, 1997.

Kenschaft, Patricia Clark, Winning Women into Mathematics,

United States: Mathematical Association of America, 1991

Nolan, Deborah, Women in Mathematics,

Berkeley, California: Mathematical Association of America, 1997

Parker, Marla, She Does Math!

Washington, DC: Mathematical Association of America, 1995.

Perl, Teri, Women and Numbers,

San Carlos: World Wide Publishing/Tera, 1993.

Articles/Journals

Kenschaft, Patricia, Clark. Fifty-Five Cultural Reasons Why Too Few Women Win at Mathematics, The Mathematical Association of America, 1991, pages 11-18.

Internet Resources

Girls Attitudes, Self-Expectations and Performance in Math by Michelle Maraffi

http://forum.swarthmore.edu/sarah/Discussion.Sessions/biblio.attitudes.html

Accessed: 11/16/00

Weaving Gender Equity into Math Reform

Three Articles on this website were used for reference:

Equity Checklist for the Standards-Based Classroom by Christina Perez

Facing Equity: Facing Ourselves by Fred Gross

Equity in Math Cooperative Groups by Hollee Freeman

http://www.terc.edu/wge/coopgroups.html

Accessed: 11/16/00

A Brief History of the Association for Women in Mathematics by Lenore Blum

http://www.awm-math.org/articles/notices/199107/blum/node2.html

Accessed: 11/25/00

Sophie Germain: Revolutionary Mathematician

http://www.sdsc.edu/Science Women/germain.html

Accessed: 11/25/00

Sofia Kovalevskaya

http://www.scottlan.edu/lriddle/women/kova.htm

Accessed: 11/25/00

1. Introduction

1. My own experience in mathematics

1. As a woman graduating from high school in the early 1970âs: Did my experiences (or lack thereof) in mathematics reflect the bias against women succeeding in mathematics, (the culture of the time) or was I really "just no good at math"?

1. Body of Paper

1. What are womenâs experiences in math? What does the data/history show about womenâs involvement in mathematics?

1. There are historical beliefs that at the fundamental level women lack the biological make-up and/or have insufficient talent to succeed in math. For some, this idea is still prevalent.
2. Historical lack of access to formal education for women.
3. Lack of access to mathematical ideas lest "womenâs health would become endangered" in intellectual pursuits. (Late 1800âs).
4. Women historically have been actively discouraged to pursue math.
5. Women have lacked access to jobs in the mathematical fields.
6. Even when women were given access to formal education (late 1800âs to early 1900âs) women were not given access to professional mathematical organizations.
7. In the 1960âs and 1970âs the focus changed from access to equity.
8. Even when the formal barriers started disappearing, women were not choosing to study math, thus locking themselves out of careers in science, medicine and technology (and the high salaries that accompanied those careers).
9. In the last two decades there has been a big effort to increase womenâs participation in math-related fields: (show some of those projects here).
10. Other relevant data:

1. 1997: 44% of math majors in US are women at Bachelorâs degree level.
2. 37% of math majors (BS) at top 39 math institutions in US are women.
3. Beyond Bachelors: women currently 24% of PhD.âs in math
4. Women represent 17.3% of Math PhD.âs candidates at top 39 math institutions.
5. College math professors: Women represent:

 

 

-19% of full time faculty across US

-less than 10% of tenured professorships across the US

-less than 5% of doctoral granting departments across US

6. No women before 1990 were awarded prizes by the American Mathematical Society.
7. For minority women, these numbers are very, very low.

1. What are the educational issues involved in teaching and helping girls gain access to mathematics in the elementary and middle schools?

1. Research shows that teachers give less attention and praise to girls in all subject areas.
2. Girls do better when grouped together.
3. Girls seem to not be making the connections to math and future careers. More education about careers related to mathematics is needed.
4. Girls have lower expectations than boys because they believe they lack ability in math.
5. Parents and teachers attitudes and belief systems affect students. Research shows that this begins as early as age four or five. Boys and girls are given different toys to play with.
6. Teachers need to continually examine and evaluate their behavior for bias in the classroom.
7. Girls are physically more mature at the 7^th to 10^th grade levels. They did to focus more on their bodies and socialization skills than boys do at this crucial age.
8. Girls need cooperate learning styles, not independent thinking or competitive processes to succeed in mathematics.
9. Integration of other subjects in elementary curriculum helps girls feel more competent in math.
10. Math needs to be connected to real-life situations, so that skill transference takes place.
11. Alternate assessment (rather than a paper and pencil test) is shown to improve girls involvement in mathematical classrooms.

1. Conclusion

1. What are the possible solutions?
2. What is currently being done to improve womenâs access to higher mathematics?
3. Who are the leaders in the move to improve access to women and mathematics and what are they doing about it?

 

This paper was written as an assignment for Ian Walton's Math G - Math for liberal Arts Students - at Mission College. If you use material please acknowledge it.