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.
