# Original "barometer to measure the height of a building" story?

#### RichardO

Joined May 4, 2013
2,270
The Barometer Story

by Alexander Calandra - an article from Current Science, Teacher's Edition, 1964.

Some time ago, I received a call from a colleague who asked if I would be the referee on the grading of an examination question. It seemed that he was about to give a student a zero for his answer to a physics question, while the student claimed he should receive a perfect score and would do so if the system were not set up against the student. The instructor and the student agreed to submit this to an impartial arbiter, and I was selected.

The Barometer Problem

I went to my colleague's office and read the examination question, which was, "Show how it is possible to determine the height of a tall building with the aid of a barometer."

The student's answer was, "Take the barometer to the top of the building, attach a long rope to it, lower the barometer to the street, and then bring it up, measuring the length of the rope. The length of the rope is the height of the building."

Now, this is a very interesting answer, but should the student get credit for it? I pointed out that the student really had a strong case for full credit, since he had answered the question completely and correctly. On the other hand, if full credit were given, it could well contribute to a high grade for the student in his physics course. A high grade is supposed to certify that the student knows some physics, but the answer to the question did not confirm this. With this in mind, I suggested that the student have another try at answering the question. I was not surprised that my colleague agreed to this, but I was surprised that the student did.

Acting in terms of the agreement, I gave the student six minutes to answer the question, with the warning that the answer should show some knowledge of physics. At the end of five minutes, he had not written anything. I asked if he wished to give up, since I had another class to take care of, but he said no, he was not giving up. He had many answers to this problem; he was just thinking of the best one. I excused myself for interrupting him, and asked him to please go on. In the next minute, he dashed off his answer, which was:

"Take the barometer to the top of the building and lean over the edge of the roof. Drop the barometer, timing its fall with a stopwatch. Then, using the formula S= 1/2 at^2, calculate the height of the building."

At this point, I asked my colleague if he would give up. He conceded and I gave the student almost full credit. In leaving my colleague's office, I recalled that the student had said he had other answers to the problem, so I asked him what they were.

"Oh, yes," said the student. "There are many ways of getting the height of a tall building with the aid of a barometer. For example, you could take the barometer out on a sunny day and measure the height of the barometer, the length of its shadow, and the length of the shadow of the building, and by the use of simple proportion, determine the height of the building."

"Fine," I said. "And the others?"

"Yes," said the student. "There is a very basic measurement method that you will like. In this method, you take the barometer and begin to walk up the stairs. As you climb the stairs, you mark off the length of the barometer along the wall. You then count the number of marks, and this will give you the height of the building in barometer units. A very direct method.

"Of course, if you want a more sophisticated method, you can tie the barometer to the end of a string, swing it as a pendulum, and determine the value of 'g' at the street level and at the top of the building. From the difference between the two values of 'g', the height of the building can, in principle, be calculated."

Finally, he concluded, "If you don't limit me to physics solutions to this problem, there are many other answers, such as taking the barometer to the basement and knocking on the superintendent's door. When the superintendent answers, you speak to him as follows: 'Dear Mr. Superintendent, here I have a very fine barometer. If you will tell me the height of this building, I will give you this barometer.'"

At this point, I asked the student if he really didn't know the answer to the problem. He admitted that he did, but that he was so fed up with college instructors trying to teach him how to think and to use critical thinking, instead of showing him the structure of the subject matter, that he decided to take off on what he regarded mostly as a sham.

#### #12

Joined Nov 30, 2010
18,224
I tend to side with the student.
Some "instructors" refuse to answer direct questions so much that it feels like I'm trying to "discover" the underlying principle like Archimedes did. I didn't go to school so I could re-invent the wheel. I went there to find out what educated people already know. I'm the kind of person you only have to tell once, so a teacher that acts like I won't remember a method unless I invent it is wasting my time. If I didn't find the method by reading the text and attending class, I simply missed the information. I did not forget it and I won't remember it better if it takes all week to figure it out. The only thing that accomplishes is using up a week to learn one thing when I could have spent the week learning a hundred things.

Still, this is the way the Homework Forum works. "Never hand them the answer." "Make them work out every detail themselves."
Phooey on that! Externet just asked for the conversion from BTUs to watts. No problem. It's a 5 word sentence to give him that last bit he was missing. If he worked in thermodynamics (like me) he wouldn't forget it. If he's a digital designer, he probably will. So what? He's up to speed in 4 minutes with a straight answer. That's what I call effective. It's also why I gave up working the Homework Forum.

I remember a physics teacher that wouldn't tell me whether it's the sine or the cosine to figure the lateral force on a door hinge. I still don't "know" the answer. I have to work it out every time I need to hang a non-standard door. By refusing to present the information in the way that works for me, he left me with a mental block that has lasted 40 years.

#### WBahn

Joined Mar 31, 2012
30,250
I can't help but consider it an apocryphal tale, but even accepting it at face value leaves me unimpressed with the student. Human beings, day in and day out, have to infer huge amounts of information in almost every exchange we are a part of. When someone asks you if you want an apple, you infer that they are offering to give you an apple right now. But that is not what they said. Maybe they just want to know if you want an apple out of idle curiosity. Maybe they are thinking of giving you an apple next week. Yet no one expects them to rule those out by saying, "I have an apple that I am willing to give you within the next ten seconds if you indicate that you would like to have one given to you." Similarly, consider how you would interpret, "I lost my <noun>." without knowing what <noun> is. Is there a single interpretation? What if <noun> is "glasses" verses "house". Almost everyone would interpret these two sentences very differently from each other, but almost identically to everyone else. But this student would consider being expected to draw the correct inference as unreasonable.

By refusing to infer the very obvious intent of the problem, the student is basically saying that he wants to be treated as if he lacks the basic communications skills that even small children are quite good at and that even many animals have at least some facility with.

#### #12

Joined Nov 30, 2010
18,224
Are you suggesting the student should naturally expect to use the height of a mercury column as a measurement standard?

#### WBahn

Joined Mar 31, 2012
30,250
Are you suggesting the student should naturally expect to use the height of a mercury column as a measurement standard?
No more than marking off barometer lengths on the wall suggests that the student should naturally expect to use the length of a barometer as a measurement standard.

#### RichardO

Joined May 4, 2013
2,270
I can't help but consider it an apocryphal tale, but even accepting it at face value leaves me unimpressed with the student.
This link to an article that is contemporary to the story makes me believe it is a true story:
http://www.nytimes.com/1964/03/08/science-teacher-chides-teachers.html?_r=0

I, like you, find the student's reason for his answer more argumentative than factual. In fact, I was quite surprised because I was expecting an explantion more like: "I just felt that the question did not allow creativity in the answer."

p.s. I think the student should have gotten full credit for his answer. It was a poorly written question that that expected a "stock", memorized answer. Maybe the context of the classroom assignments would change my thinking on that.

#### WBahn

Joined Mar 31, 2012
30,250
My guess is that the context of the class topics that were covered would make it very clear what the reasonable interpretation is and what concepts the question is intended to assess. In general, questions on an exam should be interpreted within the context of the material the exam covers. Plus, it is not unreasonable that, when asked how to achieve X using Y, that the most reasonable answer should involve characteristics that are distinctive of Y.

Now, it may very well be that a question on an early exam in a Physics I course that has only talked about gravity and the equations of motion without friction might be worded this way and, given that context, be expecting the drop and time approach, but I would argue that such a question would be unnecessarily misleading, particularly for those students that happen to already know what a barometer is and can deduce how it might be used -- as a barometer -- to answer the question. Those students probably should receive full credit but you have created a situation in which you haven't assessed whether they understand how to work with Newton's laws and other mechanics concepts.

#### Kermit2

Joined Feb 5, 2010
4,162
Short answer to what the kid was thinking?

I'm the biggest smart ass alive! Watch as I confound the instructor with my over developed wit.

He may have gotten a grade from class but he would have gotten a pink slip if he worked for me and pulled that crap act.

#### WBahn

Joined Mar 31, 2012
30,250
This link to an article that is contemporary to the story makes me believe it is a true story:
http://www.nytimes.com/1964/03/08/science-teacher-chides-teachers.html?_r=0

I, like you, find the student's reason for his answer more argumentative than factual. In fact, I was quite surprised because I was expecting an explantion more like: "I just felt that the question did not allow creativity in the answer."
This is part of why I'm dubious that the story is on the up and up as opposed to being made up by Dr. Calandra as nothing more than a contrived example to make his point. What student is going to say that they answered they way they did to protest not being shown "the structure of the subject matter". What the hell does that even mean? It sounds more like something that Dr. Calandra would come up with, especially considering that he stated that what should be emphasized are the "patterns in the subject matter." Sounds awfully familiar.

I think that Dr. Calandra's claim that teaching science "from the standpoint that it is a special sort of thinking that applies only to science is misleading" is a red herring. No one that I know of claims that the scientific method applies only to science. But I think it is pretty self-evident that the thought processes used by many people in day to day life do NOT apply to science. Look at how often people just make multiple, random changes to something hoping that something will just happen to turn out okay. We see it here all the time with homework problems. But according to Dr. Calandra we shouldn't show students that a better approach is to systematically approach the problem, anticipate what the expected result will be from a single change, review the observed result from making that change, update our understanding of how the system responds to changes, and then repeat as necessary.

p.s. I think the student should have gotten full credit for his answer. It was a poorly written question that that expected a "stock", memorized answer. Maybe the context of the classroom assignments would change my thinking on that.
If the class had just covered how air pressure changes with altitude (probably using a simplified and idealized model) and how a barometer can be used to measure air pressure (which is probably pretty likely), I wouldn't see how asking this question, in this form, is expecting a stock, memorized answer. Instead it is seeing if the student can draw a connection between two things they have studied in order to solve a problem that likely was NOT covered in detail. Now, admittedly I assume a context when I read the question because I have no choice but to do so.

In any case, it would be interesting to see what would be considered a well-written question in it's place.

#### GopherT

Joined Nov 23, 2012
8,009
Whether you like or dislike the kids answer doesn't make the obvious path more correct than the kids. The fact that you haven't even considered the possible errors with each is concerning. I'm not sure if you have measured the barometric pressure a on different levels of a building but I have. A modern laboratory building and a modern office building have pressures jumping all over the map depending on whether the air conditioner is running, circulating or turned off. If you watch closely at parallel lines of reflections on large walls of windows, you can be seen them flex as HVAC kicks on/off. Higher floors do, in general have lower pressure than lower floors but there are overlaps (large overlaps) where lower floors have less pressure than 4 to 5 floors above. Reasonable accuracy can only be assumed if the measurements are taken outdoors. I understand that most of the student's suggestions required access to the outdoors but I would argue that those methods are also flawed. I think his methods of using the barometer as a yardstick and measuring the night as he walked up the stairwell would be most accurate and the barter option with the building manage is also very creative. Whether the story is true or not, I don't care - it is still an interesting discussion.

#### WBahn

Joined Mar 31, 2012
30,250
I agree it's an interesting discussion. In fact, if I recall, my 10th grade physics teacher use this story (or one similar to it) as a light-hearted introduction into a discussion of how there are many different ways to go about answering a given question. I don't recall the details of a 35-year old classroom discussion, so I don't recall to what degree we touched on the various pros and cons. But one thing to keep in mind is that a question like this would almost certainly be asked in an introductory course in which most concepts are heavily idealized. For instance, dynamic friction is treated as something that depends only on the type of the surfaces in contact and the normal force between them, when in reality it is much more complicated. The fact that is IS more complicated isn't even mentioned in most textbooks at this level. Similarly, the variation of barometric pressure with altitude is presented as an idealized model and discussions of concepts, at that level, are within the context of that model.