Learning the language of science: Advanced math for concrete thinkers

这个项目涉及的事实是，许多大学生未能实现成为科学家的目标，许多科学家和工程师因无法掌握高级数学课题而无法参与学科的现代发展。数学是科学的语言，但学生和他们的老师往往专注于语言的语法规则，而忽视了语义--如何利用数学来表达合理的意义。在过去的20年里，PI和他的同事们一直在初级水平上研究学生的学习和技术在物理教育中的使用。这项研究表明，了解学生如何学习(或未能学习)与适当的技术工具相结合，可以创建学习环境，使学生的学习和对该学科的态度都有显著改善。这项计画是将个人投资学会早期在物理学入门工作中发展出来的想法，应用到更复杂的数学结构和高级科学课程的工具上。该项目将对学生学习的研究与现代教育学和计算机技术相结合，创建了一套非传统的课程和活动。该项目正在开发对学生学习高等科学数学障碍的更好理解，以及帮助他们克服这些障碍的新工具。为这个项目准备的阅读资料、主动学习课程和非传统问题将通过网络公开分发。

This project deals with the fact that many college students fail in their goals to become scientists and many scientists and engineers are blocked from modern developments in their discipline by their inability to master advanced mathematical topics. Mathematics is the language of science, but students and their instructors often focus on the grammatical rules of the language and ignore the semantics - how mathematics can be used to make sensible meaning. Over the past 20 years, the PI and his colleagues have been studying student learning and the use of technology in physics education at the introductory level. This research has shown that an understanding of how students learn (or fail to learn) combined with appropriate technological tools can create learning environments that produce dramatic improvements both in student learning and in their attitude towards the subject. This project is applying the ideas developed in the PIs' earlier work in introductory physics to the more complex mathematical structures and tools of upper division science courses. The project combines research into student learning with modern pedagogy and computer technology to create a set of non-traditional lessons and activities. The project is developing both an improved understanding of the barriers to students' learning advanced mathematics for science as well as new tools to help them surmount those barriers. The readings, active-learning lessons, and non-traditional problems prepared for this project are being distributed openly via the web.