A National Model for Engineering Mathematics Education: Longitudinal Impact at Wright State University
A National Model for Engineering Mathematics Education: Longitudinal Impact at Wright State University
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工程数学教育的国家模式：莱特州立大学的纵向影响
DOI：
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发表时间：
2013
期刊：
影响因子：
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通讯作者：
A. Bourne
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文献类型：
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作者：
N. Klingbeil;A. Bourne
新生无法超越传统的第一年微积分顺序是全国工程项目流失的主要原因。因此，本文将总结美国国家科学基金会资助的赖特州立大学的倡议，重新定义工程数学的教学方式，以提高学生的保留率，动机和成功的工程目标。该方法涉及EGR 101一年级工程课程的发展，取代传统的数学先决条件的核心大二工程课程沿着与所需的微积分序列的更及时的结构。自2004年秋季成立以来，赖特州立大学模式对学生保留，动机和成功的影响已被广泛报道。本文包括赖特州立大学最近的一项纵向研究的结果，从学生在数学和工程方面的表现，最终的毕业率。结果表明，该计划大大减轻了传入的数学准备对学生在整个范围内的ACT数学成绩的工程成功的影响，这使入学学生的平均毕业率增加了一倍多。此外，它这样做并没有削弱毕业生的素质，他们实际上享受了毕业GPA的轻微（但统计上显着）增加。最后，这种方法已被证明对代表性不足的群体的成员产生了最大的影响，对他们中的许多人来说，传统的工程课程根本无法获得。最后，本文对学生的感知数据进行了纵向检查，这似乎建立了一个明确的联系，程序对学生的动机和自我效能感和最终的毕业率的影响。众所周知，学生在工程方面的成功高度依赖于学生在数学方面的成功，也许更重要的是，将数学与工程联系起来的能力。然而，一年级的学生通常到达大学，几乎不了解他们的大学预科数学背景如何与他们选择的学位课程，更不用说他们未来的职业生涯。尽管全国呼吁增加工程和其他STEM学科的毕业生数量，但新生无法成功超越传统的大一微积分序列仍然是全国工程项目流失的主要原因。因此，迫切需要一个经过验证的模型，它消除了传统工程课程中第一年的数学瓶颈，但可以很容易地被全国各地的工程项目采用。这就是这项工作的重点。赖特国家模型开始与一个新的第一年工程数学课程，EGR 101工程应用数学导论的发展。本课程由工程系教授，包括讲座、实验和复习部分。使用面向应用的，动手的方法，该课程只涉及核心工程课程中实际使用的突出数学主题。其中包括传统物理学、工程力学、电路和计算机编程序列。EGR 101课程取代了上述核心课程的传统数学先决条件要求，因此学生P ge 2.76.2可以在课程中前进，而无需首先完成传统的第一年微积分序列。赖特国家模型的结论是一个更及时的结构所需的数学序列，与大学和ABET的要求。其结果是将传统的对数学先决条件要求的强调转变为对数学工程动机的强调。EGR 101讲座部分完全由基于问题的学习驱动，而实验室和复习部分则为学生提供广泛的协作学习。因此，这门课程得到了关于学生如何学习的文献的有力支持。EGR 101实验室的摘录如图1-2所示。实际上，用物理方法测量导数作为自由落体的速度（图1），或用积分作为力-挠度曲线下的面积（图2），比单纯的课堂讲授更能从概念上理解数学概念。赖特州立大学的模式于2004年秋季首次实施，其对学生保留，动机和工程成功的影响已被广泛报道。2007年引入的EGR 199作为EGR 101的前身，为最初准备不足的学生进一步加强了这一方法，并使赖特州立大学的核心工程课程，即使是数学成绩低至Calc I以下3级的新生也可以使用。初步实施的结果简述如下。初步实施的结果EGR 101课程于2004年秋季首次举办。所有符合条件的机械工程、材料科学和工程、电气工程、工程物理、生物医学工程以及工业和系统工程的新生都参加了该课程。在实施的第一年，共有158名学生在EGR 101注册，超过74%的学生以“C”或更高的成绩完成课程。该计划的最初实施对赖特州立大学的学生保留和工程成功产生了直接和巨大的影响。如图3所示，与前四年的平均基线数据相比，每个需要EGR 101的部门在2004-2005年的第一年保留率都有所增加。总体而言，要求EGR 101的专业第一年保留率从68.0%增加到78.3%。图1.衍生品实验室图2。积分实验室
The inability of incoming students to advance past the traditional first-year calculus sequence is a primary cause of attrition in engineering programs across the country. As a result, this paper will summarize an NSF funded initiative at Wright State University to redefine the way engineering mathematics is taught, with the goal of increasing student retention, motivation and success in engineering. The approach involves the development of EGR 101 a first-year engineering course replacing traditional math prerequisites for core sophomore engineering courses along with a more just-in-time structuring of the required calculus sequence. Since its inception in Fall of 2004, the impact of the Wright State model on student retention, motivation and success has been widely reported. This paper includes results of a recent longitudinal study of program impacts at Wright State University, from student performance in math and engineering to ultimate graduation rates. Results show that the program has substantially mitigated the effect of incoming math preparation on student success in engineering across the entire range of incoming ACT math scores, which has more than doubled the average graduation rate of enrolled students. Moreover, it has done so without watering down the caliber of graduates, who have actually enjoyed a slight (but statistically significant) increase in graduation GPA. Finally, the approach has been shown to have the greatest impact on members of underrepresented groups, for many of whom the traditional engineering curriculum is simply not accessible. The paper concludes with a longitudinal examination of student perception data, which appears to establish a clear link between program impacts on student motivation and self-efficacy and ultimate graduate rates. The Wright State Model It is well known that student success in engineering is highly dependent on student success in math, and perhaps more importantly, on the ability to connect the math to the engineering. However, first-year students typically arrive at the university with virtually no understanding of how their pre-college math background relates to their chosen degree programs, let alone their future careers. And despite the national call to increase the number of graduates in engineering and other STEM disciplines , the inability of incoming students to successfully advance past the traditional freshman calculus sequence remains a primary cause of attrition in engineering programs across the country. As such, there is a drastic need for a proven model which eliminates the first-year mathematics bottleneck in the traditional engineering curriculum, yet can be readily adopted by engineering programs across the country. Such is the focus of this work. The Wright State model begins with the development of a novel first-year engineering math course, EGR 101 Introductory Mathematics for Engineering Applications. Taught by engineering faculty, the course includes lecture, laboratory and recitation components. Using an application-oriented, hands-on approach, the course addresses only the salient math topics actually used in core engineering courses. These include the traditional physics, engineering mechanics, electric circuits and computer programming sequences. The EGR 101 course replaces traditional math prerequisite requirements for the above core courses, so that students P ge 2.76.2 can advance in the curriculum without first completing a traditional first-year calculus sequence. The Wright State model concludes with a more just-in-time structuring of the required math sequence, in concert with college and ABET requirements. The result has shifted the traditional emphasis on math prerequisite requirements to an emphasis on engineering motivation for math. The EGR 101 lecture sections are completely driven by problem-based learning, while the laboratory and recitation sections offer extensive collaborative learning among the students. As such, the course is strongly supported by the literature on how students learn. Excerpts from the EGR 101 laboratory are shown in Figures 1-2. Indeed, physical measurement of the derivative as the velocity in free-fall (Fig. 1), or of the integral as the area under the force-deflection curve (Fig. 2), provides a much greater conceptual understanding of the mathematical concepts than classroom lecture alone. The Wright State model was first implemented in Fall of 2004, and its effect on student retention, motivation and success in engineering has since been widely reported. The 2007 introduction of EGR 199 as a precursor to EGR 101 for initially underprepared students has further strengthened the approach, and has made Wright State’s core engineering curriculum accessible even to incoming students with math placement scores as low as 3 levels below Calc I. Results of the initial implementation are briefly summarized below. Results of Initial Implementation The EGR 101 course ran for the first time in the Fall of 2004. All eligible incoming students in mechanical engineering, materials science and engineering, electrical engineering, engineering physics, biomedical engineering and industrial and systems engineering were enrolled in the course. Through its first year of implementation, a total of 158 students were enrolled in EGR 101, with over 74% completing the course with a grade of “C” or better. The initial implementation of the program had an immediate and dramatic effect on student retention and success in engineering at Wright State. As shown in Fig. 3, every department requiring EGR 101 saw an increase in first-year retention in 2004-2005, as compared to baseline data averaged over the prior four years. Overall, majors requiring EGR 101 saw first-year retention increase from 68.0% to 78.3%. Figure 1. The Derivative Lab Figure 2. The Integral Lab