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)这个项目正在开发一门围绕证明、函数和计算的基本概念构建的全面综合课程。这三个基本概念分别是逻辑、数学和计算机科学的核心。这门扩展的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，该课程以精心搭建的高度互动的材料、迷你导师和复杂的证明实验室为特色。该项目的智力价值包括通过动态的“校对导师”向学生提供自动生成的智能建议，该教师监控学生当前在校样方面的进展。这门课程还作为一个实验室，用于研究两个广泛的问题：i)特定教学方法的有效性，例如，对证据构建策略的指导教学；ii)将逻辑的反思使用从集合论的形式背景转移到半形式背景，然后转移到可计算性理论的非正式背景。该项目的更广泛影响的潜力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.