Problem-Solving and Mathematical Research Projects: Creative Processes, Actions, and Mediations

Abstract

Based on the idea that the creative process is one that involves skills that can be learned and developed with practice, this chapter presents the design and development of a Mathematical Research Project (MRP) for teaching. It examines the output and development of the modalities of mediations during processes of instrumental genesis working from problem-solving tasks (PST) to arrive at Mathematical Research Projects (MRPs). We will respond to the question: What teacher mediations articulate student creativity in Mathematical Research Projects? It will specify (1) identification of the student’s activity by the teacher – the operational mathematical invariants of the students’ schemes, the cognitive processes the student puts into action, and the domains of mathematical knowledge – and (2) mediated activity between the teacher and students regarding the instrument, the object, and the subject.