Mystery Plots: Motivating Algebraic Model Building with Dynamic Sketches

Abstract

In this paper, we explore the use of dynamic geometry software (DGS) as a medium for changing student and teacher interactions (and attitudes) with functions. We o er three examples of sketches that may be used to encourage students to build their own functions. Moreover, we share a strategy for developing additional sketches, namely our three-step MTA process (Measure - Trace - Algebratize). Note that these steps roughly correspond to concrete, iconic, and symbolic levels of representation proposed by Bruner (1960; 1966). As our examples illustrate, the MTA approach provides students with opportunities to explore and construct remarkably non-standard functions - often beautiful, unexpected, and thoroughly original.