Novel Approaches to Rich Human-Computer Interaction with Mathematical Content

对于许多学科来说，数学表达式是我们如何表示、交互和交流科学知识的基石。然而，具有数学内容的人机交互模型并没有跟上通信和计算机交互的新趋势。可以说，目前的数学输入模型在过去的几十年里并没有发生根本性的变化，因为它们最初是为专家用户设计的，他们主要将它们用于以鼠标/键盘用户界面范例为中心的文档创建。然而，越来越多的新手用户（如学生）需要创建数学内容，他们可能不具备高度的数学知识。这通常是在新的硬件接口范围（例如智能手机）上，并且它需要能够更丰富地操作数学内容，就像在交互式和协作环境中一样，而不是文档创建所需的简单环境。

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.