, Volume 45, Issue 3–4, pp 217–233 | Cite as

How to Cope with Gauss’s Errors? Motivation for Teaching Data and Uncertainty Analysis from a History of Science Perspective

  • Susanne Heinicke


Every measurement in science, every experimental decision, result and information drawn from it has to cope with something that has long been named by the term “error”. In fact, errors describe our limitations when it comes to experimental science and science looks back on a long tradition to cope with them. The widely known way to cope with them in nowadays classrooms and introductory laboratories is the so-called traditional “approach to error treatment” dated back by many to the ideas of Gauss. However, this is not exactly true, and as one digs deeper into the history of errors (or: uncertainty) one finds not only surprising stories about the treatment of data and uncertainty but also a lot to learn from for our today’s teaching. The treatment of error did not just appear out of the blue but evolved along side with the history of experimental science, a growing insight into data and sensitivity for its trustworthiness. Virtues that today’s learners are hoped to develop just the same.


Measurement uncertainty Measurement error Gauss Data evaluation Data analysis Uncertainty 


  1. Allie, S., Buffler, A., Campbell, B., & Lubben, F. (1998). First year physics students’ perceptions of the quality of experimental measurements. International Journal of Science Education, 20(4), 447–459.CrossRefGoogle Scholar
  2. Bernoulli, D. (1778/1961). The most probable choice between several discrepant observations and the formation therefrom of the most likely induction. Biometrika, 48, 3–13.Google Scholar
  3. Bessel, F. W. (1838). Untersuchungen über die Wahrscheinlichkeit der Beobachtungsfehler. Astronomische Nachrichten, 15, 379–404.Google Scholar
  4. BIPM. (1995/2008). Guide to the expression of uncertainty in measurement (GUM). Geneva: International Organization for Standardization.Google Scholar
  5. Buffler, A., Allie, S., & Lubben, F. (2008). Teaching measurement and uncertainty the GUM way. The Physics Teacher, 46, 539–544.CrossRefGoogle Scholar
  6. Coulomb, C. (1785). Premier Mémoire sur l’Electricité et le Magnétisme. Mémoires de l’Académie Royale des Sciences, (1788), 569–577.Google Scholar
  7. De Moivre, A. (1756). The doctrine of chances. Or: A method of calculating the pobabilities of events in play. London: A. Millar.Google Scholar
  8. Fischer, P. (1845). Lehrbuch der höheren Geodäsie, Band 1. Darmstadt: Leske.Google Scholar
  9. Galilei, G. (1632). Dialogo sopra i due massimi sistemi del mondo. Florenz.Google Scholar
  10. Gauss, C. F. (1809). Theoria motus corporum coelestium in sectionibus conicis solem ambientium. Hamburg: Perthes & Besser.Google Scholar
  11. Gauss, C. F. (1821). Theoria combinationis observationum erroribus minimis obnoxiae, pars prior. Göttingen: Dieterich.Google Scholar
  12. Hagen, G. (1837). Grundzüge der Wahrscheinlichkeitsrechnung. Berlin: Dümmler.Google Scholar
  13. Heering, P. (1992). On Coulomb’s inverse square law. American Journal of Physics, 60, 988–994.CrossRefGoogle Scholar
  14. Heinicke, S., Riess, F. (2012). Missing links in the experimental work. In L. Maurines & A. Redfors (Eds.), ESERA 2011 Proceedings.Google Scholar
  15. Kepler, J. (1609). Astronomia Nova. Heidelberg: Voegelin.Google Scholar
  16. Koestler, A. (1961). The watershed, a biography of Johannes Kepler. London: Heinemann.Google Scholar
  17. Lambert, J. H. (1760). Photometria, sive de Mensura et Gradibus Luminis, Colorum et Umbrae. Augsburg: Christoph Peter Detleffsen for the widow of Eberhard Klett.Google Scholar
  18. Laplace, P. S. (1776). Recherches sur l′intégration des équations différentielles aux différences finies. Laplace Werke, t. 8. Paris, p. 69–197.Google Scholar
  19. Lippmann, R. (2003). Students’ understanding of measurement and uncertainty in the physics laboratory. Ph.D. thesis: University of Maryland.Google Scholar
  20. Robison, J. (1822). A system of mechanical philosophy. Edinburgh: John Murray.Google Scholar
  21. Séré, M.-G., Journeaux, R., & Larcher, C. (1993). Learning the statistical analysis of measurement error. International Journal of Science Education, 15, 427–438.CrossRefGoogle Scholar
  22. Simpson, T. (1756). A letter to the honourable George Earl of Macclesfield. Philosophical Transactions of the Royal Society of London, 49(1), 82–93.Google Scholar
  23. Stigler, S. (1986/2003). The history of statistics. The Measurement of Uncertainty before 1900. Cambridge and London: Harvard University Press.Google Scholar
  24. Tomlinson, J., Dyson, P., & Garratt, J. (2001). Student misconceptions of the language of error. University Chemistry Education, 5(1), 1–8.Google Scholar

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© Springer Science+Business Media Dordrecht 2015

Authors and Affiliations

  1. 1.University of MünsterMünsterGermany

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