Historically Speaking, - -

1953 ◽  
Vol 46 (8) ◽  
pp. 575-577

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.

POLITEA ◽  
2018 ◽  
Vol 1 (2) ◽  
pp. 75
Author(s):  
Ratna Istriyani

<p>Democracy as a political and the government system has demonstrated its existence in the history of the world. This existence can be seen from the many countries that implement it, especially Indonesia. The democratic process becomes an interesting phenomenon because it cannot be separated from the dynamics of the community itself.</p><p>At present the community has entered the digital era, that the utilization of information and communication technology are massive. One phenomenon of concern is the widespread use of social media. The reality of the utilization of social media not only showed the trend of community interaction and communication but also the trend of political participation which correlates with the sustainability of democracy in Indonesia. At least, it has happened in the last decades, where political figures have been using social media as a channel to construct personal image. On the other hand, social media for civil society is as a new media (alternative media) in channeling aspirations, support, and even criticism to political and government figures.</p><p>Social media trends also cannot be separated from the figure of young people as massive users of these contemporary products. Even social media is a preference for young people to participate in upholding democratization in Indonesia. It can be seen from the posts or their responses to the socio-political conditions in this country through their account lines and the number of comments they wrote on the accounts of a number of political and government figures.</p><p><strong><em>Keywords: democracy, social media, youth. </em></strong></p>


2005 ◽  
Vol 10 (1) ◽  
pp. 101-130 ◽  
Author(s):  
Thorvaldur Gylfason

Sweden has a long and distinguished tradition in economics, beginning with Knut Wicksell and continuing with Gustav Cassel, Eli Heckscher, Erik Lindahl, Gunnar Myrdal, Bertil Ohlin, and Erik Lundberg, all of whom are now gone. Yet, for several of these men, economics was not enough: Wicksell spoke out on moral issues and served time in jail, and Myrdal was for many years a high official at the United Nations and, briefly, a cabinet minister, as was Ohlin, who made his mark at home primarily as leader of the opposition in a country governed mostly by Social Democrats, serving in parliament for 32 years. For Assar Lindbeck, however, economics has been broad enough: he has devoted a long and distinguished career to economics, and to economics alone, with unfailing enthusiasm and energy over half a century. Not that he was not wanted elsewhere: over the years, he has declined challenging job offers from an international organization and a Swedish daily newspaper, to name but two examples, as well as from universities outside Sweden. Assar has managed to harness his varied and wide-ranging talents within the many mansions of economics. He is one of the most versatile economists of his generation. Indeed, he is one of the few who, for clarity, need to divide their bibliography into categories by subject: Macroeconomics and monetary economics, Public economics, Labor economics, International economics, Economic systems and economic structures, Methodology and history of economic thought, and Swedish economy. His work on these different subjects has ranged from pure theory to applied policy-oriented and empirical studies. In addition to the numerous scientific publications listed at the end of this interview, his bibliography includes nearly 200 articles for magazines and newspapers. His ivory tower has always been equipped with a high-speed elevator. But, as he points out in the conversation to follow, all his research work, as well as his journalism, is driven by an overarching interest in bettering economic policy and organization—in other words, boosting economic and social efficiency for the purpose of lifting ordinary people's standard of life. This has been, and remains, a guiding principle—a Leitmotiv, if you prefer—from which he has never swerved. Assar Lindbeck is a towering figure in Swedish economics and in Swedish national life.


1954 ◽  
Vol 1 (2) ◽  
pp. 24-25
Author(s):  
Margaret F. Willerding

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.


1987 ◽  
Vol 34 (7) ◽  
pp. 38-42
Author(s):  
Martha H. Hopkins

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.


1980 ◽  
Vol 27 (8) ◽  
pp. 40-42
Author(s):  
Stephen Krulik

Many of our students are far from receptive to the many problems of drill materials with which some teachers provide them. And yet, most students need some drill and practice before they can successfully master a new concept or skill. The history of mathematics can play an important role in making these apparently contradictory points of view compatible. Many of the concepts and ideas in the history of mathematics were developed from practical necessity rather than from a theoretical base; it is these same ideas that offer a great deal of practice material for our students. This ancient body of knowledge can provide drill that is interesting, satisfying, challenging. And, at the same time, it offers the necessary drill to achieve competence in fundamental skills and concepts.


2020 ◽  
Vol 3 (2) ◽  
pp. 57
Author(s):  
Nazan Mersin ◽  
Mehmet Akif Karabörk ◽  
Soner Durmuş

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.


1992 ◽  
Vol 85 (7) ◽  
pp. 557-561 ◽  
Author(s):  
Randolph A. Philipp

The concept of variable is one of the most fundamental ideas in mathematics from elementary school through college (Davis 1964; Hirsch and Lappan 1989). This concept is so important that its invention constituted a turning point in the history of mathematics (Rajaratnam 1957). However, research indicates that students experience difficulty with the concept of variable, a difficulty that might partially be explained by the fact that within mathematics, variables can be used in many different ways (Rosnick 1981; Schoenfeld and Arcavi 1988; Wagner 1983).


1999 ◽  
Vol 119 ◽  
pp. 86-127 ◽  
Author(s):  
Ione Mylonas Shear

The structures along the west side of the Athenian Akropolis have long delighted visitors approaching the site and have challenged scholars for generations. By happy coincidence a variety of different studies has recently been published which emphasized different aspects of the approaches to the citadel and once again remind us of the many problems still remaining to be solved.Ira S. Mark concentrated on the shrine of the Athena Nike. He dealt primarily with the Mycenaean bastion enclosed within the later ashlar masonry of the classical podium, the various early remains of the shrine, which lie roughly 1.30 m. below the floor level of the classical temple, and the historical background of the temple itself. He published a few of the many early drawings of the bastion made by Nikolaos Balanos and his associates and re-examined the early walls crowning the archaic bastion, which he divided into various stages. Although, in my opinion, his chronology needs adjustment, his division of the walls built along the edges of the basion into different phases helps us to understand in more detail the history of the site and is a welcome addition. One of these earlier walls, which had long been considered to be Mycenaean, was dated by Mark to a much later phase (Fig. 1, 15). He suggested that the wall was a post-Mycenaean addition built in this position to enclose the east side of the shrine. This wall lies parallel to the West Cyclopean Wall and had been thought to represent the eastern limit of the bastion. The fragmentary remains of this wall, which are no longer visible, were originally recorded by Panagiotis Kavvadias and Georg Kawerau and its existence has bedeviled all attempts to restore a Mycenaean gate in this area.


Author(s):  
John V. Jensen

John V. Jensen: In Denmark’s Interest … Mine clearing on Jutland’s west coast 1945 The article is about mine clearing on Jutland’s west coast in 1945. The mine clearing started shortly after the German capitulation. It was unusual because German soldiers were forced to do the work, which, with a few exceptions, was completed on 1 October 1945. The work cost the lives of around 150 German soldiers and wounded even more. In the many years that followed, the perception was that, despite the loss of German lives, the mine clearing had been achieved in a satisfactory way. This perception faced criticism in 1998 with the claim that the mine clearing was a dark chapter in Denmark’s history, and that Danish war crimes had been committed. The German Wehrmacht surrendered to the Allies in Denmark on 4 May 1945, and it was the British liberation force that gave the order for the mines to be cleared. There is evidence to suggest that the political powers in Denmark may have drawn British attention to the mines on Jutland’s west coast. At any rate, the order to clear the mines was incorporated into the terms and conditions of the capitulation. Under the British command, the mines were to be cleared by German soldiers in as short a time as possible, while the Det Danske Pionerkommando (Danish Engineer Command Battalion) was tasked with supervising the clearing work. The article shows that this German-British-Danish collaboration was far from problematic. There were conflicts from the Danish side, especially in terms of sloppiness and laziness among its own inspectors, while the Pionerkommando’s more limited collaboration with the Germans, in terms of counting and subsequent checks, was apparently less strained than one would have expected. This perception was based on the erroneous assumption that it was the Danes who were in command of the German mine clearers. It has been claimed that the mine clearing work was achieved by forced labour. The article states that this is not as clear-cut as it sometimes has been claimed. It is quite obvious that the German soldiers, who were commandeered from the marched groups immediately after the liberation of Denmark, must to a great extent have been forced because of their training. However, there were supposedly also several volunteers among the later arrivals of mine clearers, even though they were less well trained. The work in Denmark was a way of avoiding the prison camps and an alternative to working, for example, in the coal mines in Germany. One argument is that the British, and especially the Danes, had a significant interest in the Germans not getting maimed or killed in the minefields, because as long as the Germans cleared the mines, it meant that Danes did not have to do the work. It is believed that this was the harsh logic of the times. It is believed without a doubt, that the high German losses are explained by the high speed, at which the mine clearing work was carried out. It was work that had to be done, and both the British and the Danish authorities were in agreement on that. However, notwithstanding the tempo, the task’s complexity, the Germans’ work methods and relative inexperience played a role. The article questions whether there actually were any Danish war crimes. From a British (and a Danish) perspective, there were not any German prisoners of war, but military units, which had capitulated and whose labour could be exploited, for example, for mine clearing without there being any conflict with international conventions. In that sense, there were no war crimes. However, be it soldier or war prisoner, the losses remain the same.The contemporary material paints a different and more detailed picture than has been shown up until now and shows that the history of the mine clearing is less clear-cut and more complex than supposed. The tension between Danes and Germans was nowhere near as pronounced as posterity would have it, and internal Danish factors and the relationship with the British also played a role, thereby downplaying the revenge motive, which otherwise has been used to explain the German loss of life. The Danish and German soldiers had an important common interest. This has been overlooked and undermines the explanation that there were revenge and inhumanity. This revenge motive is perhaps to be found in particular outside the ranks of the soldiers, whether Danish, German or British: for example, in the wider Danish population, who conversely had nothing to do with the mine clearing.The mutual interest between the Germans, the British and the Danes was expressed precisely in a written statement from Pionerkommandoet to the ‘Jydsk-fynske Kommando’ (Jutland-Fyn Command) on 14 June 1945: “It is also in Denmark’s interests that the Germans clear the mines, and that we [the Danes] are not forced to do it ourselves”.


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