Using technology to explore mathematical relationships: a framework for orienting mathematics courses for prospective teachers

The technological revolution that has finally permeated K-12 education has direct implications for modern teacher educators whose “Hippocratic oath” is to best prepare future teachers for twenty-first-century classrooms. The goal of this article is to suggest that the heart of sound technological implementation is to encourage students to use whatever tools are available to explain the mathematical relations that underlie what they observe on the screen. We suggest ways in which Mishra and Koehler’s construct of Technological Pedagogical Content Knowledge may be customized to provide a framework for guiding prospective teachers’ efforts to develop and assess lesson plans that use technology in novel and effective ways. Data are presented in the form of two contrasting case studies to illustrate the differing degrees to which prospective mathematics teachers leveraged technology to teach themselves and their future students to explain the mathematics behind various topics.