# Quantitative skill-building

Initial Publication Date: June 21, 2019

## Quantitative skill-building

Strategies for effectively using math, graphs, and real data to build students' quantitative skills.

### 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 σn and σs for each. Compile a group table, and have each student plot the results in σns space, labelling points with θ values.
3. Have students annotate the Mohr circle with a plain English description of how σn and σs 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.

• 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).

### Tips for success

• As you design your course, make sure that math skills requried of students align with course prerequisites. If there are no pre-requisites (or if they are inadequate), design quantitative activities to build/review basic skills before moving to difficult problems or complex concepts.
• Integrate quantitative problem-solving throughout your course. Set the tone by starting with a simple calculation on the first day of class.
• Start with basic skills that students are likely to recognize (arithmetic, algebra), and provide support (tutoring, online help) for students who need review. Be deliberate about nesting or scaffolding skills so that students are prepared to move to more complex problems.
• Remind students that they already know how to do the math when they revisit a math concept in a new context.
• Give students a "why" that is placed in a geologic context, rather than just "solve for x" or "complete this operation".
• Have students work in small groups (≤4 students with a variety of skill levels, if possible) to solve quantitative
• problems, but be sure that everyone does the calculations.
• Combine higher-order learning skills with quantitative work by using follow-up discussions and reflections.
• Contextualize quantitative work within the science. Connect interpretation and scientific implications to the underlying geoscience data and math.
• Make sure that all students have a calculator that is appropriate for the tasks in your course and that they know how to use it. Consider providing simple calculators for students in order to minimize the problems that arise from having students use cell phones in class, lab, or on exams.

### More examples & variations on Quantitative Skill-building

• Provide support for a wide range of abilities. Quantitative preparation of undergraduates is highly variable. Find resources that support student learning without too much extra effort on your part. Online tools (e.g., The Math You Need, Khan Academy) or math tutors can provide resources to support students.
• Encourage students. Help students recognize that their quantitative skills are not fixed (i.e., they are not inherently "bad" at math) but that, with practice and experience, they can develop and grow their quantitative abilities.
• Given/Find/Solve approach. Teach students how to approach a word problem. In class, ask them explicitly to identify Given variables, what they are expected to Find, and any equation(s) necessary to Solve the problem.
• Two-minute graph analysis. Present students with a graph or simple diagram (e.g., the kyanite-sillimanite- andalusite phase diagram). Have students write a short description of the relationships they observe. You can extend this into a Think-Pair-Share and/or class discussion.
• Dimensional analysis.Have students take the equation for S-wave velocity and figure out what the units have to be for the rigidity modulus, m.
• A next step. Leverage students' work with graphical data to give them experience with the primary literature. Ask students to read a published paper and analyze the presentation of quantitative data in the paper's figures.
• Computational tools. Design quantitative activities to use Excel, Stereonet, ArcGIS, or other software (e.g., MATLAB), recognizing that you may need time for some extra instruction. Ease with these tools enhances marketable skills and improves career readiness.
• Field exercises. Incorporate numerical measurements such as strike and dip into your field trips. Design field exercises to capitalize on quantitative work you have already done in class. Utilize appropriate technology - the Stereonet app plots strike and dip measurements, so students can determine fold axes and axial planes and relate structures in the field to regional tectonics.

### Other On-Ramps can be found in the Navigation (left side of page) or Available On-Ramps

The On-Ramps Project provides quick-start guides for faculty interested in incorporating successful and easily implemented teaching strategies to improve student learning in the broad field of tectonics. The Project was funded by NSF grant EAR1841227 and grew out of a recommendation in the 2018 community vision document [link https://digital.lib.washington.edu/researchworks/handle/1773/40754 'Challenges and Opportunities for Research in Tectonics'.
Quantitative skill building On-Ramp authors: Cailey Condit and Kyle Fredrick.
Project leads: Philip Resor, Barbara Tewksbury, Jennifer Wenner.
Additional authors: Kim Blisniuk, Anne Egger, Jamie Kirkpatrick, Sara Mana, Kendra Murray, Beth Pratt-Sitaula, Christine Regalla, and Carolyn Tewksbury-Christle.
Graphics: Logo - C. Tewksbury-Christle; p. 1, B. Tewksbury; photos - banner & p. 2, C. Gerbi.