Proofs, Functions and Computations: A web-based course as a laboratory for enhanced teaching and learning in logic, mathematics and computer science

跨学科（99）这个项目是围绕证明、函数和计算的基本概念开发一个全面的综合课程。这三个基本思想分别是逻辑学、数学和计算机科学的核心。扩展课程建立在一个基于网络的原型课程“逻辑与证明”的基础上，其特点是精心搭建和高度互动的材料，迷你导师和一个复杂的证明实验室。该项目的智力价值包括通过一个动态的“证明导师”向学生提供自动生成的智能建议，该导师可以监控学生在证明方面的当前进展。这门课程也可以作为控制实验的实验室，用于研究两个广泛的问题：1)特定教学方法的有效性，例如，证明构建策略的辅导教学；2)逻辑的反思性使用从正式环境转移到集合论的半正式环境，然后转移到可计算性理论的非正式环境。该项目的潜在更广泛的影响在于这种方法对其他学科的适用性。

Interdisciplinary (99) This project is developing a full-scale integrative course constructed around the basic concepts of Proof, Function, and Computation. These three fundamental ideas lie at the core of logic, mathematics, and computer science, respectively. The expanded course builds on a prototype web-based offering, "Logic & Proofs," that features carefully scaffolded and highly interactive material, mini-tutors, and a sophisticated Proof Lab. The intellectual merit of the project includes the provision of automatically generated intelligent advice to students via a dynamic "Proof Tutor" that monitors the current progress of students working on proofs. The course also serves as a laboratory for controlled experiments investigating two broad issues: i) the efficacy of specific pedagogical approaches, e.g., the tutored teaching of strategies for proof construction, and ii) the transfer of the reflective use of logic from a formal context to the semiformal one of set theory and, then, to the informal context of computability theory. The project's potential for broader impacts lies in the applicability of this approach to other disciplines.