A new ontology of reasons for inferentialism: redefining the notion of conceptualization and proposing an observer effect on assessment

Abstract

The purpose of this paper is to propose a new ontology of reasons for inferentialism. The existing inferentialist approach to mathematics education has a methodological challenge in retrospective analysis and a noncollaborative issue stems from a narrow view of learning. The proposed ontology, built on a radical interpretation of the inferentialist idea of conceptual pragmatism, enables us to maintain philosophical consistency on the basis of the distinction between students’ reasons and the observer’s perspectives, on the one hand, and dealing with the collaborative nature of classroom mathematical activities without assuming the knowledge to be learned as given. In order to build the ontology, the authors will redefine the notion of conceptualization as a judgment and claim that only articulated reasons exist and that unarticulated reasons are vague and variable. The shift in the ontological perspective requires us to reject a kind of retrospective analysis. In this regard, we should consider the impact of the observer effect on the assessment of conceptual development: This effect implies that it is not until a person is asked to provide her reason that her reason comes to exist. Finally, the authors will derive implications from the ontology: the teachers’ dual roles of enhancing students’ conceptualization and of assessing their current conceptual development and the implicit connection between inferentialist approaches and design research.