Dr. Super's Triangles: Making Math Fun
		By Anne Bentzel

		Wearing his signature cowboy hat, bolo tie, and boots, Mark A. Spikell, Graduate School of Education, stands before a group of first graders holding up a bright purple triangle. "Which one should I put down? The purple one?" he asks the class at Waterford Elementary School. Students giggle and shout, "No, the green one." Spikell and his colleague Behrouz B. Aghevli, an affiliate professor at George Mason and a senior information officer at the World Bank, are engaging the students in a Bingo-like game in which students place triangular plastic pieces on a game board. "What they are really learning is transformational geometry. They are beginning to recognize shapes and discover how slides, flips, and turns can form new shapes," says Spikell. Spikell serves as the official mathematician-in-residence at Waterford Elementary, a K-5 grade school in Loudoun County. "We have had a sculptor, a poet, and an artist-in-residence, but we wanted to expand our program to include science and math," says principal Joyce Smith. Smith learned about Spikell through a packet of math problems published by the Virginia Math and Science Coalition that was sent home to students. A parent was so impressed with the quality of the problems that she called the coalition to find out more about the packet. "When we discovered a professor at George Mason was involved, we called to see if he would be interested in volunteering some of his time to teach math to our students," says Smith. For Spikell the chance to work with students, parents, and teachers to help enhance the math curriculum was an opportunity he couldn't resist. The first thing Spikell asked the students at Waterford Elementary was how they pictured a mathematician. "Some of them told me a mathematician was a magician. A few of them said a mathematician was a man at a university who spent hours in a little office coming up with formulas," he says. "What I want the students to recognize is that they are all mathematicians. From learning to organize information and keep records to learning how to make difficult choices from among different alternatives, everyone uses various aspects of math in their daily lives."
Related Links GMU Grad. School of Ed.		Teaching at Waterford Elementary also afforded Spikell and Aghevli a chance to discover up close how some new manipulatives they developed--plastic triangular and cubic pieces--work with school children. The manipulatives--which they call Dr. Super's Triangles--along with the text that Spikell and Aghevli created, allows students to gain a visual, spatial understanding of fractions, geometry, and algebra. "So many students learn math through memorization. A formula is presented to students, they memorize it and apply it, but they never quite grasp the concept," says Spikell. "Manipulatives allow students to use concrete, physical shapes to develop a deeper understanding of the concept." Aghevli came up with the idea for Dr. Super's Triangles while his daughter was learning math in school. "I started looking for teaching games I could play with her, but I wasn't happy with what I found, so I developed Dr. Super's Triangles." Realizing that he needed help testing his ideas and creating a curriculum to accompany his invention, Aghevli asked Spikell to collaborate with him. Last year Aghevli discovered an ancient Babylonian tablet that used a similar triangular pattern to the one he uses in his game. The tablet anticipates the Pythagorean theorem about 1,200 years before Pythagoras's birth. "It is wonderful to find a connection to ancient history. We have woven it into the curriculum," says Aghevli. Spikell and Aghevli are looking toward the future. Their next step: using Internet technology to bring virtual manipulatives to the classroom. "We are working to develop the resources with technology that teachers, even those teachers who lack mathematical skills, can use to teach students to go beyond formulas and equations and to finally reach a good understanding of the important, relevant skills and concepts," says Spikell. "We want to revolutionize teaching."