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

证明、函数和计算：基于网络的课程，作为加强逻辑、数学和计算机科学教学的实验室

• 批准号: 0618806
• 负责人: Wilfried Sieg
• 金额: --
• 依托单位: Carnegie-Mellon University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2006
• 资助国家: 美国
• 起止时间: 2006-09-01 至 2010-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0618806&HistoricalAwards=false
• 关键词: Proofs; Functions; Computations; web; based

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.

跨学科（99）这个项目是围绕证明，函数和计算的基本概念构建一个全面的综合课程。这三个基本思想分别是逻辑、数学和计算机科学的核心。扩展的课程建立在一个基于网络的原型产品，“逻辑证明”，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动态的“证明导师”向学生提供自动生成的智能建议，该导师监测学生在证明方面的当前进展。该课程还作为一个实验室，进行对照实验，研究两个广泛的问题：i）具体教学方法的有效性，例如，辅导教学的策略证明建设，和ii）转移的反射使用逻辑从正式的背景下，半正式的一套理论，然后，非正式的可计算性理论的背景。该项目产生更广泛影响的潜力在于这种方法对其他学科的适用性。