From a problem solving perspective, this article analyzes the physical and mathematical properties of the mirascope and further seeks to model the mirascope using new dynamic learning technology. Open-ended explorations will be discussed using the mathematical mirascope, showcasing the integration of algebra and geometry and the affordances of technological tools. Several intermediate dynamic worksheets are provided as scaffolding to serve the diverse needs of readers.
This article uses the open-source mathematics learning environment GeoGebra as a primary platform. Java runtime is required to access the dynamic materials. Although GeoGebra installation is not required, readers are advised to have GeoGebra running through either WebStart or local installation in order to experiment with the ideas proposed in the article. It is also worth noting that right-clicking in GeoGebra provides users with most tools related to a mathematical object such as tracing and styles.
(Each of the links below opens a Geogebra activity in a new window.)