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12 August 2010

Mail Time: So How *DO* You Cover Measurement and Sig Figs, If Not On the First Day?

The blog's newest follower Evan Willkomm writes in with the natural follow-up question to my post about the first day of school:

I'm a newer teacher and I'm still working to come up with a strong curriculum for general physics.  For the first two years of my teaching, I taught measurement, significant figures, and sig fig math in the first unit of the year.  This decision was made simply by opening the text that I inherited from the teacher before me and presenting the material linearly, starting with chapter 1.  After reading through some of your blog posts, I've found that you hit the ground running and introduce forces and equilibrium to your AP students and position-time graphs for general physics - all on the first day.  I'd really appreciate your thoughts on whether I should continue to include those topics or not.  How do you address sig fig math? 

Hi, Evan... good to hear from you. You're right that, at any level, one of the fundamental secrets to physics teaching is to "hit the ground running" with real experimental physics. At Woodberry, we take this approach at all levels, including AP B, AP C, regular, and conceptual.

Measurement, sig figs, and the scientific method are actually quite deep concepts. They, and abstract unit conversion mathematics, are generally taught in every science course, starting even in 6th or 7th grade -- and yet, many if not most students will graduate high school with only the most tenuous grasp of such things. Sure, I can spend a week at the start of school on these issues, but without context, I will be just as unsuccessful as a host of prior teachers. (Trust me. I've tried.)

I would suggest that all of the above ideas are best learned through the use of numerous unannounced "teaching moments." For example, on the first day of AP, we predict the reading on a spring scale to be 2.3 N. Before we look at what the scale actually reads, I ask the class how close we have to be in order to call ourselves correct. Since the scale itself has markers only ever 0.2 N, we agree that we're happy with an answer between 2.1 N and 2.5 N -- that is, +/- 0.2 N.

Or, in general physics, I might calculate the slope of a cart's constant-speed position-time graph, and ask how far we expect the same cart to travel in 3 seconds. Once again, the question of "how close is correct" will arise. This time, we might suggest that our reaction time places this time measurement within only about 0.2 or 0.3 s, so I'm happy with an answer that's within 6-10%.

In regular and AP physics lab, we're regularly calculating percent differences between two different measurements, such as a speed measurement with the slope of a crudely made position-time graph and a speed measurement with a sonic motion detector. Throughout the year everyone sees that a measurement to within 5-10% is pretty solid. Then when we're calculating answers to book or test problems, we can use that ingrained knowledge: "You haven't measured anything in lab to better than 5% accuracy all year, and yet you're telling me that the mass of the sample is 1.32452 kg? A 10% difference would be 1.45something kg... in other words, those last digits are utterly meaningless."

And finally, students get the message of "I took two points off for writing every digit on your calculator."

Do my students truly, deeply understand significant figures and measurement uncertainty after my class? Probably not. My hope is that some folks get it, and that at minimum everyone understands the fact that a fourth significant digit is very often utterly ridiculous.

But that's not the right question to ask. The right question is, do my students understand significant figures and measurement uncertainty any worse because I don't go over them at the beginning of the year?

Answer: My students understand these things AS WELL OR (USUALLY) BETTER by covering them in context rather than by covering them in isolation at the beginning of the year.

And FAR MORE IMPORTANTLY: Without question, my students display a more positive attitude toward physics, and they have a better understanding of the purpose of physics as a discipline, than when I started the year with a measurement and math unit. My class sees on day one that this isn't just another math course. They see ideas and experiments presented in a way that is completely new to them; they aren't bored, they don't think of my class as a repetition of anything in their previous schooling. Physics is about predicting and measuring how the natural world works. My class knows that within 30 minutes of the first day of school.


[P.S. for a more rigorous treatment of these issues from an Education Professor's perspective, check out Arnold Aron's classic text, *Teaching Introductory Physics."  His findings agree 100% with mine.]

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