Inferential Reasoning Levels for t-Student Statistical

In this article, we present a proposal of progressive inferential reasoning levels, from the informal to the formal, for the t-Student statistic, based on epistemic criteria identified with a historical-epistemological study on this statistic and from the investigation developed on inferential reasoning. To do this, we used some theoretical-methodological notions introduced by the Onto-Semiotic Approach to mathematical knowledge and instruction (OSA), which allowed both to characterize various meanings conferred on the t-Student statistic throughout its evolution and development, and to present a comprehensive perspective of what is considered inferential reasoning. The mathematical attributes of the t-Student statistics’ meanings are strongly linked to the indicators of the different levels of inferential reasoning presented here. Furthermore, each level is associated with informal, pre-formal, or formal inferential reasoning. The proposed levels of Inferential Reasoning for the t-Student statistic and its indicators are expected to be useful for the design of activities that gradually promote formal inferential reasoning based on informal inferential reasoning on this statistic.

Keywords:
Statistical Education; Inferential reasoning; Statistical inference; t-Student