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Guiding students through unit conversions
An instructor's guide to Unit Conversions

by Dr. Jennifer M. Wenner, University of WI Oshkosh Geology, and Dr. Eric M. Baer, Highline Community College Geology.

Jump down to: Objectives | Student Difficulties | What we left out | Resources

What should the student get out of this page?

Artist's rendering of Mars Climate Orbiter, the mission that failed because some scientists used metric units and others used imperial units. Image from http://www.jpl.nasa.gov/jplhistory/captions/marsclimateorbiter-t.php.
This page is designed to address the universal feeling of geoscience faculty that we shouldn't have to spend so much time addressing the mathematics of unit conversions. By the end of this module, students should:

  1. have a handle on the "rules" (or steps) for doing unit conversions;
  2. be able to perform unit conversions for most units used in an introductory geoscience course.

Why is it hard for students?

Many of us feel that the "simple arithmetic" involved in doing unit conversions should have been taught to our students during their elementary school days. And, to be quite honest, they probably were. However, many students still struggle with the arithmetic involved; here are some possible reasons why:

  1. It's math!
    • Many students are math phobic and as soon as arithmetic is mentioned, they shut down.
  2. It's math WITH FRACTIONS!
    • For whatever reason, students struggle with fractions. It may be because they can't remember the rules for the arithmetic manipulation of functions, or because the math of fractions IS complicated.
    • On the student page, we have included a review of how to multiply fractions since that is the arithmetic manipulation that is used in unit conversions.
  3. Students are not familiar with the units (particularly the "dreaded metric system")
    • Many students have no intuition about the metric system and, as a result, feel like they are floundering when asked to evaluate their answers
  4. Instead of being an equation into which they plug numbers, the process of unit conversions is an algorithm.
  5. cartoon of confusion with math
    • Many students are not familiar with algorithmic thinking, they don't realize that following a series of steps can actually make their lives (and calculations) easier.
    • Somewhere along the line it got "cool" to skip steps and just get the answer. I don't know why this happens but I try to impress on them that it actually takes longer if they skip a step and make a mistake. They have to start all over again.
    • Because there isn't a prescribed "formula" they struggle with the fact that there is no one right way to do this.
  6. There are multiple ways of getting an answer.
    • Students may feel uncomfortable if they "set up" the conversion in a way that is different from their lab partner.
    • Try to get students to understand that (in this case as in many in the geosciences) doing things the way that makes sense is generally the right way to do them.

What don't we include in the page?

Many textbooks and lab manuals spend a lot of time on the mathematics of equivalency - the idea that we can multiply something by 12 in/1 ft because the value of that number is actually 1 (they are equivalent). We have not spent any time on this concept because we find that it confuses students and they do not have the patience for it (see number 4 above). Instead, we try to give the students an algorithm to follow that is based in equivalent values but tries not to overwhelm the students with the abstract mathematics behind this idea.

Instructor Resources

Len Vacher at University of South Florida wrote a Computational Geology column for JGE about The Algebra of Unit Conversions (link will download a pdf file).

A number of Unit Conversion websites exist. These sites will complete conversion from any unit to any other unit:

Institute of Chemistry in Berlinhas a very complete unit converter.

SpeckDesignhas a unit conversion tool that converts common and uncommon units.

MegaConverter2 has numerous conversion windows for everything from length to shoe size!

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