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没有跟上通信和计算机交互的新兴趋势。可以说，当前的数学输入模型在几十年来没有根本性的改变，因为它们最初是为专家用户设计的，他们主要使用它们来创建围绕鼠标/键盘用户界面范例的文档。然而，越来越多地需要新手用户，例如学生，他们可能没有高度的数学复杂性，来创建数学内容。这通常是在一系列新的硬件接口上，如智能手机，它需要能够更丰富地操纵数学内容，如交互和协作环境，而不是文档创建所需的简单环境。数学输入技术必须解决的主要困难之一是数学公式通常是二维的。这种多维性给数学表达式的输入和操作带来了挑战。我们的研究将调查与数学内容的人机交互，并在各种情况下探索数字数学的新方法，从新手用户到专家用户的表达输入和操作，包括整合智能手机等新硬件设备，并考虑用户在协作环境中的需求。我们希望开发新的强大的数学用户界面模型和工具，以获得更丰富的体验，并通过观察性研究来研究它们的使用和有效性。

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.