Equation Dictionary

Jackie Caplan-Auerbach
Western Washington University
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The equation dictionary is an expansion of the traditional notecard that students bring to equation-based tests. It requires them to provide a prose explanation for the processes described by an equation as well as details about the associated variables.

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This is an upper level undergraduate course in introductory geophysics. It is required of all geology majors.

Skills and concepts that students must have mastered

No specific skills are required; in fact, this activity could be used in any applied science course. Students are introduced to equations in lecture or in the textbook, and the activity asks them to explain (in words) the processes described in the mathematical relationships presented by the equation.

How the activity is situated in the course

The dictionary is integrated into all parts of the course. Students create the dictionary over the course of the quarter, as new material and new equations are presented. They use it on homework and in-class assignments, and it is the only thing (other than a calculator) that they may bring with them to exams. I collect the dictionaries before each exam to review student understanding of the equations and their ability to describe them in words. This also allows me to identify any misunderstandings that students have about mathematical concepts or the methods presented in class.


Content/concepts goals for this activity

This activity is designed to alleviate student discomfort and fear of equations. It shows them that equations are just concise ways of explaining physical relationships and processes.

Higher order thinking skills goals for this activity

The equation dictionary requires students to synthesize their understanding of the physical processes occurring in the Earth with the equations that describe these processes.

Other skills goals for this activity

Description of the activity/assignment

When equations are presented in class or in the context of textbook reading, students first evaluate whether the equation is appropriate for use in the dictionary (is it useful in many situations or specific to one problem? Is it a "final" version of an equation, or can it be simplified? Is it likely to be used in solving geophysical problems?) Once an equation is selected for the dictionary, students add a "definition" that includes (a) a short description of each variable and relevant constants, including appropriate units, (b) a written description of the process or relationships presented within the equation, and (c) any additional notes that help them understand the equation. The dictionary may be used on homework and exams, which encourages students to describe the equations in a manner that is meaningful to them. Thus, rather than simply write down the equation for seismic moment, a student might add "Seismic moment is a function of the size of the fault as well as the rigidity of the rock. The larger the fault or the displacement, the larger the earthquake". This activity allows students to evaluate their understanding of equations and the underlying physical processes.
Addresses student fear of quantitative aspect and/or inadequate quantitative skills
Addresses student misconceptions

Determining whether students have met the goals

Prior to each test, students turn in their dictionaries for evaluation. I read over the definitions and examine whether students are accurately describing the processes associated with each equation. A student who does not understand the meaning behind an equation commonly restates words the individual variables in the equation (e.g. "S wave velocity equals the square root of the shear modulus divided by density"). In contrast, writing "the speed of an S wave is higher in a material with greater rigidity." I evaluate whether students have accurately described the underlying physics. The dictionary is also very useful in illuminating what parts of the material were not presented in a clear manner (in which case few students are able to explain the equation).

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