## Ramblings on teaching measurement uncertainty

Posted by Melissa on July 15, 2014

A couple of my colleagues and I have curricular development funds this summer to explore how we can better integrate computational and experimental activities in our curriculum. One of the topics that came up in our discussions yesterday was uncertainty: teaching propagation of uncertainty, getting students to appreciate what the uncertainty associated with a measurement really means, and the role of uncertainty in computational as well as experimental problems. As someone who teaches a lot of lab courses, I can’t tell you how often students will see two values, and their associated uncertainties, and say, “These values don’t agree because they don’t overlap within the uncertainty.” Argh!

As a department, we could probably do a better job making the discussion of uncertainty more coherent throughout our curriculum, and I know that I could do a better job of reinforcing the importance of the uncertainty in the classes I teach. One of my colleagues writes homework and exam problems regularly that require calculations with uncertainties. On the other hand, when I am not in the lab, I rarely include uncertainties in the problems that I ask students to tackle, which I think sends a message that uncertainty is peripheral.

Looking at the broader physics education landscape, when it comes to teaching uncertainty, there seem to be two groups: those who have heard of the current international standard (*Evaluation of Measurement Data – Guide to the Expression of Uncertainty in Measurement* – known as GUM and published in 1993) and those who haven’t. GUM only appeared on my radar two or three years ago. This spring was the first time I introduced students in our advanced lab course to the GUM method for handling uncertainty. If you aren’t familiar, Andy Buffler and Saalih Allie at the University of Cape Town and Fred Lubben at the University of York have developed some nice curricular materials for introducing the GUM approach in introductory physics classes (Curriculum and TPT article).

I wonder if GUM will ever gain a more significant following. It hasn’t made many inroads beyond the metrology community, and among educators, the implementation is not particularly widespread, despite the clarity with which I think it helps students navigate the maze of measurement uncertainty. For all you physics educators out there, have you heard of GUM? Do you use it in your curriculum? And if you do, what do you see as the benefits and drawbacks?

## Alex said

Thanks for pointing out GUM. I was completely unaware of it.

Given that there are a lot of things that I have zero control over in the format and curriculum of freshman labs, and that my institution is proud to provide a path to a STEM degree for students who can’t do math, I’m just happy if students understand by the end of the quarter that uncertainty can be larger than the smallest unit on the ruler or the last decimal place in the digital readout. If they get that, I declare victory.

## Melissa said

Teaching uncertainty certainly has many levels indeed, and I agree that every step of helping students understand uncertainty is an accomplishment.

## Andy "SuperFly" Rundquist said

This is the first I’ve heard of GUM (embarrassed!). It’s also interesting that it didn’t come up (at least as I recall) during our Global Physics Dept meeting on uncertainties. I’ll tell you that I use the montecarlo approach nearly all the time with my students, though that means they don’t have any quick and dirty ways of estimating propagation of error. I do like the focus on probability that the curriculum you linked to focuses on, and I spend a lot of time talking about that when teaching both error propagation and curve fitting.

## Melissa said

One of our topics of conversation was whether we should use the Monte Carlo approach in our curriculum. Are there any good references for introducing it to students?

## Andy "SuperFly" Rundquist said

I like this link, but it’s a little long: http://www.av8n.com/physics/uncertainty.htm

## Chad Orzel (@orzelc) said

If you’ll accept a little shameless self-promotion, I really like introducing uncertainty via this experiment (also published in TPT, but this version is free…). And when I’m teaching by myself, I tend to include exam problems involving the calculation of uncertainties. That’s kind of a hard sell with some other folks, though, so it tends to fall by the wayside when I’m teaching one of several sections.

I haven’t looked at the GUM stuff before, but uncertainty is one of those topics that comes up every now and again, and we all agree that we ought to do a better job of handling, then can’t really agree on what we should do, so nothing really changes.

## Melissa said

Thanks for sharing! I really like your approach of having intro students compare two different measurement techniques so as to be able to separate out the systematic and random uncertainty.