Lawrence D. Lemke

Wayne State University

These techniques are easily adaptable for application in most undergraduate courses in geology. The examples included in this exercise were drawn from a required undergraduate course in sedimentation and stratigraphy.

A basic working knowledge (high school or first-year college level) of algebra, geometry, trigonometry, physics, and chemistry are assumed.

These activities are used throughout the duration of my course. I like to review mathematical concepts (a surgical strike) at the beginning of a lecture (when students are fresh) so that students are prepared to think about their application later in the lecture without triggering a panic impulse associated with seeing a new equation. I force my students to conduct unit analyses routinely (immediately after introducing or deriving a new equation in lecture, and once or twice on each exam). I also use the perturbation approach regularly after introducing new equations to help build students' intuition about how changes in the relevant system variables will affect the behavior of the equation.

The purpose of these exercises is to reinforce what students already know about equations and the mathematical expression of physical or chemical phenomena. Examples are presented in the following areas for sedimentary geology:

- hydrodynamic forces
- settling velocity (Stoke's Law)
- sediment grain size analysis
- calcite dissolution and precipitation

This activity touches on each of the higher levels of Bloom's taxonomy of educational objectives. Examples include:

Comprehension - predict the impact that changing a system variable will have on an equilibrium relationship.

Application - calculate the value of a specific variable under specified conditions using the appropriate equation.

Analysis - analyze units for an equation or parameter; explain why turbulent flow should be expected in streams with higher gradients.

Synthesis - rearrange an equation to solve for a specific variable; substitute one equation into another and reformulate the resulting equation.

Evaluation - assess the impact of changing a system variable on an equilibrium relationship; recommend changes in systems variables to achieve a desired outcome.

A secondary goal of these exercises is to enhance students' mathematical reasoning skills (analytical derivation of equations and intuitive understanding of how system variables interrelate) and promote sound scientific work habits (careful use and double checking of proper units).

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, trig, and even rudimentary calculus in geology classes! This activity presents practical ways we can use to build student confidence in their ability to peer into the meaning of the equations they encounter in sedimentary geology. These techniques include: (1) Surgical Strike Reviews—5 to 10-minute 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.

I conduct immediate, in-class assessment through the use of example problems on the board and incomplete problems included in lecture notes (to be completed, reviewed, and evaluated during class). Unit Analysis and Perturbation type questions are also considered fair game for exam questions. Students generally respond well to these, having had multiple opportunities to practice their application during class.

A PowerPoint presentation (PowerPoint 892kB Aug12 06) based on this activity was presented at the Teaching Sedimentary Geology Workshop.