Summary: In the third century, Diophantus, the "Father of Algebra" no less, described equations of the form x + 20 = 4 as "absurd." The absurdity stemmed from the fact that the result of four is obviously less than the addend of twenty. And more than 1300 years later, Pascal argued that subtracting four from zero leaves zero because of the impossibility of taking something from nothing. Surely, then, ideas this challenging are too complex for first graders‒or are they? Recent research shows that children as young as six years of age can, in fact, reason about negative numbers and even perform basic calculations using them (Behrend and Mohs 2006; Wilcox 2008). The authors’ goal was to build on this research to further explore young children’s ideas about negative numbers. This article describes the background of their study, provides an overview of the tasks they used, discusses children’s responses to these tasks, and identifies two ways that students in their study reasoned about and approached problems involving negative numbers. (Contains 1 table and 2 figures.) (ERIC)