Mathematical Problem Solving for Engineering Students

为了满足全国对工科学生提高数学和解决问题能力的需求，一个由工程和数学专业的教师组成的团队正在开发教学技术和课程，以培养准备学习微积分的大一新生解决问题的能力。该项目在我们第一年的工程基础课程（GES 131）的一个部分测试了这些技术。目标是在未来的课程中促进知识和技能的掌握和转移。本课程的重点是：1。挑战学生，并提供他们解决“难”的问题，其中解决的方法和概念不是立即知道的熟练程度。通过学习如何描述他们用来解决问题的方法，培养学生对解决问题过程的概念理解。3. 在学生学习如何解决这些“难题”的过程中，培养自我效能感。本课程让学生参与合作学习练习，为学生学习和练习解释和自我解释技巧提供了一个主要的方法。额外的教学活动包括数学概念的累积复习、动手练习、元认知的指导、对外部访客的演讲，以及学生自己创造难题。使用传统方法将学生在这部分的学习情况与其他部分的学习情况进行比较。评估方法包括课前和课后问题解决能力测试、课前和课后自我效能问卷、反思性论文、焦点小组、观察以及后续数学和物理课程的具体考题。这项概念证明研究的成功预计将导致全面的开发工作，将编写一本教科书和一份广泛的难题清单，供其他人使用和改编。

Engineering NEC (59) In response to the national need for increased mathematics and problem solving skills among engineering students, a team of faculty members from engineering and mathematics are creating pedagogical techniques and curriculum to develop problem solving skills that targets freshman who are ready to take calculus. The project is testing these techniques in one section of our first year Foundations of Engineering course (GES 131). A goal is to promote mastery and transfer of knowledge and skills in future coursework. The emphasis of the course is to:1. Challenge students and provide them with a high level of proficiency to solve "hard" problems, in which the method and concepts for solution are not immediately known.2. Develop student's conceptual understanding of the problem solving process by learning how to describe the methods that they used to solve the problem. 3. Develop self-efficacy as students learn how to solve these "hard" problems. The course engages the students in collaborative learning exercises, which provides a primary method for students to learn and practice explanation and self-explanation techniques. Additional instructional activities include cumulative review of mathematics concepts, hands on exercises, instruction in metacognition, presentations to external visitors, and students creating their own hard problems. Student learning within this section is being compared to student performance in other sections using traditional methods. Assessment techniques include pre and post course testing of problem solving ability, pre and post course self efficacy questionnaires, reflective papers, focus groups, observation, and specific examination questions in subsequent math and physics courses. The success of this proof of concept study is expected to lead to a full development effort that would develop a textbook and an extensive list of hard problems for others to use and adapt.