Promoting Active, Inductive, and Computational Learning in Mathematical Methods for Physicists

促进物理学家数学方法中的主动、归纳和计算学习

• 批准号: 1044270
• 负责人: Gary Felder
• 金额: $ 13.87万
• 依托单位: Smith College
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2011
• 资助国家: 美国
• 起止时间: 2011-07-01 至 2016-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1044270&HistoricalAwards=false
• 关键词: Promoting; Active; Inductive; Computational; Learning

AbstractMany physics and engineering curricula include a course on mathematical techniques. This award assists in the development and testing of a suite of exercises for this type of course so students better understand the motivation for the material and to help students incorporate computer skills within the course. For example, motivational exercises walk students through the steps needed to animate graphics on a screen (for matrices) or to analyze data on star positions to show evidence of orbiting planets beyond our solar system (for Fourier series). In each case the students are led through derivations using familiar mathematics to eventually reach a point where they can see the vital need for a new mathematical technique. The computer assisted exercises lead students in tasks such as comparing exact and approximate solutions to equations or solving complicated equations and plotting the solutions. These exercises help illustrate mathematical principles while simultaneously enhancing student numerical skills in the context of challenging and interesting problems.Courses of this type pose unique challenges. First, the students often don't use the math tools developed until a year or more after they learn them. Educational research shows that material is retained best when it is learned in a meaningful context and best recalled when it comes up again in a related context. The motivational exercises being developed in this project are therefore expected to improve student retention. In addition, in our digital generation the content of these courses should be frequently updated, since traditional skills (such as solving systems of equations by hand) are often not as important as knowing how to effectively use a computer to solve the problems. The exercises being developed in this project will have a broad national impact as professors are assisted in revising their curricula to teach computer skills alongside traditional math skills.The materials developed are being made freely available on the Web and presented at national conferences. Moreover, a number of participating faculty members at different institutions are volunteering to use these materials as they are developed. The effectiveness of the exercises are being assessed with tests given in semesters before and after the introduction of the exercises, computational skills are tested before and after the class, and surveys are being utilized to gather student and faculty feedback.

摘要许多物理和工程课程都包含数学技术课程。该奖项有助于开发和测试此类课程的一套练习，以便学生更好地理解材料的动机，并帮助学生将计算机技能融入课程中。例如，激励练习引导学生完成在屏幕上制作动画图形（对于矩阵）或分析恒星位置数据所需的步骤，以显示太阳系之外绕轨道运行的行星的证据（对于傅里叶级数）。在每种情况下，学生都会使用熟悉的数学进行推导，最终达到他们可以看到对新数学技术的迫切需要的程度。计算机辅助练习引导学生完成诸如比较方程的精确解和近似解或求解复杂方程并绘制解等任务。这些练习有助于阐明数学原理，同时在具有挑战性和有趣的问题中提高学生的数学技能。此类课程提出了独特的挑战。首先，学生们通常在学习一年或更长时间后才使用开发的数学工具。教育研究表明，在有意义的背景下学习材料时，记忆效果最好，而在相关背景下再次出现时，记忆效果最好。因此，该项目中开发的激励练习有望提高学生的保留率。此外，在我们的数字时代，这些课程的内容应该经常更新，因为传统技能（例如手工求解方程组）通常不如了解如何有效地使用计算机解决问题那么重要。该项目中正在开发的练习将在全国范围内产生广泛的影响，因为教授们将得到协助修改他们的课程，在传授传统数学技能的同时教授计算机技能。开发的材料将在网络上免费提供，并在全国会议上展示。此外，不同机构的许多参与教师自愿使用这些正在开发的材料。练习的有效性正在通过练习引入之前和之后的学期进行的测试进行评估，计算技能在课前和课后进行测试，并利用调查来收集学生和教师的反馈。