Quantitative Skills > Teaching Methods > Back of the Envelope Calculations > Student Frame of Reference and Experience

Student Frame of Reference and Experience

Students' Frame of Reference

Students are personally familiar with and can easily visualize:

  • Time periods in seconds, minutes, hours, days, and years (decades to centuries)
  • Horizontal distances ranging from a few fractions of an inch to feet, yards, and a few miles.
  • Vertical distances ranging from inches to a few tens of feet.
  • Volumes ranging from a few cups to quarts and gallons.
  • Rates from a few miles per hour up to about 70 miles per hour.
  • Discharges ranging from a few cups per second to a few gallons per minute (pumping gas, filling a glass or tub).
  • Densities ranging from less than one to about 2.7 g/cm3 (less than water to average rocks).

Students have difficulty visualizing (but commonly encounter in geoscience courses):

  • Time periods that are very short (fractions of a second) or very long (millions to billions of years).
  • Horizontal distances that are very small (fractions of a millimeter or smaller) or longer than a few 10s of kms (up to light years); and this is apart from the English-metric conversion issue!!
  • Vertical distances that are more than a few tens of feet (hundreds of meters to tens or hundreds of kilometers)
  • Volumes that are either very small (atomic) or larger than a bathtub (km3)
  • Rates that are very slow (e.g., 10-14/sec or 50 km/million years) or very fast (e.g., 7 km/sec)
  • Discharges that are large (e.g., 45,000 m3/sec)
  • Densities that are large (e.g., 5 g/cm3; 19 gm/cm3)

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