Sonia Kovalevsky Mathematics Days
From AWM Newsletter, Vol. 29, No. 5, September-October 1999.
Four of the Sonia Kovalevsky High School Mathematics Days below were funded by a grant awarded to AWM by Coppin State University and the National Security Agency. Thanks, Coppin State and NSA! St. John's University secured its own funding for their SKHS Day; we encourage other schools to do so.
Virginia (Lyn) Stallings, Chair, Department of Mathematics and Statistics
I am delighted to report to you that our Sonya Kovalevsky Day celebration on March 6, 1999 was a huge success. Dr. Margaret E. Daube-Witherspoon gave a wonderful opening presentation, "Positron Emission Tomography," on the applications of PET to her research at NIH on tumor identification. Her talk demonstrated the relationships among mathematics, statistics, sciences, and communication.
One of our workshops was a special presentation by Dr. Jim White on "Gravitation: The CD." Dr. White is the creator of Mathwright and is co-director of the MAA's highly successful Interactive Mathematics Text Project. Participants went to our computer lab and had hands-on experience with this software and the Internet.
Other workshops included "Exploration of the Platonic Solids" by Dr. Hanna Sandler, "M"ssbauer Analysis of Archeological Artifacts" by Dr. Romeo Segnan, "A Crash Course on Infinity: From Zeno's Paradox to Hilbert's Hotel" by Dr. Ali Enayat, "An Incursion into Recursion: Designing Your Own Fractal Set" by our undergraduate mathematics majors Rebecca Torrey and Keith McCarron, and "The Wonderful World of Sound," by Vanessa Brown on the physics of audio technology.
We had a wonderful closing session with Dr. Henry Edwards of the University of Georgia on "Students and Computers, the World Wide Web, and Mathematical Modeling for Everyone." Dr. Edwards is coauthor with David Penney of the popular Edwards and Penney calculus text used throughout the country. The talk featured his recent work on an elementary treatment of modeling suitable for precalculus students and the development of material delivered to students on the world wide web.
Teachers attended a two-part workshop on "Writing in the Mathematics Classroom" and "Rubric Grading" given by Dr. Linda Hackett of American University. The teachers were particularly intrigued by rubric grading practices used at our university and the extent to which students can become involved in analyzing their progress in mathematics.
As always, our group problem-solving event was a favorite of many. The participants were challenged to find the shortest distance between two points around scattered slices using segments less than two inches long to create a structure rigid in two dimensions. The prizes were given to the solution using the fewest segments and to the solution that was the most artistic.
Sixty-two girls and fourteen teachers attended the conference. The evaluations underscored the popularity of all the workshops. Favorites were the logic, the incursion into recursion, and the world of sound workshops.
The Department of Mathematics and Statistics donated five calculators, and Sigma Xi generously gave us a check for the remaining calculator. Prentice-Hall also donated $200 toward prizes.
This event has become so popular that teachers are already trying to reserve a slot for next year. Per repeated requests by participating teachers, we are now considering opening the event up to young men as well. Teachers explained that there are no activities of this sort for their male students, so they are anxious to include them.
Mississippi University for Women
Jane Hurley Wenstrom, Ph.D., Division of Science and Mathematics, Mississippi University for Women
Mississippi University for Women hosted its second Sonia Kovalevsky High School Mathematics Day on March 27, 1999. It was attended by thirty-two high school girls and three teachers. Of the thirty-two students, thirteen were African-American and three were Asian-American. The organizers, panelists, and workshop leaders were all on the faculty of Mississippi University for Women (MUW) or the Mississippi School for Mathematics and Science (MSMS). We sent letters to all of the area high schools inviting them to send students to participate. We also advertised in the area newspapers, at the annual conference of the Mississippi Council of Teachers of Mathematics, and at the local Mu Alpha Theta mathematics tournament.
The program began at 9:00 a.m. The participants registered and received a packet of materials which contained a schedule of the day's activities, the AWM brochure Careers That Count, and some information about MUW. Dr. Jane Wenstrom welcomed the group and gave a brief biography of Sonia Kovalevsky and some additional history of women in mathematics. Most of the students were amazed at the struggles women had to endure in order to study mathematics.
The morning program consisted of two workshops for the students that ran parallel to two workshops for the teachers. The first student workshop on fair and unfair games was led by Dr. Dorothy Kerzel of MUW. The students played a number of games involving coins, dice, and spinners to determine whether they were fair or not. This led to a discussion of the underlying probability theory. The second student workshop on coding theory was led by Dr. Beate Zimmer of MUW. She discussed some of the mathematics behind coding messages, including binary trees, ciphertext, and block ciphers.
The first teacher workshop, led by Dr. Bonnie Oppenheimer of MUW, was an introduction to Texas Instruments' Calculator-Based Ranger (CBR). The teachers used the CBR to collect data and then worked through some sample classroom activities using the data. The second teacher workshop was an exploration of mathematics on the internet led by Dr. Jane Wenstrom. Web sites visited included the NCTM home page to view the online version of the Standards 2000 and the Ask Dr. Math archive on the Math Forum home page.
After a buffet lunch in the President's Dining Room, the teachers joined the students for the afternoon session. Dr. Oppenheimer led a workshop on spatial visualization using multilink cubes. The cubes were used to explore the relationship between 2D "blueprints" and their corresponding 3D models.
The final workshop of the day was led by Dr. LeRoy Wenstrom and Ms. Kathleen McGarvey of MSMS. They explained the physics of flight and students proceeded to build paper airplane models. The designs were taken from The Great International Paper Airplane Book by J. Mander, G. Dippel, and H. Gossage. Once the models were built, their aerodynamics were observed by flying them outside.
The local CBS affiliate WCBI sent a camera to capture some of the activity and ran a story on that night's local news broadcast. Overall, the day was a definite success. The participants really enjoyed themselves. Their responses were very positive and many were interested in attending again next year. Thank you AWM for the support to host our second Sonia Kovalevsky High School Mathematics Day!
St. John's University
Anne Hughes and Rora Iacobacci
On Monday, May 3, 1999, 212 high school women and 36 of their teachers from 27 high schools in the greater New York area met at St. John's University to participate in its eighth annual Sonia Kovalevsky Day. The schools ranged from public to private and from inner city to suburban.
The Dean of St. John's College, Sister Margaret John Kelly, Ph.D., graciously welcomed the visitors and stressed the importance of such days in helping young people to make informed career choices.
The program began with four panelists, one more than in the past. Ms. Marlene Cintron, a lawyer/ financial consultant at Merrill Lynch told the audience that she did not excel in math when she was in high school, but she hired a tutor and never gave up. "Math is everywhere so you need to confront it." She stressed that merely because they are women, they will have problems unique to them: statistically, women live longer and thus the need to save and invest is very important; when a woman starts working after college, she will, on the average, make 76 cents on the dollar compared to her white male counterparts; men with a high school diploma make more money than women with a college degree, so a woman needs to continually strengthen her mathematical skills. She urged the girls to believe in themselves and to work hard. "In the end, the numbers will be in your favor."
Maria Franzetti, a Senior Applications Programmer at New York Life, graduated with a B.S. in math when computers were a new phenomenon. After taking the only two courses offered on computers and doing an honors project, she was sure that she wanted to work in that field. She started her professional life at a small insurance company --- to "get some experience" --- and soon found herself writing programs in COBOL. During this time, she wondered how she would use her math knowledge --- all the formulas and theorems, along with the set theory and math analysis. To her surprise, she learned about all aspects of insurance, but never once was asked to solve a parabolic equation. What she did use was her math training in logical mathematical processes. She worked with the ingrained conviction from all her math courses that there must be a simple logical approach to each program she was asked to write: step by step, cause and effect, building block upon building block, she proceeded to complete the program to meet user definition. This is not to say that she didn't use her math at all, for some insurance formulas can get complicated and she had to understand the math behind them, or debug the formulas when they didn't work in the programs. Gradually, she gravitated towards those problems and assignments that dealt with actuarial analysis and soon became the liaison person between the actuarial department and the computer division. In this role she found the perfect niche which melded her math background with her computer skills and in which she thrives. In summing up, she noted that her math degree was something that she has always cherished and enjoyed --- the mathematical discipline has served her well in career and life.
The third panelist was a mathematician from the National Security Agency, Ms. Heather A. McMonagle. Heather was motivated to pursue studies in mathematics by the wonderful discussions she had with her grandfather who was a professor of mathematics. She majored in math at SUNY, Albany and was planning to become a high school math teacher. While studying for her master's degree, NSA came on campus to interview math majors and never let her go. She loves her job doing analytical work to solve real world problems, but, in particular, she loves the fact that NSA advocates versatility, which enables her to teach in various programs. In ending, she stressed that students must prepare themselves for the professional workplace with the academic skills necessary to execute their dreams.
The fourth panelist, Dr. Jennifer Phillips, an agronomist from the Goddard Institute for Space Studies (NASA), worked in the field of fashion design for the first ten years of her adult life, but found it unfulfilling and then went on to college. She is currently working on the problem of growing food in space and often travels to foreign countries to confer with engineers, soil scientists, economists, etc. She left the girls with two major thoughts: 1) Don't avoid the natural sciences even if you think you want to go into social sciences or people-oriented work since math and science will only sharpen your logical thinking skills and improve your ability to do problem solving and 2) Try not to let your confidence fail. Believe in yourself even when the world around you may not perceive young women as having strong math or logical skills.
The forum was then opened to the audience so the participants could ask questions. Clearly, the girls were captivated by the words and work of the panelists.
Teachers and students then attended two workshops of their choice. Students were very excited about the workshop on coding given by Heather McMonagle. Her workshop addressed how to make/break various substitution and transposition systems. Students received handouts corresponding to slides, and through the exercises and practice in discovering properties were able to successfully break two unidentified messages at the end of the hour. It was a moment of triumph!
Students were also very happy with the workshop on the five Platonic Solids which was led by two graduate math students at St. John's. Using computer images, manipulatives, and handouts, they engaged the students in discussions of the mathematical properties of these solids, and then guided the participants in constructing models of them. One teacher who attended commented that the enthusiasm of the leaders was infectious.
We decided to celebrate the lives of four pioneer women of the mathematical sciences in a poster exhibition presented during lunch.
The first poster profiled the life of Rear Admiral Grace Murray Hopper ("Amazing Grace," 1906- 1992), a mathematician (Ph.D., Yale University, 1934) and leader in the field of data processing who dedicated her life to the Navy. In 1952, she finished her first practical compiler (the language processor that translates an entire high-level language program into its machine language equivalent) and by 1960, she developed COBOL which is used to this day. In 1945, she traced an error in the Mark II computer to a moth trapped in a relay. The bug was carefully removed and taped to a daily logbook. Since then, whenever a computer has a problem, it's referred to as a bug. An excellent teacher, her favorite admonition to a class of aspiring naval officers was "remember your nanoseconds" (a billionth of a second) in writing efficient programs.
In her retirement speech, Admiral Hopper talked about moving towards the future and stressed the importance of giving young people positive leadership. She spoke widely on the dangers of stagnation. In her opinion, the most damaging phrase in the language is "We've always done it this way." Embracing the unconventional, the clock in her office ran counterclockwise. Her signature message to the world was, "Be innovative, open-minded and give people the freedom to try new things." After her lifelong efforts to do this, she declared, "It is easier to beg for forgiveness than to ask for permission."
The second poster profiled the life of Evelyn Boyd Granville (1924 - ), one of the first two black women in the U.S. to receive a doctorate in mathematics (Yale University, 1949). As an undergraduate at Smith College, Evelyn concentrated her studies in mathematics, theoretical physics and astronomy. After receiving her Ph.D., she accepted an appointment at Fisk University which attracted very capable math majors including Dr. Vivienne Malone-Mayes, profiled below. In July 1952, Evelyn returned to her home town of Washington, D.C. and began a 15-year span of positions in government and industry including orbit and trajectory computations ("the most interesting job of my lifetime"), numerical analysis and computer procedures for Projects Vanguard, Mercury and Apollo. She continually developed expertise as an applied mathematician.
In the summer of 1967, due to a decline in government contracts, Evelyn accepted a teaching position at California State University at Los Angeles, from which she retired in 1984, and shortly thereafter joined the faculty of Texas College in Tyler, Texas where she taught computer science until 1997. In 1989, she wrote, "My plans for the future are not firm, but I know I want to be involved in the educational process in some way. The excellent education and training I was privileged to receive place upon me an obligation to improve educational opportunities for others."
The third profile was of Dr. Vivienne Malone-Mayes (1932-1995). Vivienne received her B.A. and M.A. from Fisk University in Tennessee and, in 1961, during the heat of the civil rights movement, was accepted for doctoral studies by the University of Texas at Austin (Ph.D., 1966). Commenting on her intellectual experience at Fisk, she recalled, "One thing that I really felt Fisk had done to me was give me a sense that learning was an important thing." Two of her math professors, Evelyn Boyd Granville and Lee Lorch, directly shaped her future. Because of their influence, she changed her major from chemistry to math. "The greatest thing they did for me was teach me how to read mathematics. Lorch said, `You never sit down with a math book without a pencil and paper beside you.' He believed that students could understand the material, not just learn to do it. He was interested in teaching them the why of mathematics in addition to the how...."
In her teaching, Vivienne sought to give her students tools of self-empowerment --- she taught them to read mathematics and how to identify and solve problems. She tried to convey that math is a tool for dealing with the world, that logical and reasoning skills should not be isolated and used only in the classroom, but should be applied to life. She also believed that it was critical to allow people the room to fail: "We show the theorems that have been proven, and the correct answers, not the failed attempts and dead ends. But mistakes and false starts are critical to growth and learning."
The isolation that Vivienne experienced in her first year of doctoral studies was very difficult. She had no one to study with, but her philosophy was that ultimately you have to take it on your own shoulders. "You can't ask anybody to help out --- no one owes you this.... If you flunk, well, you just took too much. I just did the best I could." Vivienne's perseverance paid off. In the end, she not only succeeded in getting mostly A's, but was offered a job at Baylor University where she had earlier been denied admission to graduate school.
The final poster featured Patricia L. Eng, a nuclear engineer, who is currently Chief of the Transportation and Storage Inspection Section at the U.S. Nuclear Regulatory Commission. Patricia didn't plan to be an engineer while growing up, but rather wanted to be a ballet dancer or a gymnast. In the process of studying physics, and particularly the physics of the human body in motion, she gravitated to engineering. Hardly any two days are alike in her work. "Some days, I get very technical and look at engineering calculations to determine if a design is right or not, and sometimes I get out to the field where I can see hardware and how it is made. On a few occasions, I go overseas and see how different nations solve the same problems in different but effective ways."
Ms. Eng thinks the biggest challenge she has had in her career has been to know herself and trust her instincts, particularly in knowing her strengths and compensating for her weaknesses. Her current goal is to do well in her new job. She must completely change how her group is doing business, but in a way that "we are all empowered and we work together to develop the solutions." Her guiding words are, "If you are thinking of studying engineering, hang out with women who have gone into engineering.... See the possibilities and find people who can help you hang on. Then someday, you will be there to help someone else hang on."
After lunch, all gathered to hear the day's guest speaker, Ms. Peggy Oliveira, a multimedia consultant who majored in mathematics at St. John's University. Among her many professional credits, she has designed and built several computer games for the Walt Disney World Epcot Center and various computer museum venues.
Ms. Oliveira noted that if you had asked her 15 years ago, at her college graduation, if she would be doing the type of work that she does today, she most certainly would have laughed. At that time, it would have been very difficult to even imagine the tremendous impact that technology and new media would have on the economy and the workplace. Two of the jobs she has held since college did not exist when she graduated. Luckily, she was able to apply her non-job-specific math skills (logic, reasoning and problem solving) in creative ways in these new work environments. Based on her experience, she shared three rich insights for those just starting to think about the work world that they will enter:
You will have jobs in the future that do not exist today. You will develop and work on products, projects and processes that you cannot imagine right now. This will be both exciting and terrifying. You will need a solid education to be ready to meet these new challenges and to get the great jobs. Your formal education is only the beginning --- you will have to continually learn to keep up in your industry.
You will have to be a team player --- and sometimes a team leader. One of the important skills you need to develop is the ability to work well with a diverse team of people --- good teams are able to blend their different skills together to achieve new ideas and results.
You have a unique set of talents and gifts. Part of your lifelong job is to find those gifts, develop them, and use them in ways that bring joy and other good things to you, your family and the community.
To end the day, students participated in three fun math bowls, one for freshmen and sophomores and two for juniors and seniors. The problems were challenging and revealed some very clever reasoning by the students. A New York Hall of Science puzzle was given to each participant as a prize.
The student evaluations revealed an appreciation for the information and experiences of the day:
The morning panel helped me think more of what I would like to become. The talks changed my feelings about mathematics because now I know many different fields mathematics can branch off into.
Before today, I didn't consider taking mathematics as a major. Now I would.
Math now seems more relevant to everyday life. I liked learning that there is a lot of math in the heart for this linked math and science.
And from the teachers:
The panel of speakers was a powerful reminder of the importance of role models in encouraging young women to study math.
The panelists were very good. Their honesty about their challenges was important to share. I think it was great for the girls to hear that there are hurdles to overcome.
We need more days like Sonia Kovalevsky Day!
Once again, we would like to thank AWM for their unfailing cooperation and commitment, without which we could never have accomplished as much for the teachers and students.
On Wednesday, March 24, 1999, Ursuline College held its Women in Science and Math Day, of which the Sonia Kovalevsky High School Mathematics Day was a major component. This event was sponsored by the Association for Women in Mathematics and Ursuline College's Math and Science Departments, along with assistance from the Cleveland Scholarship Program. The inclusion of the Sonia Kovalevsky High School Mathematics Day as a focus of the event marks this as Ursuline's most successful Women in Science and Math Day. Ursuline was extremely pleased that 174 local high school students and twenty-eight teachers from twenty-eight schools participated. These numbers represent twice the number we originally anticipated. The participating schools ranged from small private schools to the large inner-city schools of Cleveland, Ohio, reflecting a positive trend in the increasingly larger number of minority students attending our program.
At 8:45 a.m., the students were greeted by Ursuline math and science students (navigators) and directed to the registration area where they received a packet of information. They were then welcomed to campus by Ursuline College President, Sister Diana Stano. After enjoying a continental breakfast and some mingling, students and teachers were guided by navigators to the first hands-on session of their choice. Throughout the day eleven hands-on sessions were available to the students. The sessions which focused on or included math concepts were as follows: Graphic Material, The Plot Thickens (plotting numbers with technology), Cardiovascular Fitness (utilizing formulas for EKG's, blood pressure, pulse, etc.), Nutrition & Wellness (using math in balanced diets), Fast Reactions (using math in chemistry), and The Web of Life (technology and math and science).
In addition to the hands-on activities, participants had the pleasure of listening to and talking with two speakers, both successful representatives of their fields. The keynote speaker was Dr. Tammie Bettinger, Coordinator of Scientific Research at the Cleveland Metroparks Zoo. Dr. Bettinger, in the course of giving a lively account of her experiences as a researcher at the zoo, emphasized how valuable her first career, accounting, and her background in mathematics is to her present career. The luncheon speaker was Catharine Mayhew, Biostatistican at the Cleveland Clinic Foundation. Ms. Mayhew engaged the participants with a narrative of her entry into her field and an account of the opportunities and challenges for women in the field of mathematics.
Throughout the day, conversation between professional women, college students and high school students was invaluable. Participants learned about the many interesting and diverse careers available to them if they develop good problem-solving skills and analytical thinking. They were given the opportunity to learn more about the role mathematics plays in many areas and disciplines. The high school students gained insight from the college students with respect to math majors, job opportunities and course loads. They were impressed with the variety of careers math majors were considering. Teachers were fascinated with the workshops and took away ideas for their own classrooms.
In a follow-up meeting one week after our event took place, the organizers discussed the strengths and weaknesses of our program and brainstormed ideas for next year. The organizers' assessment was that the event was an extremely successful one. Comments of the participants varied from such positive responses as "It was a very educational experience.... I loved the teachers' interest in the students and the topics being taught" to more negative reactions like "The hands-on session was boring." While the individual evaluation responses were mixed, the overall response was positive. Based on evaluation responses, at least 68 girls were helped to narrow their college/career choices. 117 of the girls felt the experience was a valuable and worthwhile one.
One of our most significant and successful changes from the previous year was the increase in hands-on sessions, and after much discussion it was agreed that even more choices in hands-on sessions should be provided next year and that perhaps an alternative format for the sessions be considered. Other suggestions were that we have only one speaker, or at least separate the speakers with hands-on sessions, and that we have a panel of professionals in the fields of math and science at the luncheon. In addition, it was agreed that, rather than a panel of coordinators, one coordinator who then delegates to others throughout the college would be more effective.
Faculty, staff and students at Ursuline College all feel that the Women in Science and Math Day and the Sonia Kovalevsky High School Mathematics Day is a worthwhile undertaking, and they are enthusiastic about next year.
Valdosta State University
Kathy Simons and Denise T. Reid
The fourth Sonia Kovalevsky High School Mathematics Day (SK Day) at Valdosta State University (VSU) in Valdosta, Georgia was held on Thursday, April 15, 1999. It was supported by a grant from the Association for Women in Mathematics, the National Security Agency and Coppin State University. Sixty students and twenty teachers from thirteen schools attended. Some participants came from across town while others made at least a two-hour trip to VSU. The students were sophomores and juniors. Many had never previously attended a math day of any kind.
The participants had a full day of activities. There were three workshops, one on graph theory, one on chaos, and one on binary numbers. The graph theory workshop was led by Dr. Gerald Petrella from VSU. During this activity, the students learned about conflict resolution and map coloring. The chaos workshop was led by two VSU mathematics students, Ms. Parmy Singh and Ms. Kim Collier. The binary number workshop was led by Dr. Denise T. Reid, also from VSU. During this workshop, the students were each given a set of "magic cards" and shown the binary mathematics behind the trick. The evaluations completed by the participants clearly indicated that the workshops were a success. The students enjoyed the hands-on activities and the interaction among the participants. The career speakers for the day were Ms. Becky McDuffie, an architect, and Ms. Yvonne Lutz of the NSA. Both speakers talked about their jobs and the mathematics involved. Ms. McDuffie's presentation included a slide presentation. Dr. Mary Fares stopped by during the day to talk with the students about the engineering program at VSU. Also included in the activities for the day was a mathematics competition consisting of twenty-five multiple choice questions.
Juice, donuts, and muffins were available when the participants arrived. During this time, the participants registered and mingled. They also had a chance to look at several displays. These displays included posters of the Platonic solids, Fibonacci numbers, and architectural design; brochures on mathematics and career opportunities; origami models and models of Escher Kaleidocycles from a previous SK Day; and a scrapbook of previous SK Days at VSU. Later a buffet lunch was served. During lunch the participants got a chance to interact with each other as well as with speakers and VSU mathematics' faculty.
Door prizes were given to both students and teachers at the opening and closing of the day's events. There were a total of ten student prizes and six teacher prizes. Texas Instruments donated six TI-36 calculators. Other donations for the day included a dictionary by Houghton Mifflin and pencils by Langboard, Inc. At the closing, the winners of the mathematics competition were announced. The first prize was a TI-92 calculator. The second and third prizes were electronic organizers.
Also in attendance for the day was Dr. Mary Kay Corbitt, Associate Dean of the College of Arts and Sciences. Dr. Corbitt gave the opening remarks of the day which included a biography of Sonia Kovalevsky. There were also several student volunteers present throughout the day. These were VSU students enrolled in mathematics classes.
The day was a success in many ways. Participants completed questionnaires at the end of the day. The responses were very positive. They appreciated the opportunity to be included in such an event. The favorite events of the day were the workshops and speakers. Both teachers and students expressed an interest in attending another SK day. This day would not be possible without the grant that you so generously gave us. We truly appreciate the opportunity to show these young girls how exciting and rewarding mathematics can be.