Word Problems: Living at the Intersection Of Quantitative Literacy and Geological-Mathematical Problem Solving

Thursday 2:10pm-2:30pm Weeks Geo: AB20
Teaching Demonstration

Session Chairs

Len Vacher, University of South Florida
Charles B. Connor, University of South Florida
Victor Ricchezza, University of South Florida

Demonstration

The demonstration activity will be presented at EER by VJR. Participants, filling the role of students for the demonstration, will break into small groups and attempt to measure a rectangular surface using the provided unruled measurement unit marker. After a brief discussion, groups will also be asked to solve the comparison problem, with a short interval for result discussion at the conclusion.

Abstract

A course in geological mathematical problems solving has been evolving in the undergraduate curriculum at the University of South Florida for nearly 20 years. Now called Computational Geology (after the column of the same name in the JGE, 1998-2005), the course evolved into a quantitative literacy (QL) course for geology students, passed through a phase spawning Spreadsheets Across the Curriculum, and now (since 2014) focuses squarely and unabashedly on word problems. Word problems instantiate triad of QL (sensu lato), which combines calculation (numeracy), communication (QL, sensu stricto), and logical argument (quantitative reasoning, including modeling). The course proceeds through more than 300 battle-tested word problems, organized into about a dozen sets including unit conversions, proportional thinking, Venn diagrams, making comparisons, ratios and rates, logarithmic scales, circles and triangles, modeling functions, probability and distributions.

This demonstration features two problems:

  1. if you are lost on an island without a ruled measuring device, how can you use a stick to determine the ratio of two rectangular areas to three significant figures, and
  2. if hE and hK represent the distance from the center of the Earth to the top of Mounts Everest and Kilimanjaro, respectively, what is hE – hK?

Context

The demonstration problems are used in two separate activities in the course, with the first being part of a larger lab opened by a formative assessment and ended with class measurements in the unfamiliar units of the unruled stick. The second is a sample from one of the problem sets given to the students to complete, then study from, for course exams. Students are required to write their own problems of similar rigor, using the problems in the problem sets as a guide.

Why It Works

The measurement lab activity is a rare use of Lagrange's continued fraction measurement method in actual field practice, and promotes critical thinking to understand why tools such as ruled unit measures work as they do. The mountain height activity illustrates the role of assumptions in model-based calculations (spherical versus spheroidal Earth). The problem sets take original geology-based calculation problems from a variety of subdisciplines and present them together to promote quantitative literacy within the geosciences and drive home the point that geology is an innately quantitative science.

Slides for Presentation