Enhancing Quantitative Skills of Physical- Students with a Geologic Glenn Blair Stracher James Herbert Shea Department of Science & Mathematics Department of Geology East Georgia College University of Wisconsin – Parkside Swainsboro, Georgia 30401 Kenosha, Wisconsin 53141 [email protected] [email protected]

ABSTRACT in this project to determine the bearing and distance Although the ability to use a geologic compass between collecting localities. is an important skill for and can be a The authors believe that all educated individuals, useful and stimulating skill for any student, most regardless of their profession, should possess some introductory geology courses do not include any quantitative skills in angular measurement. The geo- work on the use of the compass. This is unfortunate logic compass is an excellent tool for teaching these since compass work, introduced early, can help skills to all physical-geology students, regardless of improve the quantitative skills of all students by their mathematical background, while providing them giving them hands-on experience at solving prac- with the added benefits students themselves claim tical problems. The equipment needed is readily to receive. The purpose of this paper, then, is to pro- available at relatively low cost and a variety of mote the geologic compass as a worthwhile comple- compass-based exercises can be designed to ment to physical-geology courses by emphasizing its strengthen student skills. Worthwhile exercises usefulness in building quantitative skills based on include the following topics: quadrant and azi- the kinds of activities and calculations that many muth notation, magnetic declination, compass- geologists do while working in the field. traverse closure, elevation measurement, distance between two landmarks, and . COMPASS SUPPLIES AND EXERCISES A variety of geologic are available on Keywords: Apparatus; education – geoscience; edu- the market. Those offered by the Brunton, Silva, and cation – undergraduate; field trips, field study, Suunto companies are the most popular, with various summer courses; geology – teaching and curricu- models in different price ranges. One particularly lum; miscellaneous and mathematical geology. nice kit that is useful for classroom teaching is the Brunton compass and map-training kit illustrated in Figure 1. INTRODUCTION Software and textbooks useful for teaching and Physical-geology textbooks and lab manuals gener- learning compass skills include those authored by ally fail to promote the geologic compass as an effective Hassinen (1998) and Compton (1985), respectively. teaching tool. In the United States, geology students An instructor can design many different kinds of traditionally do not receive rigorous training in the compass exercises. Topics we have covered include use of the compass until they enroll in a field-geology quadrant and azimuth notation, magnetic declination, course, usually during the junior or senior year. compass-traverse closure, elevation measurements, The geologic compass has been an indispensable calculating the distance between two landmarks, and field-geology research tool for decades (Bartlett, measuring and plotting strike and dip. We use trigo- 2000; Reed, 2000), and teaching physical-geology stu- nometry in our compass-related exercises because it dents how to use one complements a course in which increases the number and complexity of the quantita- both geology majors and non-majors are enrolled. Our tive exercises students can learn to do. Consequently, justification for teaching compass skills during two students are introduced to or given a review of the consecutive three-hour physical labs includes the en- fundamentals of right-triangle trigonometry and the thusiastic verbal response we have had from students. law of sines and cosines before being taught how to Most of them said they enjoyed the experience of use the compass. The following exercises are exam- learning to use an instrument that many professional ples of compass-based exercises we find useful for geologists use. Some students said the compass skills enhancing student quantitative skills. Trexler (2000) they learned were useful in locating themselves on a and Dickinson and Hill (1997) have described addi- map while hiking. All students felt that learning to tional practical examples of the importance of com- use a compass helped them understand angular meas- pass skills. urements better than pictures in a book because it gave them something more concrete to work with. Quadrant and Azimuth Notation Other students in various disciplines are contemplat- This simple exercise requires students to plot angles ing undergraduate field-research projects requiring on a sheet of paper and to convert between quadrant compass skills. One such project, already underway and azimuth notation, something many of our stu- by a biology major, involves collecting water samples dents don’t initially know how to do. Students are for analysis from wells and streams in Emanuel and then required to take compass bearings first between Johnson Counties, Georgia. A compass is being used designated landmarks on campus and then between

Journal of Geoscience Education, v. 48, 2000, p. 447 Enhancing Quantitative Skills of Physical-Geology Students with a Geologic Compass required before contouring, this ex- Strike and Dip ercise is more complicated then the In this exercise, students simple topographic map contouring measure the strike and dip of an that physical-geology students do inclined plane in the lab (Figure by connecting point elevations on 2E) and then on several bedding a two-dimensional surface. It dem- planes in the field. We have found onstrates to students the procedure that the performance of students a mapping might have to on structural-geology exercises in use in order to determine the decli- their physical-geology laboratory nation to which his or her compass manuals is enhanced after they must be set for accurate fieldwork. learn to measure strike and dip (Stracher and Shea, 1999). Students Elevation Measurement report that they feel more comfort- Students are required to de- able plotting strike and dip sym- termine the height of a building bols in their laboratory manuals (Figure 2B) by using the tangent and that the significance of these function. This skill may then be symbols in revealing the presence utilized in the field for calculating of folds on a map is more readily the height of a cliff if, for example, understood. it is necessary to determine the Figure 1. Brunton kit for classroom thickness of an exposed outcrop of CONCLUSIONS instruction includes 24 Brunton field horizontal sedimentary strata. The The geologic compass is an ef- compasses, an instructor’s guide, in- exercise requires students to meas- fective tool for enhancing quanti- struction booklets and worksheets, ure their distance from a building topographic maps and map symbol tative skills because it promotes on campus and then the angle from learning by doing. Developing and sheets, and a color VHS video with the horizontal at eye level to the compass lessons on topics ranging using compass-based exercises is an from magnetic declination to triangu- top of the building. The tangent inexpensive, convenient, and prac- function is used to calculate H ,il- lation. The kit is reasonably priced at 2 tical way of enhancing quantita- about $325 US. lustrated in Figure 2B, and this tative skills including interpolation distance is added to H , the stu- 1 and trigonometry. Such exercises points on a topographic map. They dent’s height, to determine the ac- have the added benefit of providing must then convert between the two tual elevation of the building (or a students with an appreciation for types of notation. After completion cliff). Many students are surprised a valuable research tool and the of this exercise, a written quiz is that it is possible to determine the way it is used by many geologists administered to make sure students height of a building without hang- while doing fieldwork. In addition, have mastered the necessary con- ing a rope off the side and meas- students are taught a skill useful cepts. This exercise is easy for stu- uring its length. for hiking and some undergraduate dents to master, and many of them research projects and quite possibly seem delighted that they are able Distance Between Two Landmarks useful later in their professional to use an instrument to make the careers. kinds of measurements and angu- In this exercise, students use a compass to measure bearings be- lar conversions that geologists do. ACKNOWLEDGMENTS In addition, this exercise is a good tween landmarks on campus. They The authors thank LeeAnn lead-in to more complicated com- also pace off the distance between Srogi of West Chester University pass problems requiring calcula- these landmarks on dry land. After and two anonymous reviewers for tion of the distance between two determining the angles between helpful suggestions regarding the landmarks using the law of sines bearing lines, they use the law of manuscript. In addition, we thank or cosines as discussed later on. sines or cosines to calculate the distance between two landmarks Heather Macdonald, of the College Magnetic Declination separated by a pond, as illustrated of William and Mary, and LeeAnn After distinguishing between the in Figures 2C and 2D. All our stu- Srogi for their efforts in organiz- geographic and magnetic poles and dents immediately realize the use- ing and convening topical session discussing the significance of mag- fulness in applying mathematical 60 at the 1999 GSA National Con- netic declination, students are re- formulae to compass data acquired vention in Denver, Colorado. quired to interpolate declinations in the field – the distance across a on an isogonic map by proportion REFERENCES CITED pond can be determined without Bartlett, K., 2000, The more things and to contour interpolated decli- getting your feet wet. The law of change…: Geotimes, v. 45, no. 3, p. 16. nations by hand. This exercise ex- sines is another example of using Compton, R.R., 1985, Geology in the field: poses students to another use of proportions in geology, and the law New York, New York, John Wiley and proportions in geology besides map of cosines requires to students to Sons, 398 p. Dickinson, W.W., and Hill, N.L., 1997, An scales and requires them to solve determine the square root of a num- introductory field exercise on topo- simple equations for unknown decli- ber after calculating with exponents graphic mapping: Journal of Geosci- nations. Because of the calculations and the sine and cosine functions. ence Education, v. 45, p. 221-224.

Journal of Geoscience Education, v. 48, 2000, p. 448 Enhancing Quantitative Skills of Physical-Geology Students with a Geologic Compass

Hassinen, A., 1998, Orienteering CD-ROM: 2151 Las Palmas Drive, Suite Carlsbad, California, Suunto USA, 92009. Reed, T., 2000, The Brunton: Geotimes, v. 45, no. 3, p. 14-15. Stracher, G.B., and Shea, J.H., 1999, Enhancing quantitative and map reading skills of introductory geoscience students with a geologic compass: Geological Society of America Abstracts with Programs, v. 31, no. 7, p. 209. Trexler, J.H. Jr., 2000, Locating data on topographic maps, A field exercise in comparison of navigation methods: Journal of Geo- science Education, v. 48, p. 33-38.

ABOUT THE AUTHORS Glenn B. Stracher is Associate Professor of Geology at East Georgia College in Swainsboro, Georgia. He has been active in undergraduate quantitative-skills education. During the past four years, he has taught geochemical thermodynamics at the graduate level in the School of Earth and Atmospheric Sciences at the Georgia Institute of Technology. Glenn is currently de- veloping a WebCT course in thermodynamics for Georgia Tech He is co-author of a two-volume textbook in chemi- Figure 2. Compass exercises designed to enhance quan- cal thermodynamics, recently translated into Japanese, titative skills, especially working with angles. Exercises and is currently co-authoring a new book in chemical include: calculating closure for a compass traverse (A), thermodynamics for engineers and earth scientists. measuring the height of a building (B), using the law of Jim Shea has been teaching geology for almost 40 sines (C) or cosines (D) to calculate the distance between years and will be retiring from teaching in May of 2000. two landmarks, and using a compass with a clinometer He has just begun his 26th year as Editor of the Journal to measure the strike and dip of an inclined plane (E). of Geoscience Education. His major interest is in the historical development of geological theories.

Journal of Geoscience Education, v. 48, 2000, p. 449