Systematic approaches to experimentation: The case of Pick's theorem

In this paper two 10th graders having an accumulated experience on problem-solving ancillary to the concept of area confronted the task to find Pick's formula for a lattice polygon's area. The formula was omitted from the theorem in order for the students to read the theorem as a problem to be solved. Their working is examined and emphasis is given to highlighting the students’ range of systematic approaches to experimentation in the context of problem solving and aspects of control that are reflected in these approaches.

Research highlights▶ Students experienced on problem solving can systematize their experimentation while solving a task. ▶ Students develop certain aspects of control during experimentation. ▶ Experimentation allows solvers to make some steps towards typical proof.