I’ll confess that I’m strongly anti-sigfigs. My problem with sigfigs are the following:
– I have never met a scientist or engineer who uses sigfig rules in their daily practice or in scientific communication. My understanding is that sigfigs are a staple of “school science”, in much the same way, “the scientific method” is. Based on my experience, sigfigs are typically used in a way as to mispresent scientific practice and thinking.
– They are just rules to follow, which can be followed mindlessly. Perhaps, they are or were intended to cultivate habits for thinking about uncertainty and precision, but I have found that they almost always invoke authoritative non-sense from students.
– Thinking about spread in data and uncertainty in the determination of quantities does not require the complexity of std dev, nor the formalism of +/- notation, nor the mindless routines of sigfigs. For example, ranges can be talked about and represented graphically. I want to cultivate the thinking behind and along with the increasingly sophisticated routines we use, but only as they become relevant to the increasingly challenging practices we carry out.
– Most college professors (that I have met) who relentlessly deduct points for sigfigs also do not have meaningful criteria for evaluating the quality of student scientific work, practice, and thinking. The way I see it, many of these professors need some way of creating a spread in their grades and deductions like “sigfigs” and “units” are an easy out, which they can also defend on the basis that they reflect important scientific thinking. I’m not saying the thinking behind uncertainty or units isn’t important–I’m saying that sigfigs is for a poor proxy of scientific thinking and habits of mind, and that relentless grading of sigfigs often comes as the expense of meaningful assessment and feedback.
— Sigfigs are wholly un-generalizable, because they do not cultivate the right thinking or appreciation for their purpose. Students are left helpless when thinking about anything beyond the rules– for example what would such students do when they have uncertainty in an angle and they have to take the sine or cosine or tangent of that angle, or take the reciprocal of some quantity such as frequency and period.
As an added note, this post was inspired by this weel’s Global Physics Department for readers who aren’t aware. This Wednesday (8/10/11) we’ll be discussing various ways to teach error propagation.
http://globalphysicsdept.posterous.com/#!/
This is the “corkboard” we’ve been using to brainstorm ahead of the meeting:
http://corkboard.me/qeM6Ne6tTG
Teach. Brian. Teach. 
I’ve definitely had the most success with students when simply talking about range in measurements and seeing how that range plays out through a calculation. I get the most thinking from them, the most understanding from them, and get this… they actually use it months later when, for example, measuring a vector drawing that they’ve done and reporting the answer in Newtons. Plenty of them give a range in their answer there, which I didn’t even expect them to do (much less ask them to do), showing that they actually think it means something.
The next step for me is to get them to think about numbers that are just given in a problem being measurements, too. Just because it says the car has a mass of 1200 kg, that doesn’t mean that they (whoever they are) knew that number exactly…
Just thought I’d put in the link for the Global Physics Department for readers who aren’t aware. This Wednesday (8/10/11) we’ll be discussing various ways to teach error propagation.
http://globalphysicsdept.posterous.com/#!/
This is the “corkboard” we’ve been using to brainstorm ahead of the meeting:
http://corkboard.me/qeM6Ne6tTG
(Sorry for the PR-based comment, Brian)
I agree. Sig figs are dumb.
http://www.wired.com/wiredscience/2008/09/significant-figures-what-are-they-for-and-what-do-they-have-to-do-with-uncertainty/
I have always felt this, but have also felt I would be crucified if I ever said that aloud in my science dept. Great thought on the representing the range graphically.
I’ve always preferred explicit error ranges to implicit ones. The sig-fig rules often get messed up by the more important convention of using powers of 1000 rather than of 10. If someone says something is 100 millivolts, I have no idea what the precision is and the sig-fig conventions are useless to tell me what the trailing 0s really mean, but if they write 100±30mV, I know what they are talking about. Intermediate computation should be carried out with higher precision than the initial data, so that the computation does not introduce more error, but the final result should not be given to 17 figures, when the initial values are ±10%.
Also, I’ve found it much more conceptually sense-making to the kids to express ranges as 12 cm to 14 cm rather than 13 ± 1 cm. When they see the second one, they seem to think “the answer is 13 cm, and my teacher also wants me to write some other stuff to make her happy”, but when they do the first one, they seem to be actually thinking of it as a range and not as a single exact answer.
Range is good sometimes, but often it is better to have a “best estimate”, which may or may not be the center of the range, particularly as the “range” is usually just an estimate based on the standard deviation rather than actual measurements of the range of possibilities.
Better for what? I disagree that having a “best estimate” is better for 10th graders thinking about measurements having uncertainty for the first time. When there is a “best” part of something, they translate that as the “right” part of something. It’s such a paradigm shift for them to think about range at all.