Mathematical Problem Solving for Engineering Students

工科NEC(59)为了满足全国对工科学生提高数学和问题解决能力的需求，一组来自工程和数学的教职员工正在创建教学技术和课程，以培养针对准备学习微积分的新生的解决问题的技能。该项目正在我们第一年的工程基础课程(GES 131)的一个部分测试这些技术。目标是在未来的课程中促进对知识和技能的掌握和转移。这门课程的重点是：1.挑战学生，为他们提供高水平的熟练程度来解决“难”的问题，在这些问题中，解决的方法和概念并不是一下子就知道的。通过学习如何描述他们用来解决问题的方法，发展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“难”问题时，培养自我效能感。这门课程让学生参与协作学习练习，这为学生提供了学习和练习解释和自我解释技巧的主要方法。其他教学活动包括累计复习数学概念、动手练习、元认知指导、向外部访客演示以及学生创造自己的难题。使用传统方法将这一部分的学生学习与其他部分的学生的表现进行比较。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感问卷、反思试卷、焦点小组、观察以及后续数学和物理课程中的特定试题。这项概念验证研究的成功预计将导致一项全面的开发工作，将编写一本教科书和一系列广泛的难题，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.