Proceedings of the Annual Meeting of the Cognitive Science Society

Mathematics is critical for making sense of the world. Yet,little is known about how people evaluate mathematicalexplanations. Here, we use an explanatory reasoning taskto investigate the intuitive structure of mathematics. Weshow that people evaluate arithmetic explanations bybuilding mental proofs over the conceptual structure ofintuitive arithmetic, evaluating those proofs using criteriasimilar to those of professional mathematicians.Specifically, we find that people prefer explanationsconsistent with the conceptual order of the operations(“9÷3=3 because 3 ́3=9” rather than “3 ́3=9 because9÷3=3”), and corresponding to simpler proofs (“9÷3=3because 3 ́3=9” rather than “9÷3=3 because 3+3+3=9”).Implications for mathematics cognition and education arediscussed.