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首页> 外文会议>American Society For Engineering Education Annual Conference and Exposition >INVESTIGATING ENGINEERING STUDENTS' MATHEMATICAL MODELING ABILITIES IN CAPSTONE DESIGN
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INVESTIGATING ENGINEERING STUDENTS' MATHEMATICAL MODELING ABILITIES IN CAPSTONE DESIGN

机译：调查工程学生在Capstone设计中的数学建模能力

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Engineering capstone design is a culminating experience that is intended to provide an opportunity for students to apply their previous engineering knowledge to develop solutions to open-ended problems. Capstone design problems are often analytically complex, and their solutions integrate several disciplinary fundamentals, as well as more general design process knowledge. Often, the expectation is that a thorough or rigorous solution to a capstone level problem would include some type of computational or mathematical analysis appropriate to that discipline. However, engineering students often struggle in recognizing when and how disciplinary knowledge (e.g. mathematical analysis inherent in many engineering fundamentals) applies to their particular design solutions. This paper describes the strategy for and initial results of a study exploring how students use mathematical reasoning when developing design solutions. Specifically, we want to understand where students struggle in the development and implementation of a mathematical model. We conducted our study in a biomedical capstone (senior) design course. We presented students with a scenario based on a design problem in using phototherapy to treat jaundice, and asked specific questions relating to mathematical modeling in the solution to this problem. We developed the scenario and corresponding assignments based on previous work that identified six steps for what mathematical modeling should include. We staged the activities over a four-week period such that students addressed two of these steps at each time interval, or assignment stage. This report analyzes results from the first two activities, which focused on identifying the real-world phenomenon and simplifying or idealizing it. We found that in an open-ended statement of the problem, no students proposed using a mathematical model to assist in designing the device. When we specifically asked for a mathematical model in a second activity, only five students of thrity-eight proposed a purely mathematical model, and another two proposed experiments that would lead to predictive equations. When asked to identify parameters that would be important to model, 37% of students chose ones that were part of the design requirements, and therefore fixed, and only 35% correctly chose parameters that could be adjusted to meet the design requirements. These results show a gap in using modeling skills in design, and suggest that educational interventions are needed to improve these capabilities.
机译：工程帽设计是一种最终的经验，旨在为学生提供以前的工程知识为开发开放问题的解决方案提供机会。 Capstone Design问题通常是分析复杂的，他们的解决方案集成了几个学科基本面，以及更普遍的设计过程知识。通常，期望是，对Capstone水平问题的彻底或严格的解决方案将包括适合该纪律的某种类型的计算或数学分析。然而，工程学生往往在识别何时以及如何纪律知识（例如，在许多工程基础上固有的数学分析）适用于他们的特定设计解决方案。本文介绍了一项研究的策略和初始结果，探索学生在开发设计解决方案时如何使用数学推理。具体来说，我们希望了解学生在努力在数学模型的开发和实施中奋斗的地方。我们在生物医学帽（高级）设计课程中进行了研究。我们向学生提供了一种情况，根据使用光疗法处理黄疸的设计问题，并询问了与解决问题的解决方案中数学建模有关的具体问题。我们基于以前的工作开发了方案和相应的作业，该工作标识了数学建模应该包括的六个步骤。我们在4周的时间内上演了活动，以便学生在每个时间间隔或分配阶段解决这些步骤中的两个。本报告分析了前两项活动的结果，这些活动集中在识别现实世界现象和简化或理想化它。我们发现在一个开放的问题声明中，没有学生使用数学模型提出以帮助设计设备。当我们在第二次活动中专门要求数学模型时，只有五名学生的Thrity-8提出了纯数学模型，另外两个提出的实验将导致预测方程。当被要求确定对模型很重要的参数时，37％的学生选择了一部分设计要求的学生，因此固定，只有35％正确选择了可以调整的参数，以满足设计要求。这些结果表明，在使用设计中的建模技巧方面表现出差距，并表明需要教育干预来提高这些能力。

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