Collaborative Research: Investigating Issues of the Individual and the Collective along a Continuum between Informal and Formal Reasoning

协作研究：沿着非正式和正式推理的连续体调查个人和集体的问题

• 批准号: 0634074
• 负责人: Chris Rasmussen
• 金额: $ 25.8万
• 依托单位: San Diego State University Foundation
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2007
• 资助国家: 美国
• 起止时间: 2007-09-01 至 2012-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0634074&HistoricalAwards=false
• 关键词: Collaborative; Research; Investigating; Issues; Individual

Undergraduate engineering, science and mathematics majors in the United States begin their university mathematics training with several calculus courses, but then move on to such courses as differential equations and linear algebra. Mathematics majors and minors may also study real analysis or abstract algebra. Students often find the transition from taking calculus courses to taking more formal, proof-based mathematics courses particularly challenging, and often a stumbling block to further academic success. Sophomore and junior level courses such as differential equations, linear algebra, geometry, and courses introducing set theory and logic constitute a core collection of courses that have the potential to facilitate this transition. The main goals of this project are to make contributions to theory and methodology in terms of the continuum between informal and formal mathematical reasoning. In particular, the PIs will develop theoretical means for interpreting the transition to formal, proof-based mathematics courses. They do so by using four different perspectives on the nature of the individual and collective growth of knowledge. The methodological products will include strategies for data collection and data analysis that allow for insights into student learning within and between each of the four different theoretical perspectives. The mathematical context for this work will primarily be linear algebra, with insights drawn from our prior work in differential equations, geometry, and set theory.

美国的本科工程，科学和数学专业的专业人士通过几个微积分课程开始了他们的大学数学培训，但随后进入诸如微分方程和线性代数等课程。数学专业和未成年人也可以研究真实的分析或抽象代数。学生经常发现从参加微积分课程到参加更正式的，基于证明的数学课程特别具有挑战性的过渡，通常是绊脚石，以进一步的学术成就。大二和初中课程（例如微分方程，线性代数，几何图形和介绍集合理论和逻辑的课程）构成了有可能促进这种过渡的课程的核心课程。该项目的主要目标是根据非正式和正式数学推理之间的连续性为理论和方法论做出贡献。特别是，PI将开发理论手段来解释向正式的基于证明的数学课程的过渡。他们通过对个人性质和知识的集体增长使用四种不同的观点来做到这一点。该方法论产品将包括用于数据收集和数据分析的策略，以了解四种不同理论观点中的学生学习和之间的学生学习。这项工作的数学背景主要是线性代数，从我们先前在微分方程，几何学和集合理论中的工作中得出见解。