In this presentation the class will do two activities focused on describing how mathematical relationships are related to Earth processes. First, groups of students will use whiteboards to sketch physical processes represented by a well-known equations (e.g. F = ma or E = mc^2). Next, students will write prose descriptions of these processes. In both situations, emphasis will be placed on endmember cases and on relationships between variables. Groups will present their results and identify common themes in their descriptions.
Many students perceive equations as simply collections of variables, and when solving problems may choose an equation because it has the right variables rather than because it represents the right process. 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).
After creating Equation Journals, students understand that equations represent specific processes that may be described qualitatively or through concept sketches. A primary outcome of this assignment is to promote understanding of physical processes and reduce math phobia.
Students in my geophysics classes use equation journals instead of "cheat sheets" for exams. I review their journals on a weekly basis to see (a) if they exhibit understanding of the physical processes represented by the math, (b) if they are able to explain how different parameters affect these processes, and (c) if they have misconceptions about these relationships.
Why It Works
There are three major benefits to the Equation Journal. First, it provides students with a conceptual way of thinking about mathematical relationships. Secondly, it helps students see that equations are not simply collections of variables, they tell a story about how Earth processes work. Finally, reviewing the journals allows the instructor to identify student misconceptions. In course evaluations at Western Washington University students routinely describe the Equation Journal as helpful and informative, and many voluntarily continue to journal equations in other classes.