The Place of mathematics in modern education

NCTM Yearbooks, 11.º

NCTM | 1936 | 284 páginas | pdf |

online: ERIC

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Contents
Attacks on mathematics and how to meet them / W.D. Reeve
The reorganization of secondary education / William Betz
The meaning of mathematics / E.T. Bell
The contribution of mathematics to civilization / David Eugene Smith
The contribution of mathematics to education / Cyril Ashford
Mathematics in general education / W. Leitzmann
Mathematics as related to other great fields of knowledge / Georg Wolff
Form and appreciation / Griffith C. Evans

The exact sciences in antiquity

Otto Neugebauer

Copenhagen | 1957 - 2.ª edição

online: hathitrust.org

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Based on a series of lectures delivered at Cornell University in the fall of 1949, and since revised, this is the standard non-technical coverage of Egyptian and Babylonian mathematics and astronomy, and their transmission to the Hellenistic world. Entirely modern in its data and conclusions, it reveals the surprising sophistication of certain areas of early science, particularly Babylonian mathematics.
After a discussion of the number systems used in the ancient Near East (contrasting the Egyptian method of additive computations with unit fractions and Babylonian place values), Dr. Neugebauer covers Babylonian tables for numerical computation, approximations of the square root of 2 (with implications that the Pythagorean Theorem was known more than a thousand years before Pythagoras), Pythagorean numbers, quadratic equations with two unknowns, special cases of logarithms and various other algebraic and geometric cases. Babylonian strength in algebraic and numerical work reveals a level of mathematical development in many aspects comparable to the mathematics of the early Renaissance in Europe. This is in contrast to the relatively primitive Egyptian mathematics. In the realm of astronomy, too, Dr. Neugebauer describes an unexpected sophistication, which is interpreted less as the result of millennia of observations (as used to be the interpretation) than as a competent mathematical apparatus. The transmission of this early science and its further development in Hellenistic times is also described. An Appendix discusses certain aspects of Greek astronomy and the indebtedness of the Copernican system to Ptolemaic and Islamic methods.
Dr. Neugebauer has long enjoyed an international reputation as one of the foremost workers in the area of premodern science. Many of his discoveries have revolutionized earlier understandings. In this volume he presents a non-technical survey, with much material unique on this level, which can be read with great profit by all interested in the history of science or history of culture. 14 plates. 52 figures.

Famous geometrical theorems and problems, with their history

William Whitehead Rupert

Boston, D.C. Heath & Co. | 1900

online: 
archive.org
hathitrust.org
forgottenbooks.org

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The author, having derived much pleasure and inspiration from the brief historical notes in some of the mathematical text-books that he studied when a student in college, has thought that, by giving the history of a few of the most celebrated geometrical theorems and problems, he might place a light in the window which may throw a cheerful ray adown the long and sometimes dusty pathway that leads to geometrical truth. In the preparation of this little book most valuable assistance has been derived from Florian Cajori sHistory of Mathematics, James Gows History of Greek Mathematics, and G, J. Allmans Greek Geometry from Thales to Euclid, It is, however, toW. W.Rourse Balls reniarkably interesting Short History of Mathematics that Famous Geometrical Theorems and Problems owes the largest debt. To Professor A, D. Eisenhower, Principal of the Norristown High School, George Q.Sheppard, Professor of Mathematics, Hill School, Pottstown, Pa., Dr. George M.Philips, Principal West Chester State Normal School, and Daniel Carhart, Ce., Dean and Professor of Civil Engineering, Western University of Pennsylvania, who have read this book in manuscript, the author is indebted for valuable, suggestions and many kind words of encouragement.

The Logic of Chance: An Essay on the Foundations and Province of the Theory of Probability

Macmillan And Company. | 1988

online:
archive.org
books.google

CHELSEA PUBLISHING | 1962 - 4ª edição |

online:
catalog.hathitrust.org

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No mathematical background is necessary to appreciate this classic of probability theory, which remains unsurpassed in its clarity, readability, and sheer charm. Its author, British logician John Venn (1834-1923), popularized the famous Venn Diagrams that are commonly used for teaching elementary mathematics. In The Logic of Chance, he employs the same directness that makes his diagrams so effective.
The three-part treatment commences with an overview of the physical foundations of the science of probability, including surveys of the arrangement and formation of the series of probability; the origin or process of causation of the series; how to discover and prove the series; and the conception of randomness. The second part examines the logical superstructure on the basis of physical foundations, encompassing the measurement of belief; the rules of inference in probability; the rule of succession; induction; chance, causation, and design; material and formal logic; modality; and fallacies. The final section explores various applications of the theory of probability, including such intriguing aspects as insurance and gambling, the credibility of extraordinary stories, and approximating the truth by means of the theory of averages.

Magic Squares - Quadrados Mágicos

Geometric magic squares : a challenging new twist using colored shapes Instead of numbers por Lee C F Sallows Idioma: Inglês   Editora: Mineola, N.Y. : Dover Publications, 2013.

Before Sudoku : the world of magic squares por Seymour S Block; Santiago Alves Tavares Idioma: Inglês   Editora: Oxford [u.a.] Oxford Univ. Press 2009

Legacy of the Luoshu : the 4,000 year search for the meaning of the magic square of order three por Frank J Swetz Idioma: Inglês   Editora: Wellesley, Mass. : A.K. Peters, ©2008.

The Zen of magic squares, circles, and stars : an exhibition of surprising structures across dimensions por Clifford A Pickover Idioma: Inglês   Editora: Princeton, N.J. : Princeton University Press, cop. 2002.

The wonders of magic squares por Jim Moran Idioma: Inglês   Editora: New York : Random Houses, 1982, ©1981.

Magic squares and cubes. por W S Andrews Idioma: Inglês   Editora: New York, Dover Publications, [1960]

Infantis

Magic squares por Colleen Adams Idioma: Inglês   Editora: New York : PowerKids Press, 2006.

Measuring Up: Prototypes for Mathematics Assessment

(Perspectives on School Mathematics)
Mathematical Sciences Education Board, National Research Council
National Academies Press | 1993 | 176 páginas | 2,59 Mb

Livro on-line: nap.edu

Referência em: MathEduc

Knowing what Students Know The Science and Design of Educational Assessment

James W. Pellegrino, Naomi Chudowsky, Robert Glaser

Committee on the Foundations of Assessment, Board on Testing and Assessment, National Research Council | 2001| 366 páginas

on-line: nap.edu