QUANTITATIVE SKILLS IN GEOSCIENCES

less than 15

Lecture and lab

Public four-year institution, primarily undergraduate

This is a mid-level (Sophomores/Juniors) course, taught on an alternate-year schedule. Explicit pre-requisites include introductory Geology and College Algebra or higher-level math. Ideally, students would have completed up through Trigonometry for math and have had Earth History and one or two more core geology courses that have some quantitative applications. Most of the students are Geology majors (75% or higher), but it also attracts Geology minors and students from Environmental Sciences. Because of the two-year schedule, the topics of the course must be scaled to meet the students where they are at both in their quantitative level and their geological knowledge. However, the level of rigor is scaffolded with supplemental math activities to level the field for all students to grow into Calculus-based analyses.
The course has been scheduled as a lecture course, with an "integrated" lab, meaning that it meets within a typical 3-hour schedule each week, but lab activities are within that time frame. Traditional Monday/Wednesday/Friday schedules are not advised, as some lab-style activities take too much time and leave little room for feedback. A Tuesday/Thursday (or other two-day, 75-minute period) schedules would be better. If a one-day, 3-hour block were chosen, it is recommended to set aside specific office hours on an alternate day for struggling students.

The course combines principles and topics from across the Geological discipline. In fact, it is designed to incorporate quantitative topics from a broad swath of what students will encounter throughout their education and into the job market. From paleontology to hydrology to economic geology, instructors have the freedom to adapt content by providing students example problems from across the geology curriculum. The course is best when multiple faculty have offered input and examples that would serve students in their own majors classes.
Some broad concepts include constructing graphs from collected data and interpreting results through quantitative methods, modeling system behavior from empirical equations, dimensional analysis, and mass/energy conservation implications.

By the end of the class, students will be able to...

1. Plot geological data graphically and complete regression analyses to explain physical relationships.
2. Create and analyze 2D and 3D models of complex systems based on discrete data.
3. Convert between units and complete dimensional analyses for complex problem-solving in geological context.
4. Correctly identify and apply appropriate mathematical approaches to geoscience questions using statistical and uncertainty analyses, scale conversions, and logarithmic/exponential relationships.
5. Recognize and solve 3D and 4D equations related to physical and chemical geological applications.

The course is based on students completing problem sets with word problems from across the disciplinary spectrum in Geology. In-class time is spent on working through example problems, group time with students completing problems in a step-wise fashion with instructor intervention and feedback, and data-gathering and input.

The original design of the course was to touch on quantitative concepts across the spectrum, with some focus on the content. However, it was determined through the first offering of the course that students are further "behind" in their math aptitude than was expected. The course was revised to emphasize active learning and data collection over content. This change was rewarded with greater student engagement and improved performance on assignments and exams. Content was addressed using data, supported by the rationale for collection. For example, in one activity, students were given a wide array of objects to drop into a sand box. They were asked to design an experiment, including a hypothesis. A common choice was to use one object and to drop it from different heights, measuring the dimensions of the depression ("crater") left in the sand. Students completed their experiment, reported results, discussed problems and limitations, and produced deliverables. The instructor compared student experiments to how similar data are collected and scientific hypotheses are validated within a sub-discipline. Specifically with the example above, the instructor demonstrated how planetary geologists evaluate the timing and size of lunar craters.

Student assessment was completed through four measures:

1. A series of asynchronous, supplemental math remediation activities. The Math You Need for Geoscience Majors (https://serc.carleton.edu/mathyouneed/geomajors/index.html) was adapted for low-stakes assessment and to make sure all students were minimally familiar with these basic quantitative topics and the associated vocabulary.
2. Problem sets, done weekly, with a quantitative skill highlighted. The math topic was central and the problems were selected from multiple sources across the disciplines. For example, a trigonometry problem set included questions related to Structural Geology, Groundwater Hydrology, Geophysics, and Mineralogy.
3. Experiments and reporting. Students conducted most of their experiments within class time and were graded on participation and depth of analyses. Their reporting included written work, public speaking in "share-outs", and whole-class discussions.
4. Exams. Typically, three equally-weighted exams would be given, dividing the schedule into thirds. Though the exams aren't explicitly cumulative, the foundations established in the first exam would inform the second and those two would inform the final (third) exam. However, in the future, it has been discussed that the course would be improved and made more efficient with only two exams, including a cumulative final. This would save time and increase students' appreciation of the quantitative skills as "themes" that build upon each other and extend throughout the science.

Quantitative Skills in Geosciences Syllabus (Acrobat (PDF) 296kB Jan17 25)

The Math Your Earth Science Majors Need - co-curricular math and statistics modules for undergraduate Earth science courses