Proof Frames of Preservice Elementary Teachers

This study asked 101 preservice elementary teachers enrolled in a sophomore-level mathematics course to judge the mathematical correctness of inductive and deductive verifications of either a familiar or an unfamiliar statement. For each statement, more than half the students accepted an inductive argument as a valid mathematical proof. More than 60% accepted a correct deductive argument as a valid mathematical proof; 38% and 52% accepted an incorrect deductive argument as being mathematically correct for the familiar and unfamiliar statements, respectively. Over a third of the students simultaneously accepted an inductive and a correct deductive argument as being mathematically valid.