On the Emergence of Mathematical Objects: the Case Of

In this report we propose an alternate account of mathematical reification as compared to Sfard’s (1991) description, which is characterized as an “instantaneous quantum leap”, a mental process, and a static structure. Our perspective is based on two in-service teachers’ exploration of the function f (z) = e , using Geometer’s Sketchpad. Using microethnographic analysis techniques we found that the long road to beginning to reify the function entailed interplay between body-generated motion and object self-motion, kinesthetic continuity between different sides of the “same” thing, cultural and emotional background of life with things-to-be, and categorical intuitions. Our results suggest that perceptuomotor activities involving technology may serve as an instrument in facilitating reification of abstract mathematical objects such as complex-valued functions.