2009 AWM Essay Contest:

Grades 6 - 8 First Place

### by Angela Pham

When we think of mathematics, we think of it as a solitary subject. We think of mathematicians being closed up in a small room working out complex problems. But for Maria Droujkova, working in math is almost the complete opposite.

“It’s all about people,” Maria Droujkova says. If you want to look into a career in mathematics, you should talk to math people, meet math people, go to math related events, and organize math clubs. First talk to people, then do the math. Math games, math projects, creative math, fun math, beautiful math.

Even in her young years, Maria’s mathematical education was rooted in personal relationships. Growing up in Ukraine, education was much different than in the US. At five she loved solving math problems with her mother. In early school, she found two other children who also loved math. With the help of an encouraging teacher, they found and solved math problems together. “The teacher gave us famous mathematicians' nicknames - mine was Sonya Kovalevska.” In Maria’s adolescent years she turned toward physics, and when she was old enough for the math and science camps that her mother had her attend, she signed up for the physics division.

Maria Droujkova went to Moscow State University, a school respected throughout the Soviet Union, where she studied a branch of chaos theory. Her research led up to her thesis topic at the end of five years, which was “Bifurcations of Heart-Shaped Asymptote Polygons.” The chaos theory appealed to Maria because of the order that lay beneath complex and seemingly random events: even the smallest change can result in a whole new order. She was discovering beauty through her study of mathematics. After Maria graduated, she and her husband started looking for other countries to continue learning in. In the Soviet Union there were many restrictions on people’s activities, thoughts, and speech, even for children. As Maria began looking into math as a career, she saw that it would be too hard to accomplish where she lived. She wanted to research and discover, but Ukraine was closed to new ideas. The economy was so poor that it was almost impossible for mathematicians to work in math. “I saw a lot of my colleagues selling fruits on the streets or doing other random jobs to feed their families, and I'd rather do research.”

Because America was a good place for people who wanted to discover and the opportunities in math and science careers were wide open, Maria, 22, and her husband came to America in 1994 to enter Tulane University in New Orleans. At Tulane she got her MS degree in Applied Mathematics, which is using math in other fields. For example, math can be used to help figure out crimes, as is seen in the television show Numb3rs. Then Maria went to North Carolina State University and in 2004 got her PhD in Mathematics Education. Her dissertation topic was: "Roles of metaphor in the growth of mathematical understanding." Metaphor in mathematical understanding is the explanation of a math principle by associating it with a familiar idea. This research must have later encouraged Maria to begin in her teaching of advanced math to young children.

What’s Maria’s favorite kind of math? Beautiful math. For example, beautiful math is in the patterns of geometric shapes. Maria uses these shapes, such as kirigami snowflakes, to teach things like multiplication. Maria’s main subject of teaching is multiplicative thinking, a central focus in her work. She strives to teach multiplication in a more creative way than just a multiplication table. She encourages students to find several different ways to learn multiplication principles rather than simply memorizing the facts.

Today, Maria works as a self-employed math education consultant near Raleigh, North Carolina. She speaks at conferences and works with other educators on math projects. Her company, Natural Math LLC, offers students fun activities, software, math clubs, and advice. Maria teaches kids and parents how to accept and love math by teaching them the beauty of it. She gives her classes different creative projects to learn complicated and advanced math that would normally be taught to older students. For example, she teaches three to six year olds about fractals. She also explores psychology and develops theories on how the human brain works when it encounters mathematical problems or patterns. Home-schooling gives her a full time job and a laboratory. “I am very happy to say that my ten year old daughter is growing up in the atmosphere where she can appreciate the beauty of mathematics. When she claps her hands excitedly upon seeing an especially elegant proof, or figuring out a tricky problem, or creating a handy representation, I can see we are doing something right.”