A Proposal for the Development of an Interactive Mathematics Laboratory for Mathematics Education
William M. Farmer · 2000
Like Janus, mathematics has two faces. One face is a huge body of knowledge assembled over thousands of years. The other face is a process by which mathematical knowledge is obtained. Mathematics education has traditionally emphasized the first face of mathematics. Students are taught many mathematical facts, but they are rarely taught what the mathematics process is and how to employ it. As a consequence, engineers and scientists today often do not know how to do mathematics, and the population as a whole does not understand what mathematics is and does not appreciate its importance in today’s world. The mathematics process is both a creative and explorative process. Models about the mathematical content of the world are created by defining mathematical structures and concepts, and the models are explored by performing calculations and stating and proving conjectures. The process is the most important face of mathematics. It is the fountainhead from which mathematical knowledge flows and a central component of the infrastructure that makes today’s technological and informational world possible. Every mathematics student needs to learn the mathematics process. Of course, the best way to learn it is to practice it. But high school and university students are given little chance to experience the full process of creating and exploring mathematics. Instead, they are taught merely about byproducts of the process—facts and calculations separated from the process which made them. Many mathematics educators feel that trying to teach students to learn the mathematics process is unproductive, and accordingly, they have argued, for