Multiple representations and free-body diagrams: Do students benefit from using them

Introductory physics students have difficulties understanding concepts and solving problems. When they solve problems, they use surface features of the problems to find an equation to calculate a numerical answer often not understanding the physics in the problem. How do we help students approach problem solving in an expert manner? A possible answer is to help them learn to represent knowledge in multiple ways and then use these different representations for conceptual understanding and problem solving. This solution follows from research in cognitive science and in physics education. However, there are no studies in physics that investigate whether students who learn to use multiple representations are in fact better problem solvers. This study focuses on one specific representation used in physics--a free body diagram. A free-body diagram is a graphical representation of forces exerted on an object of interest by other objects. I used the free-body diagram to investigate five main questions: (1) If students are in a course where they consistently use free body diagrams to construct and test concepts in mechanics, electricity and magnetism and to solve problems in class and in homework, will they draw free-body diagrams on their own when solving exam problems? (2) Are students who use free-body diagrams to solve problems more successful then those who do not? (3) Why do students draw free-body diagrams when solving problems? (4) Are students consistent in constructing diagrams for different concepts in physics and are they consistent in the quality of their diagrams? (5) What are possible relationships between features of a problem and how likely a student will draw a free body diagram to help them solve the problem?; I utilized a mixed-methods approach to answer these questions. Questions 1, 2, 4 and 5 required a quantitative approach while question 3 required a qualitative approach, a case study. When I completed my study, I found that if students are in an environment which fosters the use of representations for problem solving and for concept development, then the majority of students will consistently construct helpful free-body diagrams and use them on their own to solve problems. Additionally, those that construct correct free-body diagrams are significantly more likely to successfully solve the problem. Finally, those students that are high achieving tend to use diagrams more and for more reasons then students who have low course grades. These findings will have major impacts on how introductory physics instructors run their classes and how curriculums are designed. These results favor a problem solving strategy that is rich with representations.