Novel Approaches to Rich Human-Computer Interaction with Mathematical Content

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For many disciplines, mathematical expressions are a cornerstone of how we represent, interact with, and communicate scientific knowledge. However, models for human-computer interaction with mathematical content have not kept up with emerging trends in communications and computer interaction. It could be argued that current mathematical input models have not fundamentally changed in the decades since they were originally designed for expert users, who principally used them for document creation centred around a mouse/keyboard user-interface paradigm. Increasingly, however, there is a need for novice users, such as students, who might not have a high-degree of mathematical sophistication, to create mathematical content. This is often on a new range of hardware interfaces, such as smartphones, and it entails being able to manipulate mathematical content more richly, as with interactive and collaborative environments, rather than the simpler environments required for document creation.******One of the main difficulties which a mathematical input technology must solve is that mathematical formulas are most often two-dimensional. This multi-dimensionality creates a challenge for mathematical expression input and manipulation. Our research will investigate human-computer interaction with mathematical content and explore new approaches for digital mathematics in a variety of contexts, from expression input and manipulation by novice users to expert users, including incorporating new hardware devices such as smartphones, and consider the needs of users in collaborative environments. We expect to develop new robust mathematical user-interface models and tools for richer experiences, as well as to study their use and effectiveness through observational studies.**