PICTURES AND PROSE: A QUALITATIVE WAY TO ENHANCE STUDENT UNDERSTANDING OF QUANTITATIVE PROCESSES

Many students perceive equations as collections of variables, and when solving problems may choose an equation because it has the right variables rather than because of the physical process it represents. Helping students recognize that equations tell a story about Earth processes is the objective of the Equation Journal, a modified equation sheet used in geophysics classes at Western Washington University. Rather than memorize equations or bring in a “cheat sheet” to exams, students journal about equations, writing prose descriptions of the processes represented by these mathematical relationships. The journals include information about the equation, descriptions of each of its variables (with units), and include a description of what the equations tells us about how the Earth works. Students often add additional comments that explain endmember cases, or that relate to specific Earth problems (e.g. the fact that seismic S-waves cannot propagate in fluids because they have to resistance to shearing). A second means by which students examine the physical meaning of equations is through whiteboarding: students are asked to sketch the process represented by mathematical relationships. This sketches often include the actions involved in these processes: the direction of energy flow, the angle at which waves move, or the direction of stresses. Both the journal and sketch also illuminate student misconceptions about the process or the relationship between variables. The combination of math, prose, and sketch allows students to explore their understanding of a concept through a variety of tools.