DEMYSTIFYING THE EQUATIONS OF SEDIMENTARY GEOLOGY

One of the great challenges in teaching undergraduates is finding ways to get them to apply knowledge or skills learned in one class to problems encountered in subsequent classes.  Case in point: the use of algebra, trigonometry, and even rudimentary calculus in geology classes!  Understanding mathematical equations is hard work, but it is not impossible with the right attitude and techniques.  Under ideal circumstances, we can help our students derive equations from first principles and thus promote a deeper comprehension of the equation's meaning.  Often, however, equations are empirical or time may simply not permit the derivation of complex mathematical relationships.  In this case, it can be instructive to tear equations apart to develop an intuition for the relationships that they are meant to express and a comprehension of how those relationships can be expected to change in response to changing system conditions.

This presentation suggests three practical ways instructors can build students' confidence in their ability to peer into the meaning of the equations they encounter in sedimentary geology.  These techniques are:

(1) Surgical Strike Reviews – 5 to 10-minute targeted review of relevant math principles at the beginning of the appropriate lecture;

(2) Unit Analyses – assigning fundamental units of Mass, Length, and Time to test whether an equation has been derived correctly or to explore the meaning of derivative units of measure that may be unfamiliar to students; and

(3) Perturbation Interrogation – asking students to identify whether the quantity of interest described by an equation will increase or decrease when individual components of the equation increase or decrease. 

Examples of the application of these techniques will be presented using equations drawn from an undergraduate course in sedimentation and stratigraphy; however, these techniques are easily adaptable for application in most undergraduate courses in geology.