Learning the language of science: Advanced math for concrete thinkers

这个项目涉及这样一个事实，即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由于无法掌握高等数学主题而被本学科的现代发展所阻碍。数学是科学的语言，但是学生和他们的老师经常把注意力集中在语言的语法规则上，而忽视了语义学——如何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研究学生的学习和技术在初级物理教育中的应用。这项研究表明，对学生如何学习（或不学习）的理解与适当的技术工具相结合，可以创造学习环境，从而在学生的学习和他们对学科的态度方面产生巨大的改善。该项目将pi早期在物理学入门工作中发展起来的思想应用于高年级科学课程中更复杂的数学结构和工具。该项目将对学生学习的研究与现代教学法和计算机技术相结合，创造了一套非传统的课程和活动。该项目既提高了对学生学习高等科学数学障碍的理解，又开发了帮助他们克服这些障碍的新工具。为这个项目准备的阅读材料、主动学习课程和非传统问题都通过网络公开分发。

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.