Raising Calculus to the Surface

该项目组正在研究一种新的方法，用于教学和学习多元微积分，其中学生积极探索通过测量和猜想的中心思想。这种方法的智力价值在于使用多变量函数的物理模型，具有干擦表面和附带的仪器，使学生能够绘制，测量和掌握几何概念。通过“翻转课堂”和协作学习的结合，学生团队通过活动表工作，以调查在讲座正式介绍之前的关键思想和关系。项目团队表示，通过物理模型的发现学习可以建立对多变量微积分的几何理解，在代数公式中注入意义，提高表现和态度，并提高对科学应用的理解。为了传播其调查结果并发挥该项目更广泛的影响，PI团队正在与数十名教师进行夏季研讨会，这些教师以前是从高中、两年制和四年制学院和大学招募的。参与者学习如何有效地使用表面，并在随后的学年中，所有参与者使用表面教授多变量微积分，并在各自的机构安排一个对照班进行比较。书面评估和临床访谈被用来比较使用表面的学生和接受传统教学的学生之间的学习成果。

This project team is investigating a new method for teaching and learning multivariable calculus in which students actively explore central ideas through measurement and conjecture. The intellectual merit of this approach rests on the use of physical models of multivariable functions with a dry-erase surface and accompanying instruments that allow students to draw, measure, and grasp concepts geometrically. Through a marriage of the "flipped classroom" and collaborative learning, student teams work through activity sheets to investigate key ideas and relationships before a formal introduction in lecture. The project team conjectures that discovery learning with the physical models builds geometric understanding of multivariable calculus, imbues meaning in the algebraic formulas, improves performance and attitudes, and improves understanding of scientific applications. To disseminate its findings and exercise the project's broader impact, the PI team is conducting summer workshops with dozens of faculty, previously recruited from high schools, two- and four-year colleges and universities. Participants learn how about effective use of the surfaces and during the subsequent academic year all participants teach multivariable calculus using the surfaces, as well as arrange a control class at their respective institutions for comparison. Written assessments and clinical interviews are being used to compare learning outcomes between students using the surfaces and students receiving traditional instruction.