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The purpose of this article is to show how the philosophical theory of inferentialism can be used to understand students' conceptual development in the field of mathematics. Based on the works of philosophers such as Robert Brandom, an epistemological theory in mathematics education is presented that offers the opportunity to trace students' conceptual development in both its individual and social facets through analyzing patterns of reasoning. A design experiment on decimal numbers serves as a paradigmatic example. The overall goal is to illustrate the relationship between mathematical standard and individual ways of reasoning in conceptual development processes. [ABSTRACT FROM AUTHOR]

There is a long tradition in mathematics education that deals with analyzing the role of social norms to mathematical learning processes as well as the notion of individual factors influencing these processes. The epistemological extension of conducting different theoretical approaches in order to capture both individual and social aspects of learning has offered many new insights when combining individual-cognitive and social perspectives. This paper introduces a theoretical framework, which puts individual commitments and inferences to the fore in order to analyze processes of individual concept formation and the discursive practices. Within this perspective, the social and the individual are no more dualistic poles that refer to different underlying principles when analyzing mathematical learning. Instead, the emergence of new individual commitments will be explained within the discursive practice of acknowledging and attributing commitments. In this perspective, the social and the individual dimension of concept formation can be explained within one coherent theoretical perspective. The theoretical framework will be illustrated by empirical examples from a design research study on algebraic concept formation processes. [ABSTRACT FROM AUTHOR]