Розділ 2. Спрямованість навчання дисциплін природничо-математичного циклу на розвиток інтелектуальних умінь та творчих здібностей учнів та студентів

УДК 372.851

V. Watson, M. Garner, T. Rudchenko

Kennessaw State University, USA

V.Watson, M.Garner, T.Rudchenko THE HISTORY AND FUTURE OF MATH CIRCLE ACTIVITIES AT KENNESAW STATE UNIVERSITY

A 2011 KMUMC talk by Dr. Watson on math circles for students and teachers inspired a new collaboration on the KSU Math Circle for area high school students. The KSU Math Circle Summer Camp is a two week summer program where high school students work with mathematicians on involved projects. Generously supported by two Dolciani Mathematics Enrichment Grants, students listen to presentations by mathematicians, participate in mathematical activities and present their work at the end of the two weeks to an audience of students, parents and mathematicians. We will discuss the last two years of the Kennesaw State University Math Circle and future plans.

Keywords: math circle, mathematical activities, gifted and talented students, NAMC, Dolciani grant.

Introduction. There is a national Math Circle movement in the United States. According to the National Association of Math Circles (NAMC), “Mathematical Circles are a form of education enrichment and outreach that bring mathematicians and mathematical scientists into direct contact with pre-college students.” These students, and sometimes their teachers, meet with mathematical professionals in an informal setting, after school or on weekends, to work on interesting problems or topics in mathematics. The goal is to get the students excited about the mathematics, giving them a setting that encourages them to become passionate about mathematics. Students work with mathematicians to solve interesting problems in a collaborative, supportive environment. Since 2009, there has been a collaborative team working on math circles for teachers and students at Kennesaw State University (KSU).

The Metro Atlanta Math Teacher’s Circle. At the 2009 Joint Mathematics Meetings in Washington DC, Virginia Watson attended a talk where she learned about math teachers’ circles. She returned to Atlanta and assembled a team of KSU faculty, middle school administrators and middle school teachers. Dr. Mary Garner of KSU, Dr. Virginia Watson of KSU, Ms. Angelique Smith, Principal at Champion Theme School, Ms. Barbara Johnson, a middle school teacher at Champion Theme School, and Dr. Brian Davis, Assistant Principal at Pine Mountain Middle School attended the How to Run a Math Teachers’ Circle Workshop at the American Institute of Mathematics (AIM) that summer. At this workshop they planned the launching of the Metro Atlanta Math Teachers’ Circle (MAMTC).

The first Metro Atlanta Math Teachers’ Circle meeting was in September of 2010. At the beginning the meetings moved around from KSU to Pine Mountain Middle School to the Champion Theme School. Now meetings are all held on KSU’s campus. We meet three times in the fall and three times in the spring. We are a mixture of middle school and high school teachers. We have from seven to ten participants at the meetings. The organizers of the MAMTC are Dr. Virginia Watson, Dr. Mary Garner and Ms. Beth Rogers. Some examples of problems we have worked on include the following: How many ways can you write a positive integer as the sum of positive integers? Are there any patterns in 3 x 3 Magic Squares? What patterns are there in Pascal’s Triangle?

We have been supported by two grants. In 2010 we received a National Association of Math Circle seed grant for $2000 and in 2013 we received an American Institute of Mathematics Continuing Math Teachers’ Circle grant for $1900. Our team has made presentations about Math Teachers’ Circles at the Georgia Mathematics Conference, the Mathematical Association of America Southeastern Section Meeting, the National Council of Teachers of Mathematics Meeting, and the Kennesaw Mountain Undergraduate Mathematics Conference. This last presentation led to the formation of the KSU Math Circle which is discussed below.

The KSU Math Circle and Math Circle Summer Camp. The idea for a KSU Math Circle for high school students began after a talk Virginia Watson gave at the Kennesaw Mountain Undergraduate Mathematics Conference (KMUMC) in November 2011. Dr. Tatiana Rudchenko introduced herself to Dr. Watson and said she had worked extensively on math circles in Russia. The two of them, along with Dr. Garner, decided to begin the KSU Math Circle for high school students. To bring attention to this new circle they decided to hold a two-week KSU Math Circle Summer Camp.

2012 KSU Math Circle Summer Camp

The KSU Math Circle Summer Camp of 2012 included thirteen students from six Cobb County high schools. The only requirement for participation in the summer camp was interest in mathematics. The participants met weekdays from 9:00 AM to 4:00 PM, July 16 through July 27. From 9:00 AM – 12:00 PM students worked in teams with a mathematician on a research project. Lunch was provided from 12:00 – 1:00 PM and then from 1:00 – 2:00 PM a guest lecturer addressed the group or the group played games such as Math Jeopardy or toured the KSU campus. From 2:00 – 4:00 PM student worked with their teams on their special research project. At the end of the two weeks, the students presented their work to an audience that included parents, teachers, KSU faculty and students. Several KSU faculty members, along with an outside guest speaker, returned to select a prize-winning team from the four presented projects.

The guest lecturers included:

• Dr. Igor Belykh, Professor, Mathematics Department and Neuroscience Institute at Georgia State University, member of the Center for Nonlinear Science at Georgia Institute of Technology.

• Dr. Andrey Shilnikov, Associate Professor, The Neuroscience Institute, joint with Department of Mathematics and Statistics, Georgia State University.

• Dr. Ron Gould, Professor of Mathematics at Emory University Dr. Alexander Petukhov, Professor of Mathematics at the University of Georgia.

Other lecturers included faculty from the KSU Department of Mathematics and Statistics including Dr. Louise Lawson who gave a talk about her career as an epidemiologist, Dr. Joe Demaio who talked about his research in discrete mathematics involving the movement of chess pieces, and Dr. Sean Ellermeyer who talked about his research involving game theory.

There were four special projects on which the students worked, under the direction of a KSU faculty member. Dr. Josip Derado led a group of students who investigated the mathematics of duels and truels, and developed some facts about geometric series that were needed to study these problems. Ken Keating, a lecturer in the department, led a group of students who focused on Pascal's triangle and various combinatorial identities related to it. Dr. Mary Garner’s group investigated ranking algorithms that required them to learn about ordering of sets, stochastic matrices, and eigenvalues and eigenvectors. Dr. Tatiana Rudchenko’s group explored complex numbers.

Support for the KSU Math Circle Summer Camp was provided by the Dolciani Mathematics Enrichment Grant in the amount of $5656.

We received excellent feedback about the program. The chair of the Department of Mathematics and Statistics wrote: “Based on the success of this event, I foresee that this activity is going to grow and thrive. It is an outstanding example of the efforts that we have been making to engage the community into the life of the university and our department.” One parent said “L's favorite things about your Math Circle were the lecturers, especially the ones from Russia, the "fun Friday" the first week, the final competition, and lunches on the commons. Your university's investment in these students was probably worthwhile because just in our family alone you have created a possible Math major or minor, and we now see KSU as a lot more than a teacher's college. So thanks again for your generosity and organization.”

We held Math Circle sessions for these students every-other Monday during the 2012-2013 school year. We had less than half the students show up at any one of these sessions and sometimes the attendees were new students who were friends of a student from the original group.

2013 KSU Math Circle Summer Camp

The 2013 KSU Math Circle Summer Camp took place from June 10 – 21, and all students were from Cobb County schools. Based on our experience from the 2012 camp, we decided to alter the schedule. The camp was held from 9:00 AM to 3 PM. At 9:00 AM, as campers arrived, we had a quick mathematical challenge waiting for them. Depending on when they finished the problem, sometime between 9:15 and 9:30, the participants would then split into groups to work on a special mathematical project with a KSU faculty member. They would then break for lunch between 12:00 PM and 1:00 PM. From 1:00 PM to 3:00 PM they would interact with a visiting lecturer and sometimes participate in math games with the camp faculty. As in the previous summer camp, at the end of two weeks, each team made a presentation to parents, teachers, KSU faculty and students. Several KSU faculty members select a prize-winning team from the four presentations.

The guest lecturers included:

• Dr. Alexander Ptukhove, Professor of Mathematics from the University of Georgia, who gave two talks “Low-rank Matrices and Their Role in Making Decisions” and “Mathematical Aspects of Image and Video.”

• Dr. Colm Mulcahy, Vice Chair of the Department of Mathematics at Spelman College, who gave two talks on “Mathematical Card Magic.” He is widely known for his use of mind-boggling math-based card tricks, and recently published the book Mathematical Card Magic: Fifty-Two New Effects.

• Dr. Brett Katzman, Chair of the Department of Finance and Quantitative Analyses at KSU, who gave a series of two talks on game theory entitled “Simultaneous Games & Sequential Games.”

Other lecturers included faculty from the KSU Department of Mathematics and Statistics including Dr. Virginia Watson who gave a talk about careers in mathematics, and Dr. Louise Lawson who gave a talk about her career as an epidemiologist

As in the 2012 KSU Math Circle Summer Camp, the project leaders were Dr. Mary Garner, Dr. Tatiana Rudchenko, Dr. Josip Derado, and Mr. Ken Keating. The theme of the Summer Camp was the Mathematics of Planet Earth (MPE), an international program to publicize the role of mathematics in processes affecting our planet. As the MPE site states, “Our planet is the setting for dynamic processes of all sorts, including the geophysical processes in the mantle, the continents, and the oceans, the atmospheric processes that determine our weather and climates, the biological processes involving living species and their interactions, and the human processes of finance, agriculture, water, transportation, and energy.” Dr. Rudchenko led a group of students who explored linear and nonlinear programming models and their application to real-world economics issues. Dr. Derado led a group of students who investigated a variety of problems, including the problem of forecasting the temperature at Kennesaw State University. Mr. Keating’s group used the Simplex method to solve linear programming problems. Dr. Garner’s group learned about graph theory and famous problems including the Traveling Salesman Problem.

We again received funding from the Dolciani Mathematics Enrichment Grant in the amount of $6000 and we were also supported by the KSU Foundation. Students paid a small fee of $90 to pay for their lunch for the two weeks.

The feedback from parents was excellent. During the presentations, one parent asked why the camp couldn’t run longer or have another session. Afterwards, another parent wrote: “Congratulation a successful Math camp! … From what I have seen, this camp was a great success. For my daughter, 80% of what she learned over the last 2 weeks was new knowledge. I think that is great!” A third parent wrote: “The lecturers were very interesting. I really appreciate this free educational opportunity because my family has been severely financially challenged for the past 4 or 5 years.”

Students who participated in the summer have also been participating in the KSU Math Circle in the academic year. We meet approximately every other week on a Monday evening. We provide dinner and the problem to work on. Unfortunately, participation in the KSU Math Circle during the academic year is very limited, with an average of only two or three students attending each session. We have been discussing how to increase participation by holding our meetings in the schools or moving to a Saturday time. We also need to advertise Math Circles more effectively in the schools.

Future Research Activities: Characterizing the Math Circles Experience in the Ukraine to Enrich Math Circles in the U.S. A recent issue of the Peabody Journal of Education concisely summarized the state of mathematics education in the United States (Schmidt, 2012), and also described what studies have shown about promoting the achievement of gifted and talented students (Benbow, 2012). Strong evidence was presented in these articles that even our best students fall behind the students of many other countries in mathematics achievement. The Study of Mathematically Precocious Youth (SMPY), which tracked over 5,000 individuals for 40 years, reported that educational enrichment opportunities in mathematics do correlate with later achievement. Math Circles is an educational enrichment opportunity that is new to this country, and promises to be an effective means of promoting mathematically gifted students. Math Circles have long been active in Europe and Asia and are widely believed to be partly responsible for high mathematics achievement in those countries.

Math Circles were started in this country in the 1990’s. A description of one of the first Math Circles (at Northwestern and Harvard) can be found at [3]. The only student Math Circle operating in Georgia currently is the KSU Math Circle; the nearest circles are in Mobile, Alabama, and Columbia, South Carolina. The KSU Math Teachers’ Circle was also the first of its kind in Georgia. There is no published research on Math Circles. Drs. Watson and Garner are currently finishing some research on Math Teachers’ Circles.

In future research, we would like to describe exactly how Math Circles are conducted in the Ukraine, evaluate their effectiveness, compare and contrast Math Circles in the Ukraine with Math Circles in the U.S., and explore what techniques used in the Ukraine could be adopted by Math Circles in the U.S. For example, online Math Circles are conducted in the Ukraine for students in remote sites who could not normally participate in a problem solving session with university mathematicians; how could we bring online Math Circles to rural Georgia? Math Circles in the Ukraine do not suffer from students’ lack of interest and participation; how could we increase attendance at our Math Circles during the school year?

We plan on participating in a variety of Ukrainian Math Circles, and then compare and contrast Math Circles in the Ukraine with Math Circles in the U.S. We will also develop, with collaborators in the Ukraine, a questionnaire to send to Math Circles in the Ukraine and in the U.S. to get information on their conduct and success. We’ll visit the Ukraine during the week of March 28^th 2014. We hope that this trip will lay the foundation for research that would identify the best ways to engage students in Math Circles, the effects of Math Circles on interest, achievement and retention in mathematics, and help Math Circles in the US attract and engage students. We also hope to lay a foundation for other collaborations such as study abroad.

We have been invited to the Ukraine by Dr. Olga Chashechnikova, Doctor of Pedagogical Sciences and Professor of Mathematics at Sumy State Pedagogical University named after A.S. Makarenko (Sumy, Ukraine). Dr. Chashechnikova, is also the head of the “Scientific-experimental Laboratory of Teaching Mathematics, Physics and Informatics’ Contents and Methods”. The KSU team consists of Dr. Mary Garner, Dr. Virginia Watson, and Dr. Tatiana Rudchenko; this group formed the KSU Math Circle for high school students in Summer of 2012. Dr. Garner, as Mathematics Program Coordinator, has numerous high school contacts; Dr. Watson has had training in conducting Math Circles for both teachers and high school students. Both Drs. Garner and Watson have been doing research on Math Circles for teachers. Dr. Rudchenko has extensive experience with Math Circles in the Ukraine and Russia, and has long been interested in seeking ways to bring more of the success of the circles in the Ukraine and Russia to KSU.

References

1. Benbow, C.P. (2012). Identifying and Nurturing Future Innovators in Science, Technology, Engineering, and Mathematics: A Review of Findings From the Study of Mathematically Precocious Youth. Peabody Journal of Education 87, 16-25.

2. Schmidt, W.H. (2012). At the Precipice: The Story of Mathematics Education in the United States. Peabody Journal of Education, 87, 133-156.

3. http://www.themathcircle. org/kaplanamsarticle.php.

РЕЗЮМЕ

Ватсон В., Гарнер М., Рудченко Т. История и будущее деятельности математического кружка Кеннесийского государственного университета. В 2011 году выступление доктора Ватсон на заседании математического кружка для студентов и преподавателей вдохновило нас на организацию при нашем университете математического кружка для старшеклассников. Математический летний лагерь нашего университета представляет собой двухнедельную летнюю программу, где школьники работают с математиками над предлагаемыми проектами. При щедрой поддержке двух грантов Dolciani студенты слушают презентации математиков, участвуют в математической деятельности и представляют свои работы в конце этих двух недель перед аудиторией учащихся, родителей и математиков. Мы обсудим последние два года работы этой программы и планы на будущее.

Ключевые слова: математический кружок, математическая деятельность, одаренные и талантливые студенты, NAMC, Dolciani грант.

РЕЗЮМЕ

Ватсон В., Гарнер М., Рудченко Т. Історія і майбутнє діяльності математичного гуртка Кеннесійського державного університету. У 2011 році виступ доктора Ватсон на засіданні математичного гуртка для студентів і викладачів надихнуло нас на організацію при нашому університеті математичного гуртка для старшокласників. Математичний літній табір нашого університету є двотижневою літньою програмою, де школярі працюють з математиками над пропонованими проектами. При щедрій підтримці двох грантів Dolciani студенти слухають презентації математиків, беруть участь у математичній діяльності та представляють свої роботи наприкінці цих двох тижнів перед аудиторією учнів, батьків і математиків. Ми обговоримо останні два роки роботи цієї програми і плани на майбутнє.

Ключові слова: математичний гурток, математична діяльність, обдаровані й талановиті студенти, NAMC, Dolciani грант.

УДК 54:378.147-057.875

О.М. Бабенко

Сумський державний педагогічний університет А.С.Макаренка, м.Суми