While one branch of literature is replete with investigations of problem solving and another branch frequently investigates student use of dynamic mathematics environments (DMEs), most of the studies in both of these fields consider whether or not students can solve problems. Far fewer number of studies consider the cognitive processes associated during either problem-solving experiences or DME use and only a handful of studies consider cognitive processes associated with problem solving when working in a DME. This paper reports a novel approach to investigating, defining, and categorizing the cognitive processes used by students in mathematical problem-solving while working in a DME with examples found in student work. Using this approach, problem-solving is found to be nonlinear, iterative, and idiosyncratic. Insights gained by this analysis have both theoretical and practical applications in mathematics education.