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

本项目旨在提高工科学生的能力，使他们能够将大一所学的微积分知识转移和应用到大二的工程入门课程中。在2006年的课程回顾中，工程学院发现，许多学生在第一年的数学课程中取得了成功，但在第二年的工程课程中，他们很难使用基本的数学概念来表示物理量及其关系。在工程课程特别工作组建议的推动下，2007年春季，一群工程和数学教师开始在核心工程数学课程中注入吸引人的、多样化的问题解决经验，并结合了物理科学和工程的示例应用。在2007年秋季的一项试点工作中，这些类型的应用程序被整合到工程数学序列中的第一个必修数学课程中。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，通过开发工具来评估学生对代表物理现象的数学的理解以及他们在参加问题解决讲习班之前和之后应用数学来解决涉及物理量和关系的问题的技能；同时，在学生参加问题解决研讨会之前和之后，评估他们对自己对数学的理解和运用数学在工程中取得成功的能力的信心。该项目还评估了在第一年的微积分课程中加入协作应用解决问题的内容是否会提高学生在第二年的核心工程课程（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。人们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。该项目正由一位独立的评估人员进行评估。

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.