Does Explaining Equations in Their Own Words Help Students Attach Physical Meaning to the Equations?

In order for students to correctly solve a given problem, they must have a good understanding of the different physical situations described by the equations in their toolbox. This means that students must associate equations with their physical meaning and not just see equations as collections of letters and mathematical symbols into which to plug numbers. This past fall semester, we asked students in two undergraduate Physics courses to explain important equations in their own words in a variety of pedagogical ways. To motivate and test their understanding, exams and quizzes that students took during the semester included an open-ended “Explain this equation in words” question, which we scored based on the depth of understanding shown. There are a few questions we are interested in exploring: As students practice this skill, do their explanations become better (i.e. do individual students show deeper understanding as the semester progresses)? Is a student’s score in the “Explain this equation in words” question on each exam correlated to his/her total exam score and to his/her final grade? Does the emphasis of putting equations into words result in greater conceptual understanding? We will use standardized preand post-tests given in each of our courses to see if there is a difference in gain as compared to past semesters. We will present data from three sections of our second-semester calculus-based Physics course, and from our first-semester junior-level Electricity and Magnetism course. Introduction The study we present in this paper arose from two separate trends in our university and the larger higher-education community, plus an observation. The first is the trend in Physics education to focus on teaching for conceptual understanding, for example, through Peer Instruction or Workshop Physics (which is part of The Physics Suite). The second trend is the push to improve student writing through programs such as Writing Across the Curriculum, and in particular through Writing to Learn, where short writing exercises are used to help students think through a concept or a problem. The observation was that a considerable fraction of our students, while talking to other students in class or asking the instructor a question, was referring to variables in equations by the name of the symbol instead of the physical quantity represented by the symbol; for example a student might say, “the change in potential is the same because the E is the same.” It occurred to us that students might be doing this because they were looking at equations as mathematical constructs only and not as an expression of physical relationships or laws. Attaching a physical meaning to equations affects the way we view equations, Redish says, “first, through seeing equations as relations, not as calculational methods, and second, through ‘filtering the equation through the physics’.” In a typical Physics class, we introduce equations in lecture by motivating them from an example problem and building intuitive relationships. Then we either derive or write out the equation, maybe do an example, and finally students answer conceptual questions and/or solve problems. What is missing is the piece where students reflect on the meaning of the equations. Redish suggests that we need to “find activities that help our students build knowledge into P ge 25477.2 intuitions/understanding.” This is what we are trying to achieve through having students write equations in their own words. Our hypothesis is that by giving the students continuous practice in writing they will gain conceptual understanding that will be reflected in their problem solving. Methodology We are conducting this study in three sections of Classical Physics II, the second semester calculus-based introductory physics course, and in one section of the upper-level Electricity and Magnetism. Classical Physics II is taught in a modified workshop style, with lecture, laboratory, and problem-solving combined into a two and a half hour class period. The students in the course are predominantly Electrical and Mechanical Engineering majors, but it is also a required course for Chemistry, Biology, Geology, and Physics majors. Electricity and Magnetism (E&M), on the other hand, is lecture based, although in the last two years the instructor has added an optional problem-solving session that is well attended by students. E&M is almost exclusively taken by Electrical Engineering and Physics majors. We first introduced “Equations in Words” in our courses as part of homework or in-class problem packets. We showed students an example of an equation in words to clarify the expectation that they were not to do a literal translation symbol by symbol but that they had to think about the physical meaning of the equation. A typical “Equations in Words” problem from the Waves unit in Classical Physics II is shown below: Consider the following equation: ∆L = n + 1 2 λ n = 0, 1, 2, 3, ... a) This equation applies to: b) The variables and their units are: