Application and Confidence Inventories for Assessing Curricular Change in Introductory Engineering Mathematics Instruction

这个项目是为了提高工科学生将他们在大学一年级学到的微积分应用到二年级的工程学入门课程的能力的继续努力。在2006年的课程审查过程中，工程学教师注意到，许多在一年级数学课程中取得成功的学生，在二年级的工程课程中，仍然难以使用基本的数学概念来表示物理量及其关系。在工程课程任务组建议的激励下，2007年春，一批工程和数学教师开始向核心工程数学课程注入引人入胜和多样化的问题解决经验，包括来自物理科学和工程学的范例应用。在2007年秋季的一次试点工作中，这些类型的应用程序被整合到工程数学序列中的第一门必修数学课程中。这是通过将每周两节复习课中的一节转化为协作解决问题的课程来实现的。该项目正在评估将这些活动加入课程的效果，方法是开发工具，评估学生在参加问题解决讲习班之前和之后对作为物理现象代表的数学的理解以及他们应用数学解决涉及物理量和关系的问题的技能的能力；还评估学生在参加问题解决讲习班之前和之后对他们对数学的理解和他们利用数学在工程上取得成功的能力的信心。该项目还在评估将协作应用问题解决纳入一年级微积分课程是否会提高学生在二年级核心工程课程--力学、动力学、电路和热力学--中应用数学的能力。该项目的核心问题是探索课程内容和教学方法的变化如何提高学生将数学应用于经典工程应用的能力，并提高学生解决问题的信心。正在开发工具来评估核心数学、科学和工程内容的整合程度。该项目正在由一名独立评估员进行评估。

This project is a continuation of efforts to enhance engineering students' abilities to transfer and apply the calculus they learn in their first year of college to the introductory engineering courses they take in their second year. In the course of a 2006 curriculum review, engineering faculty observed that many students who succeed in the first year mathematics courses nonetheless have difficulty using elementary mathematical concepts to represent physical quantities and their relationships in their second year engineering courses. Spurred by Engineering Curriculum Task Force recommendations, in the spring of 2007 a group of engineering and mathematics faculty began to infuse core engineering mathematics courses with engaging and diverse problem solving experiences, incorporating example applications from the physical sciences and engineering. In a pilot effort in Fall 2007 these types of applications were integrated into the first required math course in the engineering math sequence. This was accomplished by transforming one of two weekly recitation sections into a collaborative problem-solving session. This project is evaluating the effect of adding these activities to the curriculum, by developing instruments to assess students' understanding of mathematics as representative of physical phenomena and their skill in applying mathematics to solve problems involving physical quantities and relationships, both before and after their participation in the problem-solving workshops; and also to assess students' confidence about their understanding of mathematics and their ability to use mathematics to succeed in engineering, both before and after their participation in the problem-solving workshops. The project is also assessing whether the inclusion of collaborative applied problem-solving in the first-year calculus courses leads to improvement in students' abilities to apply mathematics in the core second-year engineering courses - mechanics, dynamics, electrical circuits, and thermodynamics. The project's central questions are exploring how curricular changes in both content and method of instruction might enhance student ability to apply mathematics to classical engineering applications and improve student confidence in solving problems. Tools are being developed for assessing the degree of integration of core math, science, and engineering content. The project is being evaluated by an independent evaluator.