Collective and Individual Mathematical Progress: Layering Explanations in the Case of the Sierpiński Triangle

This paper presents methodology aimed at developing a rich understanding of the interplay of mathematical progress in the different social settings in which learning in inquiry-oriented classrooms occurs: individually; in small groups; and as a whole class. For this purpose, we enhance a theoretical-methodological approach of coordinating Documenting Collective Activity and the Recognizing-Building-Constructing model of Abstraction in Context that have been developed in earlier studies. We do this using an intact lesson on the area and perimeter of the Sierpiński triangle in a mathematics education master’s level course on Chaos and Fractals. The enhancement of the methodology allows integrating Collective and Individual Mathematical Progress (CIMP) by Layering the Explanations (LE) provided by the two approaches, and thus exhibits the complexity of learning processes in inquiry-oriented classrooms.