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Barometer question

January 01, 1970

For European "barometer surveys" and questions, see Eurobarometer.

The barometer question is an example of an incorrectly designed examination question demonstrating functional fixedness that causes a moral dilemma for the examiner. In its classic form, popularized by American test designer professor Alexander Calandra in the 1960s, the question asked the student to "show how it is possible to determine the height of a tall building with the aid of a barometer."[1] The examiner was confident that there was one, and only one, correct answer, which is found by measuring the difference in pressure at the top and bottom of the building and solving for height. Contrary to the examiner's expectations, the student responded with a series of completely different answers. These answers were also correct, yet none of them proved the student's competence in the specific academic field being tested.

A storm glass or Goethe's device, an early practical type of barometer. Calandra's essay does not name the type of the device, although the answers provided by the student suggest the use of a portable aneroid barometer.

The barometer question achieved the status of an urban legend; according to an internet meme, the question was asked at the University of Copenhagen and the student was Niels Bohr.[2] The Kaplan, Inc. ACT preparation textbook describes it as an "MIT legend",[3] and an early form is found in a 1958 American humor book.[4] However, Calandra presented the incident as a real-life, first-person experience that occurred during the Sputnik crisis.[5] Calandra's essay, "Angels on a Pin", was published in 1959 in Pride, a magazine of the American College Public Relations Association.[6] It was reprinted in Current Science in 1964,[7] in Saturday Review in 1968[8] and included in the 1969 edition of Calandra's The Teaching of Elementary Science and Mathematics.[9] Calandra's essay became a subject of academic discussion.[10] It was frequently reprinted since 1970,[11] making its way into books on subjects ranging from teaching,[12] writing skills,[13] workplace counseling[14] and investment in real estate[15] to chemical industry,[16] computer programming[17] and integrated circuit design.[18]

Calandra's account edit

A colleague of Calandra posed the barometer question to a student, expecting the correct answer: "the height of the building can be estimated in proportion to the difference between the barometer readings at the bottom and at the top of the building".[19] The student provided a different, and also correct answer: "Take the barometer to the top of the building. Attach a long rope to it, lower the barometer to the street, then bring it up, measuring the length of the rope. The length of the rope is the height of the building."[20]

The examiner and Calandra, who was called to advise on the case, faced a moral dilemma. According to the format of the exam, a correct answer deserved a full credit. But issuing a full credit would have violated academic standards by rewarding a student who had not demonstrated competence in the academic field that had been tested (physics). Neither of two available options (pass or fail) was morally acceptable.[20]

By mutual agreement with the student and the examiner, Calandra gave the student another opportunity to answer, warning the student the answer would require demonstrating some knowledge of physics. The student came up with several possible answers, but settled on dropping the barometer from the top of the building, timing its fall, and using the equation of motion   to derive the height. The examiner agreed that this satisfied the requirement and gave the student “almost full credit”.[20]

When Calandra asked about the other answers, the student gave the examples:

  • using the proportion between the lengths of the building's shadow and that of the barometer to calculate the building's height from the height of the barometer
  • using the barometer as a measuring rod to mark off its height on the wall while climbing the stairs, then counting the number of marks
  • suspending the barometer from a string to create a pendulum, then using the pendulum to measure the strength of Earth's gravity at the top and bottom of the building, and calculating the height of the building from the difference in the two measurements (see Newton's law of universal gravitation)

There were, the student said, many other possible solutions.

“Probably the best,” he said, is to take the barometer to the basement and knock on the superintendent’s door. When the superintendent answers, you speak to him as follows: ‘Mr. Superintendent, here I have a fine barometer, if you will tell me the height of the building, I will give you this barometer.”

The student admitted that he knew the expected “conventional” answer, but was fed up with the professor's "teaching him how to think ... rather than teaching him the structure of the subject."[5]

Internet meme edit

According to Snopes.com, more recent (1999 and 1988) versions identify the problem as a question in "a physics degree exam at the University of Copenhagen" and the student was Niels Bohr, and includes the following answers:[21]

  • Tying a piece of string to the barometer, lowering the barometer from the roof to the ground, and measuring the length of the string and barometer.
  • Dropping the barometer off the roof, measuring the time it takes to hit the ground, and calculating the building's height assuming constant acceleration under gravity.
  • When the sun is shining, standing the barometer up, measuring the height of the barometer and the lengths of the shadows of both barometer and building, and finding the building's height using similar triangles.
  • Tying a piece of string to the barometer, and swinging it like a pendulum both on the ground and on the roof, and from the known pendulum length and swing period, calculate the gravitational field for the two cases. Use Newton's law of gravitation to calculate the radial altitude of both the ground and the roof. The difference will be the height of the building.
  • Tying a piece of string to the barometer, which is as long as the height of the building, and swinging it like a pendulum, and from the swing period, calculate the pendulum length.
  • Marking off the number of barometer lengths vertically along the emergency staircase, and multiplying this with the length of the barometer.
  • Trading the barometer for the correct information with the building's janitor or superintendent.
  • Measuring the pressure difference between ground and roof and calculating the height difference (the expected answer).

Interpretations edit

Professor of physics Mark Silverman used what he called "The Barometer-Story formula" precisely for explaining the subject of pressure and recommended it to physics teachers. Silverman called Calandra's story "a delightful essay that I habitually read to my class whenever we study fluids ... the essay is short, hilarious and satisfying (at least to me and my class)."[22]

Financial advisor Robert G. Allen presented Calandra's essay to illustrate the process and role of creativity in finance. "Creativity is born when you have a problem to solve. And as you can see from this story ["Angels on a Pin"] there are many ways of solving a problem. Creativity is the art of looking for solutions that are out of the ordinary, different, unorthodox."[23]

O'Meara used the barometer question to illustrate the art of steering students' activities to a desired outcome: "if the question is not aligned [with the desired learning outcome] then the problem becomes an exercise of problem solving for its own value."[24] The teacher can steer the students either through careful design of the questions (this rules out barometer questions), or through guiding the students to the desired choices. In case of the original barometer question, the examiner may explicitly say that the problem has more than one solution, insist on applying the laws of physics, or give them the "ending point" of the solution: "How did I discover that the building was 410 feet in height with only a barometer?"[24]

Herson used the Calandra account as an illustration of the difference between academic tests and assessment in education. Tests, even the ones designed for reliability and validity, are useful, but they are not sufficient in real-world education.[25]

Sanders interpreted Calandra's story as a conflict between perfection and optimal solutions: "We struggle to determine a 'best' answer, when a simple call to a building superintendent (the resource man) would quickly provide adequate information."[26]

Footnotes edit

  1. ^ Calandra, Alexander (December 21, 1968). "Education in America: Angels on a Pin". The Saturday Review: 60.
  2. ^ http://naturelovesmath-en.blogspot.in/2011/06/niels-bohr-barometer-question-myth.html [user-generated source]
  3. ^ Kaplan, p. 52.
  4. ^ Reader's Digest Treasury of Wit & Humor, p. 303
  5. ^ a b Calandra, Alexander, "Angels on a Pin". Reproduced in Barnes et al., pp. 228-229. p. 229.
  6. ^ Pride, volumes 3-4 (1959). American College Public Relations Association. p. 11.
  7. ^ Attribution and date (Current Science (Teacher's Edition), 44 (January 6–10, 1964), pp. 1-2.) as in: Van Cleve Morris et al. (1969). Modern movements in educational philosophy. Houghton Mifflin. p. 82.
  8. ^ Attribution and date (Saturday Review, December 21, 1968) as in Weimer, p. 234.
  9. ^ Attribution and year of publication ("Published in the AIChE Journal vol. 15 no. 2, 1969, p. 13. ") as in Sanders, pp. 196-197.
  10. ^ Discussed by Calandra et al. in: Van Cleve Morris et al. (1969). Modern movements in educational philosophy. Houghton Mifflin.
  11. ^ Reproduced in entirety in: Muse Milton (1970). Selected readings for the introduction to the teaching profession. McCutchan Pub. Corp. ISBN 0-8211-1218-X, pp. 100-103.
  12. ^ Reproduced in entirety in Barnes et al., pp. 228-229; paraphrased in Herson, pp. 21-22 etc.
  13. ^ Reproduced in entirety in: Skwire, David (1994). Writing with a thesis: a rhetoric and reader. Harcourt Brace College Publishers. ISBN 0-03-079101-4. pp. 40-42.
  14. ^ Reproduced in entirety, in German, in: Otto F. Kernberg (2005). WIR: Psychotherapeuten über sich und ihren "unmöglichen" Beruf. Schattauer Verlag. ISBN 3-7945-2466-7. pp. 318-319.
  15. ^ Reproduced in part in: Allen, pp. 12-13.
  16. ^ Paraphrased in: Sanders, pp. 196-197.
  17. ^ Paraphrased in Peter van der Linden (1994). Expert C programming: deep C secrets. Prentice Hall PTR. ISBN 0-13-177429-8. p. 344.
  18. ^ Reproduced in entirety in: Jim Williams (1992). Analog Circuit Design: Art, Science and Personalities. Newnes. ISBN 0-7506-9640-0. pp. 3-4.
  19. ^ A classic in-depth discussion of the subject was presented in 1823 by Rev. Baden Powell in Measurement of Heights by the Barometer, published in volume 22, numbers I through V, of the Annals of Philosophy. For a modern presentation of the same subject, see Silverman, pp. 40-48. The particular formula sought by Calandra's examiner is marked with index 2.12 on page 41.
  20. ^ a b c Calandra, Alexander, "Angels on a Pin". Reproduced in Barnes et al., pp. 228-229. p. 228.
  21. ^ snopes.com: The Barometer Problem
  22. ^ Silverman, p. 40.
  23. ^ Allen, p. 13.
  24. ^ a b O'Meara, p. 108.
  25. ^ Herson, pp. 20-21.
  26. ^ Sanders, p. 197.

References edit

  • Robert G. Allen (2004). Nothing Down for the 2000s: Dynamic New Wealth Strategies in Real Estate. Simon and Schuster. ISBN 0-7432-6155-0.
  • Louis B. Barnes, Carl Roland Christensen, Abby J. Hansen (1994). Teaching and the case method: text, cases, and readings. Harvard Business Press. ISBN 0-87584-403-0.
  • Walter Grarzer (2004). Eurekas and euphorias: the Oxford book of scientific anecdotes. Oxford University Press. ISBN 0-19-860940-X.
  • Kaplan ACT Premier Program 2009. Kaplan, Inc. ISBN 1-4195-5237-6.
  • Naomi L. Herson (1986), Evaluation for Excellence in Education, in: Evaluation for excellence in education: presentations given at a workshop/seminar. Canadian Education Association. ISBN 0-920315-16-X.
  • Jodi O'Meara (2010). Beyond Differentiated Instruction. Corwin Press. ISBN 1-4129-8203-0.
  • Roy E. Sanders (2005). Chemical process safety: learning from case histories. Gulf Professional Publishing. ISBN 0-7506-7749-X.
  • Mark P. Silverman (2002). A universe of atoms, an atom in the universe. Springer. ISBN 0-387-95437-6. The cited chapter reproduces an earlier publication:
    • Mark P. Silverman (1998). Flying High, Thinking Low? What Every Aeronaut Needs To Know. The Physics Teacher. 1998, vol. 36. pp. 288–293. The solution sought by Calandra's examiner is indexed with (4) in the very end of p. 289.
  • Maryellen Weimer (2002). Learner-centered teaching: five key changes to practice. John Wiley and Sons. ISBN 0-7879-5646-5.

See also edit

January 01, 1970
barometer, question, european, barometer, surveys, questions, eurobarometer, barometer, question, example, incorrectly, designed, examination, question, demonstrating, functional, fixedness, that, causes, moral, dilemma, examiner, classic, form, popularized, a. For European barometer surveys and questions see Eurobarometer The barometer question is an example of an incorrectly designed examination question demonstrating functional fixedness that causes a moral dilemma for the examiner In its classic form popularized by American test designer professor Alexander Calandra in the 1960s the question asked the student to show how it is possible to determine the height of a tall building with the aid of a barometer 1 The examiner was confident that there was one and only one correct answer which is found by measuring the difference in pressure at the top and bottom of the building and solving for height Contrary to the examiner s expectations the student responded with a series of completely different answers These answers were also correct yet none of them proved the student s competence in the specific academic field being tested A storm glass or Goethe s device an early practical type of barometer Calandra s essay does not name the type of the device although the answers provided by the student suggest the use of a portable aneroid barometer The barometer question achieved the status of an urban legend according to an internet meme the question was asked at the University of Copenhagen and the student was Niels Bohr 2 The Kaplan Inc ACT preparation textbook describes it as an MIT legend 3 and an early form is found in a 1958 American humor book 4 However Calandra presented the incident as a real life first person experience that occurred during the Sputnik crisis 5 Calandra s essay Angels on a Pin was published in 1959 in Pride a magazine of the American College Public Relations Association 6 It was reprinted in Current Science in 1964 7 in Saturday Review in 1968 8 and included in the 1969 edition of Calandra s The Teaching of Elementary Science and Mathematics 9 Calandra s essay became a subject of academic discussion 10 It was frequently reprinted since 1970 11 making its way into books on subjects ranging from teaching 12 writing skills 13 workplace counseling 14 and investment in real estate 15 to chemical industry 16 computer programming 17 and integrated circuit design 18 Contents 1 Calandra s account 2 Internet meme 3 Interpretations 4 Footnotes 5 References 6 See alsoCalandra s account editA colleague of Calandra posed the barometer question to a student expecting the correct answer the height of the building can be estimated in proportion to the difference between the barometer readings at the bottom and at the top of the building 19 The student provided a different and also correct answer Take the barometer to the top of the building Attach a long rope to it lower the barometer to the street then bring it up measuring the length of the rope The length of the rope is the height of the building 20 The examiner and Calandra who was called to advise on the case faced a moral dilemma According to the format of the exam a correct answer deserved a full credit But issuing a full credit would have violated academic standards by rewarding a student who had not demonstrated competence in the academic field that had been tested physics Neither of two available options pass or fail was morally acceptable 20 By mutual agreement with the student and the examiner Calandra gave the student another opportunity to answer warning the student the answer would require demonstrating some knowledge of physics The student came up with several possible answers but settled on dropping the barometer from the top of the building timing its fall and using the equation of motion d 1 2 a t 2 displaystyle d tfrac 1 2 a t 2 nbsp to derive the height The examiner agreed that this satisfied the requirement and gave the student almost full credit 20 When Calandra asked about the other answers the student gave the examples using the proportion between the lengths of the building s shadow and that of the barometer to calculate the building s height from the height of the barometer using the barometer as a measuring rod to mark off its height on the wall while climbing the stairs then counting the number of marks suspending the barometer from a string to create a pendulum then using the pendulum to measure the strength of Earth s gravity at the top and bottom of the building and calculating the height of the building from the difference in the two measurements see Newton s law of universal gravitation There were the student said many other possible solutions Probably the best he said is to take the barometer to the basement and knock on the superintendent s door When the superintendent answers you speak to him as follows Mr Superintendent here I have a fine barometer if you will tell me the height of the building I will give you this barometer The student admitted that he knew the expected conventional answer but was fed up with the professor s teaching him how to think rather than teaching him the structure of the subject 5 Internet meme editAccording to Snopes com more recent 1999 and 1988 versions identify the problem as a question in a physics degree exam at the University of Copenhagen and the student was Niels Bohr and includes the following answers 21 Tying a piece of string to the barometer lowering the barometer from the roof to the ground and measuring the length of the string and barometer Dropping the barometer off the roof measuring the time it takes to hit the ground and calculating the building s height assuming constant acceleration under gravity When the sun is shining standing the barometer up measuring the height of the barometer and the lengths of the shadows of both barometer and building and finding the building s height using similar triangles Tying a piece of string to the barometer and swinging it like a pendulum both on the ground and on the roof and from the known pendulum length and swing period calculate the gravitational field for the two cases Use Newton s law of gravitation to calculate the radial altitude of both the ground and the roof The difference will be the height of the building Tying a piece of string to the barometer which is as long as the height of the building and swinging it like a pendulum and from the swing period calculate the pendulum length Marking off the number of barometer lengths vertically along the emergency staircase and multiplying this with the length of the barometer Trading the barometer for the correct information with the building s janitor or superintendent Measuring the pressure difference between ground and roof and calculating the height difference the expected answer Interpretations editProfessor of physics Mark Silverman used what he called The Barometer Story formula precisely for explaining the subject of pressure and recommended it to physics teachers Silverman called Calandra s story a delightful essay that I habitually read to my class whenever we study fluids the essay is short hilarious and satisfying at least to me and my class 22 Financial advisor Robert G Allen presented Calandra s essay to illustrate the process and role of creativity in finance Creativity is born when you have a problem to solve And as you can see from this story Angels on a Pin there are many ways of solving a problem Creativity is the art of looking for solutions that are out of the ordinary different unorthodox 23 O Meara used the barometer question to illustrate the art of steering students activities to a desired outcome if the question is not aligned with the desired learning outcome then the problem becomes an exercise of problem solving for its own value 24 The teacher can steer the students either through careful design of the questions this rules out barometer questions or through guiding the students to the desired choices In case of the original barometer question the examiner may explicitly say that the problem has more than one solution insist on applying the laws of physics or give them the ending point of the solution How did I discover that the building was 410 feet in height with only a barometer 24 Herson used the Calandra account as an illustration of the difference between academic tests and assessment in education Tests even the ones designed for reliability and validity are useful but they are not sufficient in real world education 25 Sanders interpreted Calandra s story as a conflict between perfection and optimal solutions We struggle to determine a best answer when a simple call to a building superintendent the resource man would quickly provide adequate information 26 Footnotes edit Calandra Alexander December 21 1968 Education in America Angels on a Pin The Saturday Review 60 http naturelovesmath en blogspot in 2011 06 niels bohr barometer question myth html user generated source Kaplan p 52 Reader s Digest Treasury of Wit amp Humor p 303 a b Calandra Alexander Angels on a Pin Reproduced in Barnes et al pp 228 229 p 229 Pride volumes 3 4 1959 American College Public Relations Association p 11 Attribution and date Current Science Teacher s Edition 44 January 6 10 1964 pp 1 2 as in Van Cleve Morris et al 1969 Modern movements in educational philosophy Houghton Mifflin p 82 Attribution and date Saturday Review December 21 1968 as in Weimer p 234 Attribution and year of publication Published in the AIChE Journal vol 15 no 2 1969 p 13 as in Sanders pp 196 197 Discussed by Calandra et al in Van Cleve Morris et al 1969 Modern movements in educational philosophy Houghton Mifflin Reproduced in entirety in Muse Milton 1970 Selected readings for the introduction to the teaching profession McCutchan Pub Corp ISBN 0 8211 1218 X pp 100 103 Reproduced in entirety in Barnes et al pp 228 229 paraphrased in Herson pp 21 22 etc Reproduced in entirety in Skwire David 1994 Writing with a thesis a rhetoric and reader Harcourt Brace College Publishers ISBN 0 03 079101 4 pp 40 42 Reproduced in entirety in German in Otto F Kernberg 2005 WIR Psychotherapeuten uber sich und ihren unmoglichen Beruf Schattauer Verlag ISBN 3 7945 2466 7 pp 318 319 Reproduced in part in Allen pp 12 13 Paraphrased in Sanders pp 196 197 Paraphrased in Peter van der Linden 1994 Expert C programming deep C secrets Prentice Hall PTR ISBN 0 13 177429 8 p 344 Reproduced in entirety in Jim Williams 1992 Analog Circuit Design Art Science and Personalities Newnes ISBN 0 7506 9640 0 pp 3 4 A classic in depth discussion of the subject was presented in 1823 by Rev Baden Powell in Measurement of Heights by the Barometer published in volume 22 numbers I through V of the Annals of Philosophy For a modern presentation of the same subject see Silverman pp 40 48 The particular formula sought by Calandra s examiner is marked with index 2 12 on page 41 a b c Calandra Alexander Angels on a Pin Reproduced in Barnes et al pp 228 229 p 228 snopes com The Barometer Problem Silverman p 40 Allen p 13 a b O Meara p 108 Herson pp 20 21 Sanders p 197 References editRobert G Allen 2004 Nothing Down for the 2000s Dynamic New Wealth Strategies in Real Estate Simon and Schuster ISBN 0 7432 6155 0 Louis B Barnes Carl Roland Christensen Abby J Hansen 1994 Teaching and the case method text cases and readings Harvard Business Press ISBN 0 87584 403 0 Walter Grarzer 2004 Eurekas and euphorias the Oxford book of scientific anecdotes Oxford University Press ISBN 0 19 860940 X Kaplan ACT Premier Program 2009 Kaplan Inc ISBN 1 4195 5237 6 Naomi L Herson 1986 Evaluation for Excellence in Education in Evaluation for excellence in education presentations given at a workshop seminar Canadian Education Association ISBN 0 920315 16 X Jodi O Meara 2010 Beyond Differentiated Instruction Corwin Press ISBN 1 4129 8203 0 Roy E Sanders 2005 Chemical process safety learning from case histories Gulf Professional Publishing ISBN 0 7506 7749 X Mark P Silverman 2002 A universe of atoms an atom in the universe Springer ISBN 0 387 95437 6 The cited chapter reproduces an earlier publication Mark P Silverman 1998 Flying High Thinking Low What Every Aeronaut Needs To Know The Physics Teacher 1998 vol 36 pp 288 293 The solution sought by Calandra s examiner is indexed with 4 in the very end of p 289 Maryellen Weimer 2002 Learner centered teaching five key changes to practice John Wiley and Sons ISBN 0 7879 5646 5 See also editManhole cover question Microsoft interview Retrieved from https en wikipedia org w index php title Barometer question amp oldid 1193703343, wikipedia, wiki, book, books, library,

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