"MathBrush: A Case Study for Pen-based Interactive Mathematics"

by George Labahn, Edward Lank, Mirette Marzouk, Andrea Bunt, Scott MacLean, and David Tausky

Summary

This paper introduces MathBrush to provide a pen-based interface to support mathematical problem-solving tasks, which are currently done on computer algebra systems (CAS). It recognizes and transforms 2-dimensional hand-written mathematical expressions into 1-demensional text string, which can then be passed to the back-end CAS.

MathBrush support large and complex input and output expressions. It incorporates a context sensitive pop-up menu based on a cursory analysis of the mathematical expression and manipulations most likely to be performed (e.g. inverse, rank on matrices). It has an editing-in-place mechanism that allows interaction with CAS output, which enables separate operations on subexpressions. It supports two- or three-dimentional plotting and angles and limits of the plots can be adjusted. Users can select a new CAS to check for alternative answers to their problems.

Evalution methods include thinkalouds and semi-structured interview. Equation entry is a three step process. Users first draw the mathematical equation. They then interact with the equation in an input validation panel (IVP) to correct any character recognition errors. Finally, they render the equation to validate structural analysis. Extraneous ink, esp. dots resulted in errors in parsing. Features like scratch-out and translation(circling and moving terms around) was not used. Correcting recognition that uses a separate input validation panel to correct character recognition followed by a rendering step to present structural analysis caused confusion due to lack of perception in how structural analysis is performed. Mathematical interactions were a strength of the system.

Users tend to modify their writing to adjust to the tolerances of recognition (slowing down, taking care with symbole spacing, etc).


Discussion

This paper focuses on UI introduction, detail in recognition is not mensioned. I'm wondering if ambiguity solving techniques is used in MathBrush, by which I mean that possible interpretations of the expression are sent to CAS and those interpretations that yield errors will not likely be what the user meant to input, so they can be eliminated at this point.