An historical phenomenology of mean and median

Educational Studies in Mathematics

Volumn 62, Issue 2, 2006, Pages 149-168

  Bakker, Arthur ^a   Gravemeijer, Koeno P E ^b  

^a UNIVERSITY OF LONDON   (United Kingdom)

^b UTRECHT UNIVERSITY   (Netherlands)

Author keywords

History of statistics; Inspiration for instructional activities; Preparation phase of design research

Indexed keywords

EID: 33746674367     PISSN: 00131954     EISSN: 15730816     Source Type: Journal    
DOI: 10.1007/s10649-006-7099-8     Document Type: Review

References (49)

1. Bakker, A.: 2004, Design Research in Statistics Education: On Symbolizing and Computer Tools, CD Beta Press, Utrecht, The Netherlands.
2. Bakker, A. and Gravemeijer, K.P.E.: 2004, 'Learning to reason about distribution', in D. Ben-Zvi and J. Garfleld (eds.), The Challenge of Developing Statistical Literacy, Reasoning, and Thinking, Kluwer, Dordrecht, The Netherlands, pp. 147-168.
3. Brousseau, G.: 1997, 'Theory of didactical situations in mathematics', in N. Balacheff, M. Cooper, R. Sutherland, and V. Warfield (eds. and trans.), Kluwer, Dordrecht, The Netherlands.
4. Cobb, P., McClain, K. and Gravemeijer, K.P.E.: 2003, 'Learning about statistical covariation', Cognition and Instruction 21, 1-78.
5. Cortina, J.L.: 2002, 'Developing instructional conjectures about how to support students' understanding of the arithmetic mean as a ratio', in B. Phillips (ed.), Proceedings of the Sixth International Conference of Teaching Statistics [CD-ROM], International Statistical Institute, Voorburg, The Netherlands.
6. Cournot, A.A.: 1843/1984, Exposition de la théorie des chances et des probabilités [Treatise of the theory of chances and probabilities], Librairie philosophique J. Vrin, Paris.
7. David, H.A.: 1995, 'First (?) occurences of common terms in mathematical statistics', The American Statistician 49, 121-133.
8. David, H.A.: 1998, 'First (?) occurences of common terms in probability and statistics - A second list, with corrections', The American Statistician 52, 36-40.
9. Eisenhart, C.: 1974, The development of the concept of the best mean of a set of measurements from antiquity to the present day', 1971 ASA Presidential Address. Unpublished manuscript.
10. Eisenhart, C.: 1977, 'Boscovich and the combination of observations', in M.G. Kendall and R.L. Plackett (eds.), Studies in the History of Statistics and Probability, Vol. 2, Charles Griffin, London.
11. Euclid: 1956, The thirteen books of The Elements. Translation with introduction and commentary by Sir Thomas L. Heath (T. H. Heath, trans.). New York: Dover.
12. Fauvel, J. and Van Maanen, J. (Eds.).: 2000, History in Mathematics Education. Kluwer Academic Publishers, Dordrecht, the Netherlands.
13. Freudenthal, H. : 1983a, Didactical Phenomenology of Mathematical Structures. Dordrecht, the Netherlands: Reidel.
14. Freudenthal, H.: 1983b, 'The implicit philosophy of mathematics: History and education', in Proceedings of the International Congress of Mathematicians. Warsaw, pp. 1695-1709.
15. Freudenthal, H.: 1991, Revisiting Mathematics Education: China Lectures. Dordrecht, the Netherlands: Kluwer Academic Publishers.
16. Galton, F.: 1889, Natural Inheritance. Macmillan, London.
17. Godard, R. and Crépel, P.: 1999, 'An historical study of the median', in Proceedings of the Canadian Society for History and Philosophy of Mathematics, Canadian Mathematical Society: Ottawa, pp. 207-218.
18. Gravemeijer, K.P.E. : 2002, 'Emergent modeling as the basis for an instructional sequence on data analysis', in B. Phillips (ed.), Developing a Statistically Literate Society. Proceedings of the International Conference on Teaching Statistics [CD-ROM]. Cape Town, SouthAfrica, July 7-12, 2002.
19. Gulikers, I. and Blom, K.: 2001, "An historical angle', a survey of recent literature on the use and value of history in geometrical education', Educational Studies in Mathematics 47, 223-258.
20. Hacking, I.: 1975, The Emergence of Probability. A Philosophical Study of Early Ideas About Probability, Induction and Statistical Inference. Cambridge University Press, London.
21. Hald, A.: 1990, A History of Probability and Statistics and their Applications before 1750, John Wiley and Sons, New York.
22. Harter, H.L.: 1977, A Chronological Annotated Bibliography on Order Statistics (Vol. 1): US Air Force.
23. Heath, T.H.: 1981, A History of Greek Mathematics. Dover, New York.
24. Huygens, C.: 1895, Oeuvres Complètes de Christiaan Huygens (Vol. VI). Den Haag, the Netherlands: Nijhoff.
25. Konold, C. and Pollatsek, A.: 2002, 'Data analysis as the search for signals in noisy processes', Journal for Research in Mathematics Education 33, 259-289.
26. Kotz, S. and Johnson, N.L. (eds.): 1981, Encyclopedia of Statistical Sciences, Wiley, New York.
27. Laplace, P.S.: 1812/1891, Théorie analytique des probabilités. Oeuvres complètes Vol. 7. Gauthier-Villars, Paris.
28. Legendre, A.M.: 1805, Nouvelles méthodes pour la détermination des orbites des comètes, Courcier, Paris.
29. Mokros, J. and Russell, S.J.: 1995, 'Children's concepts of average and representativeness', Journal for Research in Mathematics Education 26, 20-39.
30. Monjardet, B.: 1991, 'Elements pour une histoire de la médiane métrique', in J. Feldman, G. Lagneau and B. Matalon (eds.), Moyenne, Milieu, Centre: Histoire et Usages, Ecole des Hautes études en Sciences Sociales, Paris, pp. 45-62.
31. Pannekoek, A.: 1961, A History of Astronomy, Allen and Unwin, London.
32. Peirce, C.S.: 1958, CP, Collected Papers of Charles Sanders Peirce. Harvard University Press, Cambridge, MA.
33. Perry, M. and Kader, G.: 1998, 'Counting penguins', Mathematics Teacher 91(2), 110-116.
34. Petrosino, A.J., Lehrer, R. and Schauble, L.: 2003, 'Structuring error and experimental variation as distribution in the fourth grade', Mathematical Thinking and Learning 5, 131-156.
35. Plackett, R.L.: 1970, The principle of the arithmetic mean', in E. Pearson and M.G. Kendall (eds.), Studies in the History of Statistics and Probability, Vol. 1, Griffin, London.
36. Porter, T.M.: 1986, The Rise of Statistical Thinking, 1820-1900. Princeton University Press, Princeton.
37. Portney, S. and Koenker, R.: 1997, The Gaussian hare and the Laplacian tortoise: Computability of squared-error versus absolute-error estimators', Statistical Science 12, 279-300.
38. Radford, L.: 2000, 'Historical formation and student understanding of mathematics', in J. Fauvel and J. van Maanen (eds.), History in Mathematics Education: The ICMI Study, Kluwer Academic Publishers, Dordrecht, the Netherlands.
39. Rubin,E.: 1971, 'Quanti tative commentary on Thucydides', The American Statistician 1971 (December), 52-54.
40. Sheynin, O.: 1996, The History of the Theory of Errors, Verlag Dr. Markus HänselHohenhausen, Egelsbach, Germany.
41. Simon, M.A.: 1995, 'Reconstructing mathematics pedagogy from a constructivist perspective', Journal for Research in Mathematics Education 26, 114-145.
42. Simpson, J.A. and Weiner, E.S.C. (eds.).: 1989, The Oxford English Dictionary, 2nd edn., Vol. 1, Clarendon Press, Oxford.
43. Stamhuis, I.H.: 1996, 'Christiaan Huygens correspondeert met zijn broer over levensduur [Christiaan Huygens corresponds with his brother about life span]', De Zeventiende Eeuw 12(1), 161-170.
44. Steinbring, H.: 1980, Zur Entwicklung des Wahrscheinlichkeitsbegriffs - Das Anwendungsproblem in der Wahrscheinlichkeitstheorie aus didaktischer Sicht. Bielefeld: Institut für Didaktik der Mathematik der Universität Bielefeld.
45. Stigler, S.M.: 1984, 'Boscovich, Simpson and a 1760 manuscript on fitting a linear relation", Biometrika 71(3), 615-620.
46. Stigler, S.M.: 1986, The History of Statistics. The Measurement of Uncertainty Before 1900, Harvard University Press, Cambridge, MA.
47. Strauss, S. and Bichler, E.: 1988, The development of children's concepts of the arithmetic mean', Journal for Research in Mathematics Education 19, 64-80.
48. Székely, G.: 1997, 'Problem corner', Chance 10(4), 25.
49. Véron, J. and Rohrbasser, J.-M.: 2000, 'Lodewijk et Christiaan Huygens: La distinction entre vie moyenne et vie probable', Mathématiques et Sciences Humaines 38(149), 7-21.