|About the Book|
While mathematics is widely believed to be important for success in introductory physics there has been little research to distinguish the importance of different mathematical skills. Even though most math diagnostic tests focus on algorithmicMoreWhile mathematics is widely believed to be important for success in introductory physics there has been little research to distinguish the importance of different mathematical skills. Even though most math diagnostic tests focus on algorithmic manipulation and computation, we argue that algebraic representation is as, if not more, important a skill for physics expertise.-The primary focus of this dissertation is the study of symbolic physics questions. A comfort with both constructing and interpreting symbolic equations is important for physics expertise because symbolic mathematics is the foremost language of physics. Even so, students in introductory physics often express a strong preference for numeric questions.-I will describe the results of studies that show that differences in score as high as 50% can be achieved between numeric and symbolic versions of the same question. I will also describe careful studies involving the analysis of both student written work and video from student interviews that revealed why students find symbolic questions difficult. We find that the main cause of students poor performance on symbolic questions is due to confusion about the meaning of symbols and symbolic equations. Symbolic solutions require a greater attention to meaning than do numeric solutions. When solving a symbolic question students must actively identify known quantities while reading the question, keep track of symbol states, and keep track of the relationships between symbols.-I will present data that show that the difficulties associated with symbolic physics questions are the most pronounced for the students most likely to fail physics. Further, a math diagnostic exam we have created indicates that word problems that stress mathematical representation are better predictors of success than algorithmic manipulation questions.