Mathematical Problem Solving for Engineering Students

工程NEC（59）为了满足全国对工程专业学生数学和解决问题能力的需求，一个由工程和数学教师组成的团队正在创建教学技术和课程，以开发针对准备参加微积分的大一新生的解决问题能力。该项目是测试这些技术在我们的工程课程（GES 131）的第一年基础的一部分。一个目标是促进掌握和转让的知识和技能，在未来的课程。本课程的重点是：1.挑战学生，并为他们提供一个高水平的熟练程度，以解决“困难”的问题，其中的方法和解决方案的概念是不立即知道。2.通过学习如何描述他们用来解决问题的方法，培养学生对问题解决过程的概念性理解。3.在学生学习如何解决这些“困难”问题时，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主要方法。额外的教学活动包括数学概念的累积复习，动手练习，元认知教学，向外部访问者介绍，以及学生创建自己的难题。学生在这一部分的学习是比较学生的表现在其他部分使用传统的方法。 评估技术包括课程前和课程后的问题解决能力测试，课程前和课程后的自我效能问卷，反思论文，焦点小组，观察，以及随后的数学和物理课程的具体考试问题。 这一概念验证研究的成功预计将导致全面的开发工作，这将开发一本教科书和一个广泛的困难问题清单，供其他人使用和适应。

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.