Collaborative Research: Beyond Procedures: A Research-Based Approach to Teaching Mathematical Methods in Physics

协作研究：超越程序：基于研究的物理数学方法教学方法

基本信息

批准号：
1912087
负责人：
John Thompson
金额：
$ 45.41万
依托单位：
University of Maine
依托单位国家：
美国
项目类别：
Continuing Grant
财政年份：
2019
资助国家：
美国
起止时间：
2019-09-01 至 2024-08-31
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=1912087&HistoricalAwards=false
关键词：
Collaborative Research Beyond Procedures Based

项目摘要

This interdisciplinary project brings together physics education research (PER) and research in undergraduate math education (RUME). It combines efforts at identifying and addressing student conceptual difficulties in physics with efforts toward understanding the ways students use and reason about mathematics in physics contexts. The work targets the mathematical methods course, a key course for physics majors as it begins the transition to using advanced calculus, linear algebra, etc. in physics problems and serves as a gateway to the upper-division in physics. The project will strengthen the research base in a portion of the curriculum that has, to this point, largely gone unexamined, and will touch upon, and build upon, work in related areas, such as research on other upper division physics courses, as well as the extensive research base in undergraduate mathematics education. Prior mathematical success is a strong indicator of success in physics, and the gap of knowledge available between what is taught in mathematics courses and physics course may be a significant source of attrition for physics majors that can be addressed through this work. The project will investigate the development of students' mathematical understanding in the context of learning and understanding middle- and upper-division physics. The team will conduct an integrated program of research, curriculum development, and assessment of topics found in middle- and upper-division physics courses, with particular focus on the sophomore- or junior-level mathematical methods course. The primary objectives of the project are: (a) to conduct research on student understanding of mathematics in upper-division physics contexts, with an emphasis on the core mathematical methods and reasoning covered in an intermediate-level mathematical methods course; and (b) to develop a library of modular curricular materials (such as, student-centered tutorials and Peer Instruction tasks) emphasizing mathematical methods and reasoning suitable for use in a wide variety of upper-division physics courses.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

这个跨学科项目汇集了物理教育研究（PER）和本科数学教育研究（RUME）。它结合了识别和解决物理学中的学生概念困难的努力，以及在理解学生在物理环境中使用数学的方式和理由的努力。该作品针对数学方法课程，是物理专业的关键课程，因为它开始过渡到物理问题中的高级演算，线性代数等，并用作通往物理学上限的门户。该项目将在课程的一部分中加强研究基础，到目前为止，该课程在很大程度上尚未进行，并将在相关领域（例如其他上层物理学课程的研究）以及在本科数学教育的广泛研究基础上进行研究和建立。先前的数学成功是物理学成功的有力指标，并且在数学课程和物理课程中所教的知识之间可用的知识差距可能是可以通过这项工作来解决物理专业的重要损耗来源。该项目将在学习和理解中等和上限物理学的背景下研究学生数学理解的发展。该团队将对中级和高级物理学课程中发现的主题进行研究，课程开发以及评估的综合计划，尤其关注大二或初级数学方法课程。该项目的主要目标是：（a）对学生对数学的理解进行研究，并着重于中级数学方法课程中涵盖的核心数学方法和推理；（b）开发一个模块化课程材料库（例如，以学生为中心的教程和同伴指导任务），强调数学方法和适合在各种高级物理课程中使用的推理。本奖颁奖典礼反映了NSF的法定任务，并通过使用基金会的范围和广泛的评估来进行评估，并被认为是值得评估的。

项目成果

期刊论文数量（4）

专著数量（0）

科研奖励数量（0）

会议论文数量（0）

专利数量（0）

Modifying symbolic forms to study probability expressions in quantum mechanics

修改符号形式以研究量子力学中的概率表达式

DOI：
发表时间：
2023
期刊：
Proceedings of the Annual Conference on Research in Undergraduate Mathematics Education
影响因子：
0
作者：
Riihiluoma, William;Topdemir, Zeynep;Thompson, John R.
通讯作者：
Thompson, John R.

Student understanding of eigenvalue equations in quantum mechanics: Symbolic forms analysis

学生对量子力学中特征值方程的理解：符号形式分析

DOI：
发表时间：
2023
期刊：
Proceedings of the Annual Conference on Research in Undergraduate Mathematics Education
影响因子：
0
作者：
Pina, Anthony R;Topdemir, Zeynep;Thompson, John R.
通讯作者：
Thompson, John R.

Physics student understanding of divergence and curl and their constituent partial derivatives

物理学生对散度和旋度及其组成偏导数的理解

DOI：
发表时间：
2023
期刊：
Proceedings of the Annual Conference on Research in Undergraduate Mathematics Education
影响因子：
0
作者：
Topdemir, Zeynep;Loverude, Michael E.;Thompson, John R.
通讯作者：
Thompson, John R.

Using Network Analysis Techniques to Probe Student Understanding of Expressions Across Notations in Quantum Mechanics

使用网络分析技术来探究学生对量子力学中跨符号表达式的理解

DOI：
发表时间：
2022
期刊：
Proceedings of the 24th Annual Conference on Research in Undergraduate Mathematics Education
影响因子：
0
作者：
Riihiluoma, William;Topdemir, Zeynep;Thompson, John R.
通讯作者：
Thompson, John R.