sentences:  In another study, Annie Keith observed a class of 15 second grade students who convinced each other that zero was an even number based on even-odd alternation and on the possibility of splitting a group of zero things in two equal groups.More in-depth investigations were conducted by Esther Levenson, Pessia Tsamir, and Dina Tirosh, who interviewed a pair of sixth-grade students who were performing highly in their mathematics class.One student preferred deductive explanations of mathematical claims, while the other preferred practical examples.