Career: Differential Equations: Building a Theory of Student Reasoning and Understanding

职业：微分方程：建立学生推理和理解的理论

• 批准号: 0423067
• 负责人: Chris Rasmussen
• 金额: $ 38.07万
• 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: 2004
• 资助国家: 美国
• 起止时间: 2004-01-01 至 2006-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0423067&HistoricalAwards=false
• 关键词: Career; Differential; Equations; Building; Theory

Advances in technology and the calculus reform movement have resulted in several recent curricular reform efforts in differential equations. These reform efforts have decreased the traditional emphasis on analytic techniques for finding exact solutions to well-posed problems and increased the use of computing technology to incorporate qualitative and numerical methods for understanding the behavior of solutions to differential equations. Research on student learning of differential equations, however, has lagged behind these curricula efforts.This project will enlarge our understanding of how emerging analyses of student thinking, technology, context problems, and symbol use can be profitably coordinated to promote student learning of advanced, undergraduate mathematics, using differential equations as a specific case. The proposed research project will illustrate how theory-driven work at the elementary and secondary level can inform, guide, and sustain the learning and teaching of university mathematics in technology-rich classrooms. Long-range research plans include analyses that focus on effective means by which university mathematics instructors proactively support students' mathematical development in technology-rich classrooms.In broad terms, the research methodology employed in this project falls under the heading of "developmental research" and highlights the relationship between research and practice, centering on the learning-teaching process with particular attention to the mental activities of students. Three, semester-long classroom teaching experiments and individual student interviews will be conducted over a period of five years. Data sources will include videorecordings of all classroom sessions, videorecordings of student interviews, copies of student work, and records of project meetings. Data analysis will follow the constant comparative method adapted for longitudinal classroom videorecordings and multiple data sources.

技术的进步和演算改革运动的进步导致了微分方程最近的一些课程改革工作。 这些改革的努力减少了对分析技术的传统重视，以找到精确的解决方案，并增加了计算技术的使用，以结合定性和数值方法，以理解解决方案解决方案的行为。 但是，关于学生对微分方程的学习的研究落后于这些课程努力。该项目将扩大我们对学生思维，技术，上下文问题和符号使用的新兴分析的理解，可以有利地协调以促进学生对高级，本科数学的学习，以特定的情况为特定的情况。 拟议的研究项目将说明如何在基础和中学级别的理论驱动的工作为技术富裕教室中大学数学的学习和教学提供信息。远程研究计划包括分析的分析，这些分析专注于有效的手段，通过这些手段，该项目在技术丰富的课堂中积极支持学生的数学发展。从广义上讲，该项目所采用的研究方法属于“发展研究”的标题，并突出了研究与实践之间的关系，集中在学习教学过程中，特别关注学生的精神活动。 三个学期的课堂教学实验和个人访谈将在五年内进行。 数据源将包括所有课堂会议的视频记录，学生访谈的视频记录，学生工作副本以及项目会议记录。 数据分析将遵循适用于纵向课堂视频和多个数据源的恒定比较方法。