Visual structure in mathematical expressions

Abstract

Mathematics uses formulae to express knowledge about objects concisely and economically. Mathematical formulae are at the same time an indispensable tool for the initiated and a formidable barrier to novices. Surprisingly little is known about the cognitive basis of this practice. In this paper we start to rectify this situation with an investigation of how humans read (and understand) mathematical expressions. A previous exploratory study suggested the interplay of visual patterns and content structure as a key ingredient of decoding and understanding math expressions that differentiates between math-literate and -illiterate subjects. The main contribution of this paper is an eyetracking study on mathematically trained researchers conducted to verify the mathematical practices suggested by the first study and refine our understanding of the mechanisms.