Quantitative skill-building

A simple example

SCENARIO: Many students learn to use Mohr circles but never really understand them or the underlying stress equations. To improve students' understanding of Mohr circles and simultaneously build their quantitative skills:

1. Have students describe each part of the fundamental equations of stress (what symbols stand for, units, etc.) and annotate the equations with their descriptions (e.g., as a concept sketch). Have them add a description in plain English of what the equations mean.
2. Assign several different values of θ to each pair of students, and have them calculate σ_n and σ_s for each. Compile a group table, and have each student plot the results in σ_n /σ_s space, labelling points with θ values.
3. Have students annotate the Mohr circle with a plain English description of how σ_n and σ_s vary with plane orientation. Have students work in small groups to figure out how to use just σ₁ and σ₃ to plot a Mohr circle, as well as find σn and σs for a given plane.

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Why add quantitative skills to your course?

• Because mathematics is a tool used in all geoscience disciplines, students must have personal experience with realistic, robust quantitative problems.
• Math aversion, math anxiety, and lack of confidence are common among undergraduate geoscience students. Providing support for students to complete quantitative problems in tectonics successfully is one way to help students build confidence and become more comfortable doing math.
• Students commonly have abstract math skills but need review and help in placing those skills in the context of the geoscience courses that they take. Providing bridges between skills and application supports student success.
• Collaborative graphical and data interpretation are active- learning strategies that connect course content to real- world applications.

How much class time does it take?

• Quantitative activities can take from 5 minutes (a simple back-of-the-envelope calculation) to a class period (e.g.,the Mohr circle exercise) to several class periods (complex data processing and interpretation).

From NAGT's Teach the Earth Portal

• The Math You Need, When You Need It is a set of tutorials that place foundational math concepts in a geological context.
• Teaching Quantitative Skills offers best practices and tips for including quantitative analyses in a geology course.
• Visit Using Data in the Classroom for using data in your geoscience courses.
• Teach Stress and Strain with these ideas.
• Use seismograph data for locating earthquakes.
• Use Excel in metamorphic petrology for thermobarometry of pelitic schist.
• Hungry for more? Try a lab exercise built around determining viscoelastic rheology using cake.

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Research papers on Quantitative Skills

• Wenner, Jennifer M. and Eric M. Baer, 2015, The math you need, when you need it (TMYN): Leveling the playing field: Numeracy v. 8, no. 2, article 5.
• Manduca, C. A., Baer, E., Hancock, G., Macdonald, R. H., Patterson, S., Savina, M., and Wenner, J., 2008, Making undergraduate geoscience quantitative: Eos Trans. AGU, v. 89, no.16, p. 149–150.