Math majors' visual proofs in a dynamic environment: the case of limit of a function and the ϵ–δ approach

Abstract

Despite few limitations, GeoGebra as a dynamic geometry software stood as a powerful instrument in helping university math majors understand, explore, and gain experiences in visualizing the limits of functions and the ϵ − δ formalism. During the process of visualizing a theorem, the order mattered in the sequence of constituents. Students made use of such rich constituents as finger-hand gestures and cursor gestures in an attempt to keep a record of visual demonstration in progress, while being aware of the interrelationships among these constituents and the transformational aspect of the visually proving process. Covariational reasoning along with interval mapping structures proved to be the key constituents in the visualizing and sense-making of a limit theorem using the delta-epsilon formalism. Pedagogical approaches and teaching strategies based on experimental mathematics – mindtool – consituential visual proofs trio would permit students to study, construct, and meaningfully connect the new knowledge to the previously mastered concepts and skills in a manner that would make sense for them.