Proceedings of the Annual Meeting of the Cognitive Science Society

In mathematical cognition, problem difficulty is a central vari-able. In the present study, problem difficulty was operational-ized through five arithmetic operators — addition, subtrac-tion, multiplication, division, and modulo — and through thenumber of carries required to correctly solve a problem. Thepresent study collected data from human participants solvingarithmetic problems, and from multilayer perceptrons (MLPs)that learn arithmetic problems. Binary numeral problems werechosen in order to minimize other criteria that may affect prob-lem difficulty, such as problem familiarity and the problemsize effect. In both humans and MLPs, problem difficulty washighest for multiplication, followed by modulo and then sub-traction. The human study found that problem difficulty wasmonotonically increasing with respect to the number of car-ries, across all five operators. Furthermore, a strict increasewas also observed for addition in the MLP study