Extending the Concept of Number in a Playground for Learning Mathematics
Researchers from the Dynamic Number Project brought mathematics to life by explaining and demonstrating their work in the 2011 Moore Lecture last week at the Friday Institute for Educational Innovation.
“Mathematics education researchers have been highly innovative in the way they have developed technology and to explore how mathematics and math learning can be re-conceptualized through the use of multiple and dynamic representations available in various software applications—not just putting math into technology but actually seeing what the technology does to mathematics,” said Dr. Jere Confrey, Senior Research Fellow, Joseph D. Moore Distinguished Professor and Dynamic Number Project advisor.
The Dynamic Number Project uses the Geometer's Sketchpad, a dynamic geometry software application, to construct and explore concepts from number and algebra, including fractions, decimals, and functions. In Sketchpad, students and teachers create geometric functions and can drag input points to determine output points, produce visual images of compositions, and even transform photographic images.
The seminar was presented by project team members from KCP Technologies, the research and development arm of Key Curriculum Press: Senior Scientist Dr. Daniel Scher (Principal Investigator), KCP Technologies President Steve Rasmussen (Co-Principal Investigator), and Senior Curriculum and Materials Developer Scott Steketee.
"With even a brief amount of play and working with these fractions in a dynamic geometric setting, students gain significant understanding,” said Dr. Scher. “These strong, dynamic visual representations help students resolve confusion over the nature of fractions. By building any fraction whatsoever with the software, especially fractions like 1/500 or 13/57 that students don’t typically encounter, young learners gain powerful insights into the properties of fractions."
The Dynamic Number Project research has been conducted with students in grades 2-8. Sketchpad’s dynamic environment is ideal for this project because its representations are visually compelling, animations of the numbers and functions are easy to build, and experiments are simple to perform.
“The Sketchpad application has the ability to geometrically transform photographs and illustrations. “With this program students develop an understanding of how the fancy computer graphics they see on television come from mathematical functions,” explained Steketee.
Dr. Confrey, host of the event as the Joseph D. Moore Distinguished Professor of Mathematics Education, concluded, “The importance of the Dynamic Number Project is that it examines how the concept of number can be extended when placed into a dynamic geometry environment. The inherent discreteness of numbers can be juxtaposed with the inherent continuity of lines, regions and angles, and explored for new meanings supported in technological contexts and tools.”
Introducing Dynamic Number as a Transformative Technology for Number and Early Algebra is a research and development project undertaken by KCP Technologies to extend and operationalize research in number, operation, and early algebra. For more information regarding the Dynamic Number Project visit: http://www.kcptech.com/dynamicnumber and Geometer’s Sketchpad visit: http://www.dynamicgeometry.com/