Educational Research - the Ethics and Aesthetics of Statistics

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150 J.P. Van Bendegem et al. This important observation that a visual and a written representation of the same data are not (and should not be) isomorphic raises equally important questions for the use of diagrams and drawings in various forms of reasoning, including mathematical reasoning. As it happens, this is not a new idea. One of the oldest examples of this idea features in Plato’s Meno dialogue. This example concerns knowledge acquisition (Hoffmann 2007). 8 Although Plato is not really interested in diagrammatic reasoning but rather in processes of ‘recollection’ of ideas, interestingly enough, the example offers evidence of the diagram functioning as an external ‘scaffold’. Let us briefly recapitulate the story. Socrates asks a young slave boy to perform a geometrical task. If the side of a square is 2 ft, we know that the surface of the square equals 4 ft 2 . What then is the length of the side of a square of double surface – a surface of 8 ft 2 ? Obviously, the slave’s first answer is a length of 4 ft. Socrates explains the slave’s error by drawing the first square and then transforming it following the slave’s answer (see figure below on the left). By looking at the visual scaffold of the diagram, the slave can immediately grasp his error if, that is, he can interpret the basics of Euclidian geometry. He sees that, by doubling the length of the side, the square becomes four times larger than the original square. Then Socrates goes further, realising transformations on the squares, drawing diagonals on the first square and reaching the agreement of the slave that two triangles together have the same surface as the original square. By further transformations in the second square, he obtains four triangles, forming a square with the right surface (see figure below on the right). 9 E H F E H F D C I D C I A B G A B G As Hoffmann indicates, the transformation of thought by creating the diagonals and finding the answer by looking at these diagonals is a creative, both visual and cognitive act, involving a leap of and in thought. Both the Neurath and the Meno examples refer to the importance of diagrammatic reasoning in cognitive processes. By using, creating and reading diagrams, humans solve problems, understand knowledge and make cognitive leaps in complex situations. The diagrams do not merely facilitate understanding, but also offer an external scaffold to help and broaden internal cognitive capacities. Moreover, as external representations, diagrams not only have a cognitive function, but also a communicative one and here we can connect back to Otto Neurath.
10 The Good, the Beautiful and the Literate: Making Statistics Accessible for Action 151 Matters become quite interesting if one realises that ISOTYPE was mainly to be used for societal matters. It was Neurath’s hope that well-informed citizens would reach ‘wiser’ decisions that would benefit the community. They need not know about logic, mathematics or physics reach this goal, at least not directly. First of all they need to be informed about societal, political and economical matters. Taking a scientific outlook, this implies that part of the research done in order to gather the relevant data will inevitably rely on statistics. Now it is notoriously difficult to explain statistics to the non-mathematician, that is, most of us. Therefore, Neurath sought and found a way round this problem by representing the statistical data graphically or pictorially without loss of any of the essential characteristics. I emphasise the word ‘essential’ because a great deal of attention is given in ISOTYPE to the elimination of irrelevant components or details that tend to blur the picture rather than to highlight the essentials. The two pictures that follow illustrate this point nicely. Above you can see a diagram as ‘ordinarily’ presented, and beneath the result after translation in ISOTYPE. 10 Rauschgiftproduktion weltweit 100† Opium 100† kokain Mexiko, Guatemala Kolumbien, Peru, Bolivien Afghanistan, Iran, Pakistan Prognosenfür 1993. Quellen: Bundesnachrichtendienst, UN International Drug Control Program Burma, Laos, Shanland, Thailand
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Educational Research: The Ethics an
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Paul Smeyers · Marc Depaepe Editor
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Earlier Volumes in this Series Educ
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viii Contents 10 The Good, the Beau
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2 The Lure of Statistics for Educat
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32 M. Depaepe of methodological bot
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34 M. Depaepe tapping other sources
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36 M. Depaepe In the context of dem
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38 M. Depaepe combination. Moreover
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40 M. Depaepe 4. See Pelleriaux (19
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42 M. Depaepe Schneider, J. (2010).
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44 J.J.H. Dekker (see Section 4.4).
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46 J.J.H. Dekker from their own par
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48 J.J.H. Dekker a cohort study tha
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50 J.J.H. Dekker child” (Van IJze
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52 J.J.H. Dekker USA resulted in ev
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54 J.J.H. Dekker of the problem”.
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56 J.J.H. Dekker Dekker. J. J. H.,
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212 P. Standish research none of us
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216 About the Authors co-editor-in-
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218 About the Authors voor Wetensch
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220 Author Index Elkins, G. R., 190
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222 Author Index Silverman, J. G.,
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224 Subject Index I Inequality, 29-
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