Collaborative Research: UTMOST: Undergraduate Teaching in Mathematics with Open Software and Textbooks

Extreme 2.0项目将设计、开发和研究使用开放软件和电子教科书进行本科数学教与学的创新方法。这个项目将研究学生在电子教科书以各种形式和在各种设备上免费提供时使用这些教科书的情况。这些教科书将通过无缝集成领先的数学开源计算系统Sage来支持交互计算。这种整合的主要工具将是SageMathCloud和Sage Cells，SageMathCloud是一个丰富的在线环境，用于学生和他们的课程教师之间的计算和协作，而Sage Cells是独立的交互式计算模块，可以嵌入任何网页，而不需要安装软件或事先了解Sage，因为命令是预先加载的。此外，Extreme 2.0将支持进一步采用MathBook XML，这是一个创作平台，可以创建功能强大的开放源码教科书--特别是可以存在于印刷版和包含Sage Cells的在线格式的教科书。该项目包括对Sage Cells的技术改进，这将使教师更容易为他们的特定课程需求创建自己的Sage Cells。将对Sage细胞目录进行整理，这将进一步降低广泛采用的障碍。在线动态教科书提供了一个独特的机会，可以直接衡量它们如何使用的方方面面。Extreme 2.0旨在利用技术来提高数学教育的质量和广度，研究学生和教师如何使用电子教科书和现代在线工具在真实课堂上就技术科目进行交流。Extreme 2.0将与多个机构的教师合作，所有教师都将使用MathBook XML教科书，其中一些是网络版，另一些是印刷版。在线版本将托管在云中，服务器将被配置为以极其细粒度的级别记录所有用户活动。自动在线数据收集将与课堂数据收集方法相结合，提供一种手段来验证收集的信息，这些信息可以在以后与学生在课程内容知识方面的收获相关联。Extreme 2.0还将帮助已经转换为Mathbook XML格式的本科数学教科书的作者在下一步加入交互功能，如Sage Cell和网络练习。这将极大地增加具有这些先进功能的书籍的数量，同时扩大Extreme项目可以进行研究调查的领域。

The UTMOST 2.0 project will design, develop and study innovative approaches to the teaching and learning of undergraduate mathematics using open software and electronic textbooks. This project will study students' use of electronic textbooks when these are made freely available in a variety of formats and on a variety of devices. These textbooks will support interactive computation through a seamless integration of Sage, the leading open-source computing system for mathematics. The main vehicles for this integration will be SageMathCloud, a rich online environment for computation and collaboration between students and their course instructor, and Sage cells, self-contained interactive calculation modules that can be embedded in any web page while requiring no software installation or prior knowledge of Sage, because the commands are pre-loaded. Additionally, UTMOST 2.0 will support the further adoption of MathBook XML, an authoring platform that enables the creation of highly functional, open-source textbooks--in particular, textbooks which can exist both in print and in an online format that contains Sage cells. The project includes technical improvements to Sage cells which will make it easier for instructors to create their own Sage cells for their particular course needs. A catalog of Sage cells will be curated, which will further lower the barrier to widespread adoption. Online dynamic textbooks provide a unique opportunity to directly measure all aspects of how they are used. UTMOST 2.0 is designed to leverage technology to enhance the quality and breadth of the mathematical education research into how students and teachers use electronic textbooks and modern online tools for communication about technical subjects in real classrooms. UTMOST 2.0 will work with instructors at multiple institutions, all of whom will use MathBook XML textbooks, some in the online version and some in the printed version. The online version will be hosted in the cloud, on a server that will be configured to record all user activity at an extremely fine-grained level. The automatic online data collection will be combined with classroom data collection methods, providing a means to validate the information collected that can later be correlated with student gains in course content knowledge. UTMOST 2.0 will also assist authors of undergraduate mathematics textbooks that have already converted to the Mathbook XML format in the next steps of incorporating interactive features such as Sage cells and WeBWorK exercises. This will greatly increase the number of books with those advanced features and simultaneously expand the areas in which the UTMOST project can perform its research investigations.