Developing understanding of number system structure from the history of mathematics

2009 ◽  
Vol 21 (2) ◽  
pp. 96-115 ◽  
Author(s):  
Mala Saraswathy Nataraj ◽  
Michael O. J. Thomas
Keyword(s):  
History Of Mathematics ◽  
Number System ◽  
System Structure ◽  
History Of

History of Mathematics in Teaching Arithmetic

1954 ◽  
Vol 1 (2) ◽  
pp. 24-25
Author(s):  
Margaret F. Willerding
Keyword(s):  
Historical Development ◽  
History Of Mathematics ◽  
Modern Society ◽  
Number System ◽  
Favorable Attitude ◽  
Political Conflicts ◽  
Units Of Measurement ◽  
Motivation For Learning ◽  
History Of ◽  
Attitude And Motivation

Learning about the historical deveLopment of some phases of arithmetic not only serves as a basis for better understanding of our civilization but also aids in creating a favorable attitude and motivation for learning. Many teachers, because of their lack of knowledge, overlook the history of mathematics as a source of enrichment in teaching arithmetic. The development of our number system, of fractions, and units of measurement is as exciting to many pupils as the accounts of wars and other political conflicts in the struggle for freedom. In fact, modern society is very dependent upon number and quantity and the ways in which these are interpreted and used.

Number Facts—or Fantasy?

1987 ◽  
Vol 34 (7) ◽  
pp. 38-42
Author(s):  
Martha H. Hopkins
Keyword(s):  
History Of Mathematics ◽  
Elementary Classroom ◽  
Number System ◽  
Decimal System ◽  
Historical Information ◽  
History Of ◽  
Numeration Systems ◽  
Number Facts ◽  
Programs Of Study ◽  
New Math

Articles in the Arithmetic Teacher have stressed the use of the history of mathematics to enhance motivation in the elementary classroom (Cowie 1970; Jackson 1964; Kreitz and Flournoy 1960; Krulik 1980; Willerding 1954). The increased emphasis on other numeration systems in the “new math” produced several articles that encouraged teachers to include historical information about the development of the decimal system in their programs of study (Baker 1963; Delaney 1963; Fisher et al. 1963; Schaaf 1961; Young 1964). The rationale for including these topics was that they would help students appreciate the development of our number system and would stimulate interest, enthusiasm, and a better understanding of our civilization.

scholarly journals Awareness of Preservice Mathematics Teachers about Prehistoric and Ancient Number Systems

2020 ◽  
Vol 3 (2) ◽  
pp. 57
Author(s):  
Nazan Mersin ◽  
Mehmet Akif Karabörk ◽  
Soner Durmuş
Keyword(s):  
System Analysis ◽  
Descriptive Analysis ◽  
History Of Mathematics ◽  
Number System ◽  
Ancient Greek ◽  
Black Sea Region ◽  
Ancient Egyptian ◽  
Number Systems ◽  
Counting Methods ◽  
History Of

This study seeks to analyse the awareness of the pre-service teachers on the counting methods, systems and tools used in the prehistoric method and the Ancient period and to examine the distribution of this awareness by gender. A total of 42 sophomore-level students studying at a university in the Western Black Sea region, Turkey, participated in this exploratory case study. The data were obtained through a form consisting of 6 questions, one of which is open-ended, after the 14-week course of history of mathematics. The data collection tool included questions on the counting methods used in the pre-historic period and the Ancient Egyptian, Ancient Roman, Babylonian, Ancient Greek and Mayan number systems. The data were analysed through descriptive analysis and content analysis. The findings indicated that the pre-service teachers most reported the methods of tallying, tying a knot, token, circular disc. Also, the question on the Ancient Egyptian number system was answered correctly by all pre-service teachers, the lowest performance was observed in the question on the Mayan number system. Analysis of the answers by gender revealed that the male pre-service teachers were more likely to give false answers compared to the female pre-service teachers.

Historically Speaking, - -

1953 ◽  
Vol 46 (8) ◽  
pp. 575-577
Keyword(s):  
Binary System ◽  
High Speed ◽  
History Of Mathematics ◽  
Number System ◽  
Historical Background ◽  
Interesting Phenomenon ◽  
Information And Communication ◽  
History Of ◽  
The Many ◽  
And Algebra

The binary system as a special case of the generalized problem of scales of notation has had a sudden resurgence of popularity. This is largely due to its use in modern high-speed electronic calculators and in new developments in the theory of “information” and “communication.”1 However, this new utility of the binary system arrived at the same time that an even greater emphasis was being placed on “meaning” and “understanding” in the teaching of mathematics. In arithmetic (and algebra) many teachers have felt that understanding of our number system was enhanced, and in some cases first achieved, through a study of numbers written to some base other than ten. These two motives, utilitarian and pedagogical, have led to several articles on the history of the binary system and related topics,2 but it seems that none of them have stressed several additional pedagogical values to be derived from a proper survey of the historical background of scales of notation. This topic is not only intrinsically inter esting, but it also illustrates well the role of generalization and abstraction in mathematics, the roles of necessity and intellectual curiosity in mathematical invention, a few of the many connections between mathematics and philosophy and religion, and the interesting phenomenon of simultaneity in discovery which recurs so often in the history of mathematics.

Riemann–Weyl in Deleuze's Bergsonism and the Constitution of the Contemporary Physico-Mathematical Space

2015 ◽  
Vol 9 (1) ◽  
pp. 59-87 ◽  
Author(s):  
Martin Calamari
Keyword(s):  
Field Theory ◽  
Gauge Field ◽  
Fibre Bundle ◽  
History Of Mathematics ◽  
Gauge Field Theory ◽  
Contemporary Science ◽  
Explicit Mention ◽  
History Of ◽  
Key Features ◽  
Bernhard Riemann

In recent years, the ideas of the mathematician Bernhard Riemann (1826–66) have come to the fore as one of Deleuze's principal sources of inspiration in regard to his engagements with mathematics, and the history of mathematics. Nevertheless, some relevant aspects and implications of Deleuze's philosophical reception and appropriation of Riemann's thought remain unexplored. In the first part of the paper I will begin by reconsidering the first explicit mention of Riemann in Deleuze's work, namely, in the second chapter of Bergsonism (1966). In this context, as I intend to show first, Deleuze's synthesis of some key features of the Riemannian theory of multiplicities (manifolds) is entirely dependent, both textually and conceptually, on his reading of another prominent figure in the history of mathematics: Hermann Weyl (1885–1955). This aspect has been largely underestimated, if not entirely neglected. However, as I attempt to bring out in the second part of the paper, reframing the understanding of Deleuze's philosophical engagement with Riemann's mathematics through the Riemann–Weyl conjunction can allow us to disclose some unexplored aspects of Deleuze's further elaboration of his theory of multiplicities (rhizomatic multiplicities, smooth spaces) and profound confrontation with contemporary science (fibre bundle topology and gauge field theory). This finally permits delineation of a correlation between Deleuze's plane of immanence and the contemporary physico-mathematical space of fundamental interactions.

Newton and the Origin of Civilization

2012 ◽  
Author(s):  
Jed Z. Buchwald ◽  
Mordechai Feingold
Keyword(s):  
Good Reason ◽  
History Of Mathematics ◽  
Primary Sources ◽  
Ancient History ◽  
Isaac Newton ◽  
History Of ◽  
Ancient Civilizations ◽  
And Mathematics ◽  
One Year ◽  
Radical Ideas

Isaac Newton’s Chronology of Ancient Kingdoms Amended, published in 1728, one year after the great man’s death, unleashed a storm of controversy. And for good reason. The book presents a drastically revised timeline for ancient civilizations, contracting Greek history by five hundred years and Egypt’s by a millennium. This book tells the story of how one of the most celebrated figures in the history of mathematics, optics, and mechanics came to apply his unique ways of thinking to problems of history, theology, and mythology, and of how his radical ideas produced an uproar that reverberated in Europe’s learned circles throughout the eighteenth century and beyond. The book reveals the manner in which Newton strove for nearly half a century to rectify universal history by reading ancient texts through the lens of astronomy, and to create a tight theoretical system for interpreting the evolution of civilization on the basis of population dynamics. It was during Newton’s earliest years at Cambridge that he developed the core of his singular method for generating and working with trustworthy knowledge, which he applied to his study of the past with the same rigor he brought to his work in physics and mathematics. Drawing extensively on Newton’s unpublished papers and a host of other primary sources, the book reconciles Isaac Newton the rational scientist with Newton the natural philosopher, alchemist, theologian, and chronologist of ancient history.

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