Abstract
The aim of this paper is to discuss different approaches to the quality (or uncertainty) of measurement data considering both historical examples and today’s students’ views. Today’s teaching of data analysis is very much focussed on the application of statistical routines (often called the „Gaussian approach” to error analysis). Studies on students’ understanding of measurement however show, that though the majority can be enabled to apply those routines most of the students fail to construct a coherent understanding of the matter. Analysing two historical examples of measurement practice of the time around 1,800 when the statistical approach was established, we point out what often neglected key idea gave rise to the statistical approach to data analysis (the appreciation of randomness in data distribution) and how the emergence of this idea was embedded in a very sophisticated insight on measurement and the nature of measurement data (experimental expertise). These two aspects can vividly be illustrated using the different approaches to data handling of Coulomb and Gauss around the time of 1,800. Gauss’s appreciation of the randomness in data distribution consequently led him to other analytical routines as those employed by Coulomb. This is an important aspect concerning the teaching of the statistical routines of data analysis. However, the deep experimental expertise of both Gauss and Coulomb in both cases prevented an application by rote of some routines and shaped their approaches to very successful instruments of data handling. We therefore argue that both the key idea of randomness as well as an elaborated experimental expertise has to be taken into consideration much more than before by instructors and teachers in order to support the students to construct a coherent understanding on the nature and the handling of measurement data and especially the assessment of their quality.
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Notes
See e.g. Hon (2005, p. 37): “Scientific approaches and methods that seem self-evident in our days have a historical background. That is also true for the concept of measurement error…. Here it is essential to investigate the tacit assumptions that are inherent in the different conceptions”.
These changes are far from uncommon, the value for the speed of light changes throughout the nineteenth and most of the twentieth century, likewise, Millikan corrects his values for the elementary charge during his series of experiments.
Furthermore, neither the French nor the German language provided the respective author with appropriate terms. Thus, where necessary, the original terms as used in the publications concerned are added in brackets to the translation to emphasise the interpretation that comes with the translation.
The first prize competition dealt with questions on the magnetisation and suspension of needles and the diurnal variation of the magnetic field of the earth, the second one on friction. On Coulomb see Gillmor (1971).
On the establishment of Coulomb’s style of experimentation see Heering (2006).
For our argumentation it is irrelevant whether Coulomb had a theoretical understanding of the process under investigation and confirmed this by measurements or whether he carried out experiments and determined from the results a mathematical relation. The crucial aspect for our argumentation is Coulomb’s comparison of his data with a mathematical relation that required a regular behaviour of the data. Any irregularity was considered to be a deviation and thus an error.
Likewise, the Scottish natural philosopher John Robison published an experiment in 1803 where he demonstrated the inverse square law in electrostatics. However, Robison used a method which required that he take the mean of a series over some three to five measurements, and subsequently take the mean of all the means in order to come up with his relation (see Beneken 2000).
Most measurements of the Magnetischer Verein were taken on 28 days between 1836 and 1841 for a period of 24 h every 5 min by 50 observatories in Europe, Asia, Africa, Northern America and the South Seas. The results were transferred to Göttingen and processed by Gauss and Weber. The publication of their Magnetic Atlas of the Earth represents a milestone in the history of science.
Reportedly, the first reference appeared in Kohlrausch’s laboratory manual “Leitfaden der Praktischen Physik” for the University of Göttingen, 1870, more clearly in its second edition 1884.
Lubben and Millar (1996) stated that the items indicated different steps in the building of an understanding of the nature of measurement data although every student would not necessarily go throw all steps or in the given order.
162 students at ten different German universities were surveyed prior and post to first year laboratory instruction. The instrument was based on the questionnaire developed by Allie et al. (1998) and contained 12 open ended questions on different aspects of a given laboratory context, the Nature of Science and the common terminology.
Some students add that these are the reasons commonly applied in school or first year laboratory experiments where the dominant setting of a task is a closed question and the possibility of measurement repetition usually reduced by instruction and/or the limited time. Commonly not more than five readings are taken, often also only a single or an additional second reading for assurance.
In this context a ball is released to roll down a slope from some height h. It leaves the slope horizontally an das the slope is fixed on a table it travels some distance d before it hits the floor, leaving an imprint at the point of impact.
See also Volkwyn et al. (2008).
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We are indebted to two anonymous reviewers whose comments helped us significantly to restructure the paper in order to communicate our ideas more clearly.
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Heinicke, S., Heering, P. Discovering Randomness, Recovering Expertise: The Different Approaches to the Quality in Measurement of Coulomb and Gauss and of Today’s Students. Sci & Educ 22, 483–503 (2013). https://doi.org/10.1007/s11191-011-9430-8
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DOI: https://doi.org/10.1007/s11191-011-9430-8