Improving students' mathematical sense-making in engineering: Research and development

在这个项目中，来自马里兰大学物理系、机械工程系和电子与计算机工程系的一个团队将重新设计一门大一物理课程的顺序，以提高学生的数学理解能力或“理解能力”。工科学生。将通过比较修读传统课程的学生和修读二年级机电工程必修课程的学生，来评估这些改进的效果。将讨论两个具体的研究问题。什么因素对学生有影响？数学理解困难？重新设计的物理入门课程能提高学生吗？在以后的工程课程中的数学理解和整体表现？先前的研究表明，为了解决第一个问题，研究团队不仅要调查数学技能缺陷，还要调查学生的数学技能缺陷。缺乏对相关物理/工程概念的理解，缺乏在形式主义和现实世界关系之间转换的能力或倾向，以及naïve关于如何学习和应用数学的信念。这些因素和它们之间的相互作用将使用多种方法进行探索，包括分析学生在小组中解决具有挑战性问题的视频。第二个问题将使用团队？S以前的工作是修改基于代数的生命科学专业入门物理序列。对于工程师来说，有效地使用数学不仅仅是操纵方程和应用算法。它涉及到数学意义？或者通过在纸上的符号关系和世界上的因果关系和功能关系之间进行翻译来寻找连贯性和意义。尽管数学意义对学生来说很重要？成功的建模和设计，许多工程专业的学生在这方面有困难。对数学的准备不足和缺乏信心往往会使学生气馁，而改进数学意义构建的教学方法可以增加工程专业学生的数量和多样性。

In this project a team from the University of Maryland Departments of Physics,Mechanical Engineering, and Electrical & Computer Engineering, will redesign a freshman physics course sequence to improve mathematical comprehension or ?sense-making? in engineering students. It will assess the effects of these improvements by comparing students who had taken the traditional courses with students who had taken the modified courses in sophomore level required mechanical and electrical engineering courses. Two specific research questions will be addressed. What factors contribute to students? difficulties with mathematical sense-making? Can redesigned introductory physics courses improve students? mathematical sense-making and overall performance in their later engineering courses? Previous research suggests that to address the first question the research team must probe not just for mathematical skill deficiencies but also for students? lack of understanding of the relevant physics/engineering concepts, lack of ability or propensity to translate between formalism and real-world relations, and naïve beliefs about how to learn and apply math. These factors and interactions among them will be explored using multiple methods, including analysis of video of students solving challenging problems in small groups. The second question will be addressed using the team?s previous work in modifying the algebra-based introductory physics sequence for life science majors. For engineers, effective use of mathematics is more than manipulating equations and applying algorithms. It involves mathematical ?sense-making? or looking for coherence and meaning partly by translating between symbolic relations on the page and causal and functional relations in the world. Although mathematical sense-making is central to students? success with modeling and design, many engineering students have trouble with it. Underpreparation and underconfidence in math often discourage students, and improved methods of teaching mathematical sense-making can increase the number and diversity of engineering majors.