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*From*: Jeff Bigler <jcb@mit.edu>*Date*: Sun, 30 Sep 2012 10:33:22 -0400

For several years, I've read John Denker's posts about the problems with

sig figs. His arguments convinced me reasonably early on that sig figs

give students a poor and misleading concept of uncertainty, and I found

that students coming into my physics classes had learned how to apply

sig figs from their chemistry classes, but had no idea what it meant or

why they were doing it.

My concern wasn't so much about whether it would be better for students

to teach them about estimating, specifying, and propagating uncertainty,

but about how much class time it would take, and whether that was better

use of their time than the content it would replace.

What ended up convincing me was the realization that one of the big

holes in most kids' K-12 science education is that they don't learn

anything about error analysis; anything I could teach them about it

would have benefits far beyond simply giving them a better tool than sig

figs. So this year I decided to teach them a unit on uncertainty and

error analysis as part of the math & measurement topic.

I based what I teach them on an error analysis tutorial from Columbia

University, at <http://phys.columbia.edu/~tutorial/>. I taught them how

to estimate uncertainty and how to propagate uncertainties through their

calculations. This took about 3 class days, including a hands-on

measuring/estimating activity. (Most of my students have not taken a

statistics course, so I opted not to spend an extra couple of class days

getting them to understand what standard deviation is. The kids who

have taken statistics already know; for the others, it's a function on

their calculator and if they want to understand it, I'm happy to teach

them after school.)

Because most of the formulas we use involve only multiplication,

division and exponents, most of the time their error analysis will

consist of estimating uncertainties in measurements, calculating the

relative error of each, adding the relative errors, and converting the

relative error of their final result back to an absolute error. A

typical high school lab has only two or three measured quantities and

only a handful of data points, so this doesn't add a huge burden of

additional work for the students. The fact that I can already see that

they have a sense of what their uncertainties mean (whereas they had no

idea after a year of chemistry with sig figs) is evidence that this was

class time well spent.

As an amusing aside, honors students tend to cling more tenaciously than

average students to ideas they were taught by their previous teachers.

My honors students vastly preferred the idea of specifying uncertainty,

but they didn't want to let go of sig figs. In order to help illustrate

the problem with sig figs, I showed them one of John Denker's graphs as

a way of explaining the limitation. The graph was a Gaussian

distribution of 3.8675309 +/- 0.1 using all of the digits vs. rounding

to tenths vs. rounding to hundredths. (I looked for it on av8n.com, but

it looks like John has since edited the page it appeared on, and the

graph is no longer there.) One of my students looked at the number and

blurted out, "Oh my God! Jenny!"

My question for the list is: what else would it be useful (and

practical) for kids to learn about error analysis in high school?

--

Jeff Bigler

Lynn English HS; Lynn, MA, USA

"Magic" is what we call Science before we understand it.

**Follow-Ups**:**Re: [Phys-L] teaching error analysis in high school***From:*John Denker <jsd@av8n.com>

**Re: [Phys-L] teaching error analysis in high school***From:*John Denker <jsd@av8n.com>

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