Personal Inferences as Warrants of Undergraduate Students' Arguments in Calculus Contexts

The purpose of this paper is to highlight issues related to students' personal inferences that arise when students verbally explain their justification for calculus statements. We conducted clinical interviews with three undergraduate students who had taken first-semester calculus but had not yet been exposed to formal proof writing activities through undergraduate mathematics courses. We analyzed these students' verbal justification of four statements, each of which described a different relationship between two quantified variables in calculus contexts. In this paper, we document students' personal inferences that were evoked in their justifications and discuss how they are similar to or different from the logical inferences that have been accepted and practiced by the mathematics community for mathematical arguments. [For the complete proceedings, see ED630210.]