## Friday, August 6, 2010

### Pet peeve of the day - significant digits

Geology courses typically don't have much math incorporated into them (at least not to the same extent as physics and chemistry classes), especially at the introductory level I teach at a community college.  The math that I do incorporate into my classes typically involves simple algebraic equations, unit conversions, and the graphing of data.

Here's a typical geology lab problem (after an introductory lecture discussing topographic maps, map scales, unit conversions, etc).  I'll have them measure the distance between two features on a topographic map with a ruler.  Let's say they're 5.25 inches apart.   It's a typical USGS topo map with a scale of 1:24,000.  Then I ask them how many miles apart those features are on the ground.

In every class, I will generally have a few students who do the following:

5.25 in x 24,000 = 126,000 in on the ground
126,000 in x (1 ft / 12 in)  = 10,500 ft on the ground
10,500 ft x (1 mi / 5,280 ft) = 1.98863636 mi

and write the answer as 1.98863636 miles because that's what the calculator said it was.

These are the better students.

I've also had students who will forget about the map scale and report on their lab that the features are [5.25 in / (12 x 5,280)]  or 0.00008286 miles apart on the ground or multiply by 12 and 5,280 to given me an answer of 7,983,360,000 miles apart on the ground (I've really had students tell me two features on a map were billions of miles apart on the ground!).  There are also always a few students who just give up and tell me how much they hate math.

As an aside, this is why at my institution, our department recently instituted a formal college algebra level math course as a corequisite for any geology lab course.  We can't assume anymore that a high school graduate is capable of doing what used to be 8th grade level mathematics!

Anyway, back to the good student with the 8 decimal place answer, after patiently explaining why 1.98863636 miles is better reported as simply 2 miles given probable measurement error, I then tell them that, in the future, I will consider nonsensical answers like 1.98863636 miles to be incorrect and will take off points for them.  Usually fixes the problem.

I understand why these types of errors occur on labs - an over-reliance on calculators from a young age in the public school system and resultant failure to develop a "number sense" as to what constitutes a reasonable answer.  What I don't understand is how they got through 12 years of public schooling without anyone smacking them down for this much earlier in the game.