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.