DENSITY OF THE EARTH -- A SET OF COORDINATED SPREADSHEET MODULES TO PROMOTE QUANTITATIVE LITERACY IN GEOLOGICAL CONTEXT

Quantitative literacy (QL), or numeracy, is the problem-solving habit of mind with which one applies mathematical reasoning and skills to analysis in nontechnical context (see Mathematics and Democracy by Lynn Steen et al., online at www.woodrow.org/nced). Geological numeracy is the intersection of QL and earth science content. We are developing geological-numeracy spreadsheet modules to help bring QL into earth science courses, and earth science content into QL courses. Of particular interest are courses in the history of mathematics and/or science. Our first set of modules, Density of the Earth, illustrates how we link spreadsheet problems to a theme involving a milestone in the understanding of Earth, space and/or time.

The central module of the set aims to illustrate Polya's classic problem-solving heuristic (George Polya, How to Solve It, Princeton U. Press, 1959) and invokes a strategy adapting breakthroughs by Erastothenes, Galileo, Newton and Cavendish. A key linked module works with GPS data at ends of a 50-m tape (for Earth's circumference, then Earth's volume) and travel times of Florida oranges dropped off buildings (for g, then Earth's mass). This module exposes the QL pitfall of calculating after averaging vs. averaging after calculating. Other linked modules include calculation of rock density from mineral composition, specific weights and porosity, and calculation of Earth density from density variation with depth in Earth. Quantitative content of the set of modules includes weighted averages, circle formulas, the concept that an integral is a sum, and most importantly, rearranging equations to produce spreadsheet formulas.