An Evaluation of Two-Dimensional Digital Input Models for Mathematical Structure: Effects on Working Memory, Cognitive Load, and Efficiency

Typesetting 2-dimensional mathematical notation can present challenges to users who rely upon WYSIWYG (what you see is what you get) word processing editors, which allow for direct manipulation of text. These editors use various models to represent 2-dimensional mathematical structure within the 1-dimensional word processing environment. The 2-dimensional nature of mathematical notations manifests itself in a variety of ways, and we hypothesize that two distinct models, structure-based (Microsoft Word Equation Editor) and free-form (MC\(^2\): Mathematics Classroom Collaborator) handle different types of mathematical structure with varying degrees of success. To test this hypothesis, an eye-tracking study was conducted to compare how these two models affect task efficiency for mathematical “expert” and “novice” users, as well as working memory interference, and cognitive load. The study required users to transcribe mathematical expressions containing three types of structure: linear (1-dimensional), exponential, and rational (fractions). Handwriting was used as a control. Results showed superior performance by the structure-based model for the transcription of fractions, while the free-form model displayed ameliorated performance for the transcription of exponents. Handwriting was found to be significantly more efficient, but cognitive effects were inconclusive. Few differences were found with respect to user mathematical experience level. These findings show evidence that neither of these models is superior for the typesetting of all mathematics, but rather that features of each model are better equipped to handle different mathematical structures. Therefore, word processing editors can improve the facility of typesetting 2-dimensional mathematics by incorporating elements of both tested models to improve the overall user experience. Such optimization will ultimately facilitate the digital learning and communication of mathematical content.