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

技术的进步和微积分改革运动导致了最近几次微分方程式课程的改革。这些改革努力减少了传统上对分析技术的重视，以寻找适定问题的准确解，并增加了计算技术的使用，以结合定性和数值方法来理解微分方程解的行为。然而，对学生学习微分方程的研究落后于这些课程的努力。本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如何能够有益地协调，以促进学生学习高等本科数学的理解，并以微分方程为具体案例。拟议的研究项目将说明中小学的理论工作如何在技术丰富的课堂上为大学数学的学习和教学提供信息、指导和支持。长期研究计划包括分析大学数学教师在技术丰富的课堂上主动支持学生数学发展的有效手段。从广义上讲，该项目采用的研究方法属于“发展研究”的标题，并突出研究与实践之间的关系，以学习-教学过程为中心，特别关注学生的心理活动。第三，为期一学期的课堂教学实验和个别学生访谈将在五年内进行。数据来源将包括所有课堂课程的录像带、学生访谈的录像带、学生作业的副本和项目会议的记录。数据分析将遵循适用于纵向课堂录像和多种数据来源的恒定比较法。

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.