A Dynamic Pen-Based Interface for Writing and Editing Complex Mathematical Expressions With Math Boxes

Abstract

Math boxes is a recently introduced pen-based user interface for simplifying the task of hand writing difficult mathematical expressions. Visible bounding boxes around subexpressions are automatically generated as the system detects relevant spatial relationships between symbols including superscripts, subscripts, and fractions. Subexpressions contained in a math box can then be extended by adding new terms directly into its given bounds. When new characters are accepted, box boundaries are dynamically resized and neighboring terms are translated to make room for the larger box. Feedback on structural recognition is given via the boxes themselves. In this work, we extend the math boxes interface to include support for subexpression modifications via a new set of pen-based interactions. Specifically, techniques to expand and rearrange terms in a given expression are introduced. To evaluate the usefulness of our proposed methods, we first conducted a user study in which participants wrote a variety of equations ranging in complexity from a simple polynomial to the more difficult expected value of the logistic distribution. The math boxes interface is compared against the commonly used offset typeset (small) method, where recognized expressions are typeset in a system font near the user’s unmodified ink. In this initial study, we find that the fluidness of the offset method is preferred for simple expressions but that, as difficulty increases, our math boxes method is overwhelmingly preferred. We then conducted a second user study that focused only on modifying various mathematical expressions. In general, participants worked faster with the math boxes interface, and most new techniques were well received. On the basis of the two user studies, we discuss the implications of the math boxes interface and identify areas where improvements are possible.