The Alignment of Ordering and Space in Arithmetic Computation

Two experiments explore the role that spatial format has on arithmetic computations. In printed arithmetic expressions containing both multiplications and additions, terms that are multiplied are often placed closer together than terms that are added. These experiments test whether that external tendency plays a role in how reasoners construct interpretations of simple compound arithmetic expressions (such as “2 + 3*4”). Evidence is found to support two such influences: First, reasoners use spacing information when choosing an operation to apply (e.g., whether to add or to multiply two numbers). Second, reasoners also use spacing patterns to select an order in which to apply operations in compound expressions. Terms placed closer together tend to be computed sooner. Although spatial relationships besides order are entirely formally irrelevant to expression semantics, reasoners use these regular spatial relationships to support their success with various formal properties.