A model for effective real-time entry of mathematical expressions

Many science and engineering courses contain substantial mathematical content. In addition, the rapid development of online learning, in both traditional and Web-based courses, and the ubiquitous presence of laptop computing, is placing increased demands on students to enter mathematical expressions into a computer. Furthermore, it is often required that the expressions are written in real-time (e.g., in class note-taking, automated assessment in a timed testing environment, or for a live online discussion). Technology-based difficulties that affect the writing of expressions will result in inaccurate assessment or may impede the transfer of knowledge. Obstacles to the easy input of mathematical expressions include the large number of specialized symbols in mathematics and the two-dimensional layout structure of many mathematical expressions. Most software packages, such as Microsoft Word, that allow complex mathematical content to be input employ a structure-based approach, where symbols and structural elements are chosen from palettes and input separately. In this paper, we argue that structure-based expression editors, which were largely designed for document creation, are not appropriate for real-time tasks in education. They force a user to write expressions differently than they would on paper, and so interfere with normal thought processes. As an alternative, we introduce a new model for expression entry that, like a structure-based approach, uses palettes for symbol selection, but for structures allows users to freely place symbols as they would on paper. Supported by usability studies, we argue that this hybrid approach allows for the much more effective entry of mathematical content.