Didactic situations in project-based learning: The case of numerical patterns and sequences

The article presents a multiple-case study examining the project-based learning model where mathematical projects of middle school student teams originate from different tasks on the topic of numerical sequences. Learning situations in PBL are identified and characterized using the analytical apparatus of the Theory of Didactic Situations. A long-term project can be conceptualized as a complex system of alternating didactic situations shaped by the interaction of students and teachers with the global milieu and the local milieu of each student team. Students' transition from open to a structured inquiry by self-constraining the milieu was a successful strategy that promoted acculturation to ways of mathematical exploration. The student project's milieu can be modified by introducing auxiliary problems containing elements necessary for future mathematical situations. The situations of institutionalization in PBL are dedicated to the processes of mathematical exploration as well as mathematical content. The practical principles for implementing PBL into mathematics instruction are presented.