Mathematical Proof and Proving (MPP) - Design and Implementation of a Special Undergraduate Course

这个项目源于两个常见的假设：1)数学证明和证明是数学的核心；2)形式证明的概念和数学证明的活动即使对大多数优秀的本科生来说也是令人生畏的困难。由此可见，有必要开设注重数学证明的本科课程，以解决学生的困难。该项目解决了这一需求。包括在该项目是一个基于证明的新生水平的课程。课程材料包括大约50个精心构建的案例问题，这些问题需要以调查和参与的方式进行证明。对于五种中心证明方法中的每一种，都有6-10个问题可以用这种方法证明。对于每种方法，问题在数学主题方面有所不同。一个特定的问题可以用来说明不止一种类型的证明。这是纽约大学数学教育家和数学家之间的合作。数学教育工作者带来了他们在有效教与学方面的专业知识和对教学证明研究文献的了解，而数学家则带来了他们在数学学科方面的专业知识，可以确保课程满足数学本科专业的要求。数学家和数学教育者之间的这种独特合作加强了课程的质量和影响。开发和实施专业发展资源和活动。教师发展资源允许未来的课程由一名数学家或数学教育家教授。

This project stems from two common assumptions: 1) mathematical proof and proving are at the heart of mathematics; and 2) the notion of formal proof and the activity of mathematically proving are dauntingly difficult even for most good undergraduate students. It follows that there is a need for undergraduate courses that focus on mathematical proofs in ways that attend to students' difficulties. The project addresses this need.Included in the project is a proof based freshman level course. Course material includes approximately 50 carefully constructed case-problems that create the need to prove in an investigative and engaging way. For each of five central methods of proof there are 6-10 problems that can be proved by this method. For each method, the problems vary in terms of the mathematical topic. A particular problem may serve to illustrate more than one type of proof. This is a collaboration between mathematics educators and mathematicians at NYU. The mathematics educators bring their expertise on effective teaching and learning and knowledge of the research literature on teaching proofs, while the mathematicians bring their expertise in the discipline of mathematics and can ensure that the course meets the requirements of undergraduate majors in mathematics. This unique collaboration between mathematicians and mathematics educators strengthens the quality and impact of the course. Professional development resources and activities are developed and implemented. The faculty development resources allow future courses to be taught by a single faculty member who is either a mathematician or a mathematics educator.