In this report, we give a sociocultural account of the mediating functions handheld graphing calculators and social interaction play in students' mathematical understanding. We discuss the evolution of students' abilities to symbolize, model, and develop collective mathematical practices about polynomial inequalities in instrumented activity. In our sociocultural model we foreground the social nature of technological tools and the social transactions that take place in a classroom context which assist students as a collective to establish viable shared practices and collective representations. Graphing calculators as psychological tools are characterized as providing intentional, transcendental, and social mediation. [For complete proceedings, see ED489597.]