Dissertation Abstract

The Development Of The Mathematical Concept Of Randomness:

Educational Implications

by

Deborah Jo Bennett

Degree: PH.D.

Year: 1993

Pages: 00211

Institution: NEW YORK UNIVERSITY; 0146

Advisor: Kenneth P. Goldberg

Source: DAI, 54, no. 02A, (1993): 0449

The evolution of the concept of "randomness" is explored hrough the method of historical research. This dissertation examines the use of chance mechanisms through artifacts originating in Mesopotamia, the Indus valley, Egypt, and Babylonia as early as the third millennium B.C. and explores notions about randomness in antiquity through the literature of the ancient Vedic, Greek, Hebrew, and Chinese cultures.

An early understanding of randomness is examined in the works of Cicero, the rabbis, and de Fournival. The formalization of laws of chance is inspected in the writings of Cardano, Galileo, Fermat and Pascal, and C. Huygens. Pioneers like Graunt, Petty, DeWit, Hudde, C. and L. Huygens, Halley, and J. Bernoulli developed a broader view of chance--a view that some natural phenomena could be viewed as chance events. The controversy of chance versus determinism is seen in the works of Hobbes, Montmort, De Moivre, Hume, and Laplace, and the influence of indeterminism is later examined in the works of J. S. Mill, Venn, Fechner, and C. S. Peirce.

This dissertation examines publications by Galileo, Simpson, Lambert, D. Bernoulli, Laplace, Gauss, and Adrian where the theory of the distribution of errors is created--a theory in which errors in measurement were considered to occur like chance events. The developers of sampling distribution theory relied on statistical experimentation using random samples; such experiments are seen in the work of Galton,De Forest, Edgeworth, Fechner, Weldon, K. Pearson, and Gosset.

Formalization of the notion of randomness is revealed in works by Venn, von Mises and those building on von Mises' work. Formalization of the notion of disorder is examined in the works of Kolmogorov and Chaitin. Attempts to construct tables of random digits are examined; attempts to construct artificial sources of random digits by expanding irrational numbers or by algorithm are examined; and tests developed to validate these sources are examined.

Finally, educational implications are examined in light of the increased emphasis on probability and statistics at all levels of the curriculum. Recommendations are made for the presentation of notions of randomness and chance in the classroom. The importance of correct intuition and active learning in the instruction of the concept of chance are emphasized.

SUBJECT(S)

Descriptor: EDUCATION, MATHEMATICS

Accession No: AAG9317657

Provider: OCLC

Database: Dissertations