The notion of definition is a central building block of mathematics. In addition to specific definitions, it is desirable that students learn about meta-mathematical aspects of definitions such as their role of classification, and about characteristics of definitions such as arbitrariness. We investigated how such meta-mathematical aspects emerge when students are led to construct a definition such as point of inflection or tangent line, and how the constructing process interacts with meta-mathematical aspects. We used Abstraction in Context as theoretical framework because of its suitability to analyze processes of knowledge construction. We found that meta-mathematical aspects of definitions influence and are influenced by students' processes of constructing definitions. We argue that awareness of meta-mathematical aspects improves students' conception of mathematical definitions.