We discuss classroom activity comprised of small groups of students collaboratively tinkering with programs of dynamically manipulable figural models, posing problems regarding their mathematical properties and behaviors. We analyzed data from students' discourse taken from two classroom interventions employing a framework of creative mathematical action-in-context, in order to study student-generated ideas. We approached students' actions taking a fallible mathematics epistemological approach and employed constructionist and social creativity theory in our analysis. Our results show that student agency in the disciplined field of mathematical thinking need not curtail the potential for undisciplined creative action: on the contrary, given appropriate tools and discursive environments it may in fact create space for actions with creative potential for students. On their own accord, the students in the study used generalized number theory to resolve engineering a parallelogram that can never be a rectangle, and used recursion to program a model embedding geometrical progression in order to create a spiral based on the golden ratio.