Educational Research - the Ethics and Aesthetics of Statistics

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158 J.P. Van Bendegem et al. 10.4 Conclusion In this chapter we have merely initiated a train of thoughts about statistics, its ethics and aesthetics, and its literacy. We still do not know whether we should take our umbrella or not, but realising that we do not know seems to have some value in and of itself. It indicates the borderlines where quantitative measures cease to have a societal relevance, where the quantitative needs to be translated into the qualitative, in this case, into the visual, and where access means relevant access. Notes 1. This in itself is quite a tricky matter: some will claim that statistics can only be seen as applied and that thus the phrase ‘statistics as a part of pure mathematics’ does not make sense. From that perspective the combination of ethics and statistics as a branch of pure mathematics could refer to the empty set. However, there is no unanimity on this question and so, as long as no definite proof of emptiness has been produced, we consider the combination as meaningful. An additional argument in favour of non-emptiness is the fact that statistics is part of the classification scheme (section 62) of the American Mathematical Society and, in fact, the first subsection is Foundational and Philosophical Topics (see http://www.ams.org/). 2. Unless, of course, one now sees probability theory as part of algebra. Talking about sigmaalgebras and functions defined over such structures, satisfying certain conditions, often in the forms of integrals, is quite a stretch away from statements such as ‘the probability to get a 3 with a fair dice is 1/6’. More specifically, Kolmogorov’s approach made it a lot easier to deal with infinite cases. If one wonders whether this notion makes any sense, just think of a rotating wheel and any question involving the probability of the angle of rotation, which is a continuous, hence infinitely fine-grained variable. 3. So it is claimed by Heinrich Neider in his memories about Neurath. See Neurath and Cohen (1973, p. 49). 4. It is, for example, quite curious that in the extensive and authoritative publications of Tufte on visual representations of information (see Tufte, 1983, 1990, 1997) only in the third part ISOTYPE is briefly mentioned and the name of Otto Neurath is lacking altogether. 5. In Neurath and Cohen (1973), Marie Neurath quotes from one of Otto Neurath’s papers on ISOTYPE (pp. 224–248). So at least in 1973 it was known that some texts had to exist. 6. The example is taken from the text of Neurath himself (see Nemeth & Stadler, 1996, p. 330). 7. Here, we should allow room for discussion. It could be a drawing of a person standing still in a framework of some kind (a scanner at an airport?), or of a person leaving or entering a room, or it could be a still from a film. In that sense the figure is definitely ambiguous and open to multiple interpretations. 8. Hoffmann (2007) in his article ‘Cognitive Conditions of Diagrammatic Reasoning’ offers a very deep analysis of Plato’s case and the cognitive importance of diagrammatic reasoning. 9. These two figures have been taken from Hoffmann’s article (2007, pp. 15 and 20). 10. These two figures have been taken from the contribution of Angela Jansen in Nemeth and Stadler (1996, pp. 147 and 148). 11. The name of the museum betrays Neurath’s interest in architecture. As it happens, Neurath not only lectured at the Bauhaus and convinced Rudolf Carnap to do likewise, but he also participated as non-architect – an adaptation of the statutes was required to allow for his presence – in the CIAM (Congrès International d’Architecture Moderne), one of its founders being Josef Frank, who was the brother of Philipp Frank, a member of the Wiener Kreis. 12. It is therefore in my view not surprising that one of the contributions to the ‘International Encyclopaedia of Unified Science’ – or, to be more specific, the launching of the
10 The Good, the Beautiful and the Literate: Making Statistics Accessible for Action 159 Encyclopaedia – was written by Charles Morris, one of the core figures in semiotics in the twentieth century, entitled ‘Foundations of the Theory of Signs’ (Chicago: University of Chicago Press, 1938). Interestingly enough, Morris sees semiotics both as a subdiscipline of the human sciences and as a general science of all sciences since all sciences need signs to express themselves. To make the picture complete, also consider that Morris was heavily inspired both by logical empiricism and by C. S. Peirce. The semiotic connection then becomes inescapable. References Evans, J. (1992). Mathematics for adults: Community research and ‘barefoot statisticians’. In M. Nickison & S. Lerman (Eds.), The social context of mathematics education: Theory and practice (pp. 202–216). London: Southbank Press. Frankenstein, M. (1998). Reading the world with maths: Goals for a critical mathematical literacy curriculum. Proceeding of the 1st International Mathematics Education and Society Conference, Nottingham [online report]. Retrieved January 29, from http://www.nottingham. ac.uk/csme/meas/papers/frankenstein.html Gal, I. (2002). Adult statistical literacy: Meanings, components, responsibilities. International Statistical Review, 70(1), 1–25. Gal, I. (2004). Statistical literacy. Meanings, components, responsibilities. In D. Ben-Zvi & J. Garfield (Eds.), The challenge of developing statistical literacy, reasoning and thinking (pp. 47–78). Dordrecht: Kluwer. Garfield, J. B., & Ben-Zvi, D. (2008). Developing students’ statistical reasoning: Connecting research and teaching practice. New York: Springer. Haack, D. (1979). Statistical literacy: A guide to interpretation. North Scituate: Duxbury Press. Hacking, I. (1975). The emergence of probability. Cambridge: Cambridge University Press. Hoffmann, M. H. G. (2007). Cognitive conditions of diagrammatic reasoning. [online working paper] Retrieved February 13, from http://www.spp.gatech.edu/faculty/workingpapers/ wp24.pdf (Forthcoming 2010 in J. Queiroz & F. Stjernfelt (Ed.), Peircean diagrammatical logic [Special issue]. Semiotica.) Joslyn, S., adav-Greenberg, L., & Nichols, R. M. (2009). Probability of precipitation. American Meteorological Society, (February issue), 90, 185–193. Lehrer, K., & Marek, J. C. (Eds.). (1997). Austrian philosophy past and present. Essays in honor of Rudolf Haller (Vol. 190). Boston studies in the philosophy of science. Dordrecht: Kluwer . Moreira, L. (2002). Mathematics education and critical consciousness. Proceedings of the 26th Conference of the International Group for the Psychology of Mathematics Education, UK, 3, 369–376. Morris, C. (1938). Foundations of the theory of signs. Chicago, IL: University of Chicago Press. Nemeth, E., & Stadler, F. (Eds.). (1996). Encyclopedia and utopia: The life and work of Otto Neurath (1882–1945) (Vol. 4, Vienna Circle Institute Yearbook). Dordrecht: Kluwer. Neurath, M., & Cohen, R. S. (Eds.). (1973). Otto neurath: Empiricism and sociology: Vol. 1. Vienna circle collection. Dordrecht: Reidel. Organisation for Economic Co-operation and Development. (2004). Learning for tomorrow ′ s world: First results from PISA 2003. Paris:OECD. Peirce, C. S. (1998). The essential peirce: Vol. 2. Peirce edition Project. Bloomington, IN: Indiana University Press. Tufte, E. R. (1983). The visual display of quantitative information. Cheshire: Graphics Press. Tufte, E. R. (1990). Envisioning information. Cheshire: Graphics Press. Tufte, E. R. (1997). Visual explanation images and quantities: Evidence and narrative. Cheshire: Graphics Press. United Nations Educational, Scientific and Cultural Organization (1948). Universal declaration of human rights [online report]. Retrieved January 29, from http://portal.unesco.org/education
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viii Contents 10 The Good, the Beau
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