Equivalent Representations in the Learning of Algebra

1997 ◽  
Vol 90 (8) ◽  
pp. 616-619
Author(s):  
Frances Van Dyke ◽  
Timothy V. Craine

In the past few years, much discussion has taken place about what direction the teaching of algebra should take in view of the NCTM's Standards documents (1989, 1991, 1995), the increased availability of graphing technology, and the movement toward “algebra for all.” Because we view algebra as a language for expressing relationships between quantities and for exploring patterns, we support a functional approach to the subject in which all ideas are put in a context and graphing calculators are used extensively. Within tills framework, however, students who are trying to learn algebra experience subtle difficulties. On the one hand, students fail to recognize the underlying equivalence when the same set of points is represented by a graph or an equation or a table. On the other hand, when given an algebraic representation for a particular function, students fail to see that they can use the rules of algebra to produce an equivalent expression. In both situations, they tend to see changes in form as producing unrelated representations.

Author(s):  
Daiva Milinkevičiūtė

The Age of Enlightenment is defined as the period when the universal ideas of progress, deism, humanism, naturalism and others were materialized and became a golden age for freemasons. It is wrong to assume that old and conservative Christian ideas were rejected. Conversely, freemasons put them into new general shapes and expressed them with the help of symbols in their daily routine. Symbols of freemasons had close ties with the past and gave them, on the one hand, a visible instrument, such as rituals and ideas to sense the transcendental, and on the other, intense gnostic aspirations. Freemasons put in a great amount of effort to improve themselves and to create their identity with the help of myths and symbols. It traces its origins to the biblical builders of King Solomon’s Temple, the posterity of the Templar Knights, and associations of the medieval craft guilds, which were also symbolical and became their link not only to each other but also to the secular world. In this work we analysed codified masonic symbols used in their rituals. The subject of our research is the universal Masonic idea and its aspects through the symbols in the daily life of the freemasons in Vilnius. Thanks to freemasons’ signets, we could find continuity, reception, and transformation of universal masonic ideas in the Lithuanian freemasonry and national characteristics of lodges. Taking everything into account, our article shows how the universal idea of freemasonry spread among Lithuanian freemasonry, and which forms and meanings it incorporated in its symbols. The objective of this research is to find a universal Masonic idea throughout their visual and oral symbols and see its impact on the daily life of the masons in Vilnius. Keywords: Freemasonry, Bible, lodge, symbols, rituals, freemasons’ signets.


Author(s):  
Gyöngyi Pásztor ◽  
Anita Dózsa

The subject of the present study is Transylvania as a tourist destination, more precisely the analysis of what Transylvania means for the foreign tourists visiting here, and what meaning they attach to it. The timeliness of the issue is given by two factors. On the one hand the number of events with a touristic appeal has grown in the past years in Transylvania, and similarly the number of tourists has risen. On the other hand, writings that recommend Transylvania as an outstanding destination are more and more frequent in the international public sphere, in other words, it increasingly appears on the map of international tourism.


1872 ◽  
Vol 9 (95) ◽  
pp. 196-202
Author(s):  
Horace B. Woodward ◽  
J. H. Blake
Keyword(s):  
The Past ◽  
The One ◽  

It would at first sight seem superfluous that anything more should be written upon the relations of the Rhætic Beds in England, for during the past twelve years they have received so much attention—the principal sections have been described, and the beds have been well and successfully searched for fossils. But whilst there has been no lack of petrological and palæontological evidence,—and we ought to be very thankful to railway companies in the western counties for opening up so many fine sections,—still it is somewhat astonishing to remark, there has been and there still appears to be a considerable diversity of opinion on the subject of the relations of the beds. Some authorities have placed them with the Lias, others with the Trias; some regard them as quite an independent formation, others as passage-beds belonging as much to the one as to the other.


1914 ◽  
Vol 7 (2) ◽  
pp. 203-230
Author(s):  
Ephraim Emerton

The decade just passed has witnessed an unusual activity in the production of books about Martin Luther. This activity has been greatly stimulated by the re-introduction of a method of controversy which reasonable men had been hoping was forever silenced. Until about a generation ago there had been two obvious and hopelessly opposed ways of approach to the subject of Luther's character and work. From the one side he was presented as an angel of light; from the other as the type of a depraved and malicious spirit, moved to activity not through any desire to improve the condition of his people but because, being the malignant thing he was, he could not act otherwise. It need hardly be said to the readers of this Review that both of these views of Luther are essentially false. They are perfectly intelligible, one equally with the other. They are the natural precipitation of the bitter controversies that gathered about him in his life, and continued long after his death to complicate the political and economic struggles out of which the new Europe of our day was born. In the light of our modern historical method, both views appear crude and unscientific. They represent a way of looking at historical characters and historical events to which we are apt to apply the crushing word “old-fashioned.” And in fact it did seem, up to a very few years ago, that these primitive judgments, which classified men into good and bad, angels and fiends, had become a thing of the past.


Author(s):  
Carmen Moreno Balboa

¿Ha cambiado el concepto de ciudad en tan sólo 2400 años? Si la ciudad la componen los ciudadanos ¿son éstos distintos de los ciudadanos de las antiguas polis? Si el ciudadano es quien participa en las funciones de gobierno de su ciudad, ¿quién es ahora realmente, ciudadano? ¿Quién quiere serlo? y quién quisiera participar de dichas funciones, ¿cómo podría conseguirlo?En la sociedad actual se producen dos situaciones antagónicas que afectan al desarrollo de la ciudad, por un lado las administraciones, actuando orientadas al interés general, reconocen pero congelan las posibilidades de participar de la población en el urbanismo y la creación de ciudad; y por otro lado la sociedad se mueve y actúa al margen de las administraciones en la mejora de su entorno y sus condiciones de vida, desde las denominadas iniciativas urbanas. Cuáles son los motivos de esta situación y cómo hacer que ambos movimientos coincidan en la generación del denominado “Urbanismo Colaborativo”, es el objeto de este trabajo.AbstractHas the concept of city changed in only the past 2400 years? If the city is the one consisting the citizens, are these any different of the citizens ancient polis? If the citizen is one participating in his city’s government functions, who is the real citizen now a days? Who wants to be one? Who wants to participate in those functions? How could someone acomplish that?In today’s society, there are two antagonistic situations that are affecting the development of the city, on the one hand the administrations, acting orientated to the general interest, they recognize but freeze the possibilities that the citizens have of participating in urbanism and the creation of the city. And on the other hand, the society moves and acts outside of the administrations for the improvement of their environment and their living conditions, doing this from the named urban initiatives. What causes this situation and how to put together both movements and for them to agree in the generation of the named “Collaborative Urbanism” is the subject and what this study wants to acomplish.


2016 ◽  
Vol 8 (3) ◽  
pp. 681 ◽  
Author(s):  
Aleksandar Palavestra

Miloje M. Vasić, "the first academically educated archaeologist in Serbia", has a strange destiny in the Serbian archaeology. On the one hand, he has been elevated to the post of the "founding father" of the discipline, with almost semidivine status and iconic importance, while on the other hand, his works have been largely unread and neglected. This paradoxical split is the consequence of the fact that Vasić has been postulated as the universal benchmark of the archaeological practice in Serbia, regardless of his interpretation of the past on the grounds of the archaeological record – the essence of archaeology. Strangely, the life and work of Vasić have not been the subject of much writing, apart from several obituaries, two short appropriate texts (Srejović, Cermanović), and rare articles in catalogues and collections dedicated to the research of Vinča (Garašanin, Srejović, Tasić, Nikolić and Vuković). The critical analysis of his whole interpretive constellation, with "The Ionian colony Vinča" being its brightest star, was limited before the World War II to the rare attempts to rectify the chronology and identify the Neolithic of the Danube valley (Fewkes, Grbić, Holste). After the war, by the middle of the 20th century, the interpretation of Vasić has been put to severe criticism of his students (Garašanin, Milojčić, Benac), which led to the significant paradigm shift, the recognition of the importance of the Balkan Neolithic, and the establishment of the culture-historical approach in the Serbian archaeology. However, from this moment on, the reception of Vasić in the Serbian archaeology has taken a strange route: Vasić as a person gains in importance, but his works are neglected, though referred to, but almost in a cultic fashion, without reading or interpreting them. Rare is a paper on the Neolithic of the Central Balkans that does not call upon the name of Vasić and his four- volume "Vinča", in which Neolithic is not mentioned at all. This paradox becomes clearer if Vasić is regarded through the prism of the problematic, but not yet challenged and universally praised values in the Serbian archaeology: material, fieldwork and authority, as opposed to interpretation, which is regarded as ephemeral. From this point of view it becomes clear how the image of Vasić grows into the icon of the Serbian archaeology, while his work slides into the domain of the oral tradition, half-truths, and apocryphal anecdotes. Considering that the majority of the Serbian archaeological community shares the belief that there is an absolute archaeological method and "pure" archaeological material, both representing "the data not burdened by theory", the field journals of Vasić and his published works become the source of the "material", while his interpretation of the past is neglected. As long as these "data" are not considered in connection to the whole opus of Vasić, the research questions and strategies that directed his work, the Serbian archaeology will be inhabited by two separate images: one – forefather and founder, the researcher of the Neolithic Vinča, "the first real Serbian archaeologist", whose face gazes at us sternly from the bronze busts and enlarged photographs, and the other – vulnerable and insulted dreamer, convinced in his philhellene delusion. Only the integration of these two images will pay due homage to Miloje M. Vasić.


1882 ◽  
Vol 28 (123) ◽  
pp. 356-369
Author(s):  
Achille Foville

The conditions established to regulate the admission of patients into lunatic asylums have given rise, in every country, to a great deal of discussion. On the one hand, many unacquainted with medicine are inclined to dread the abuse of the power to confine individuals not really insane under the pretext of insanity, and with more or less criminal intent; therefore these persons contend that admissions to asylums should be preceded by intricate formalities and repeated inquiries, with the interference of some public authority, such as a commission of either judicial or administrative officers. On the other hand, physicians advocate the necessity of prompt recourse to an asylum, not only for the patient's own benefit, but for his family's welfare; they demonstrate that a man labouring under acute insanity cannot be left to himself during the time required to set in motion the working of such complicated machinery as that proposed to be brought into action prior to his admission into a hospital; they further reject all interference of the public authorities to this end, as hurtful to private family feeling and the maintenance of professional secrecy, demanding, likewise, the greatest facilities for easy admission, guaranteed, nevertheless, by any number of subsequent examinations, or other means of inquiry into the case; and, finally, they hold that such supposed illegal confinements do not exist, since it has not been proved that any one really of sound mind has ever been shut up in any asylum, and that, therefore, the liberty of the subject is in no danger whatever. So in this respect we may rest confident, seeing that the past gives us full assurance for the future. Such is, upon the whole, the main point of dispute in every discussion on the subject, which happens to spring up again and again in different countries.


2010 ◽  
Vol 69 (3) ◽  
pp. 217-234
Author(s):  
Marc Reynebeau

Het historische debat over de collaboratie van de Vlaamse beweging tijdens de Tweede Wereldoorlog bleef lang verstoord door moralistische en politieke argumenten, wat het inzicht in de historische complexiteit van het onderwerp vaak versluierde. De voorbije decennia is echter ook op dit terrein een uitgesproken verwetenschappelijking merkbaar. Dat maakt het boek Verbrande schrijvers, een nieuwe bundeling opstellen over flamingantische schrijvers tijdens de Tweede Wereldoorlog, zo opmerkelijk. Enerzijds doet Marnix Beyen daarin een veelbelovend voorstel om een nieuw onderzoeksparadigma op dit terrein te introduceren. Anderzijds getuigen de inleiding en enkele cruciale bijdragen van een ingesteldheid die moeilijk te rijmen is met de academische presentatie van het boek. Die vallen niet alleen op door een opvallend gebrek aan wetenschappelijke rigueur en van weinig kennis van zaken. Ze getuigen vooral van een ‘neonationalistische’ bevlogenheid die de historiografie over dit onderwerp opnieuw in haar oude zwakten doet hervallen: moralisme en politieke vooringenomenheid.________A burning smell surrounding collaborationist authors: Old and new arguments for justification in the debate about Flemish collaborationThe historical debate about the collaboration of the Flemish Movement during the Second World War has long been perturbed by moralistic and political arguments, which often obscured the insight into the historical complexity of the subject. However, during the past decades a distinctly more scientific approach may be noted in this area as well. That is why the book Verbrande schrijvers, a new collection of articles about authors supporting the Flemish Movement during the Second World War is so remarkable. On the one hand, Marnix Beyen proposes in this book the introduction of a very promising research paradigm in this area. On the other hand, the introduction and several crucial contributions manifest a mentality that is hardly consonant with the academic presentation of the book. They are noteworthy not only because of a notable lack of scientific consistency and a lack of expertise. They particularly manifest a ‘neo-nationalist’ enthusiasm that causes the historiography about this subject to fall prey again to its old weaknesses: moralism and political bias. 


2010 ◽  
Vol 4 (2) ◽  
pp. 135-156 ◽  
Author(s):  
Dorothea E. Schulz

Starting with the controversial esoteric employment of audio recordings by followers of the charismatic Muslim preacher Sharif Haidara in Mali, the article explores the dynamics emerging at the interface of different technologies and techniques employed by those engaging the realm of the Divine. I focus attention on the “border zone” between, on the one hand, techniques for appropriating scriptures based on long-standing religious conventions, and, on the other, audio recording technologies, whose adoption not yet established authoritative and standardized forms of practice, thereby generating insecurities and becoming the subject of heated debate. I argue that “recyclage” aptly describes the dynamics of this “border zone” because it captures the ways conventional techniques of accessing the Divine are reassessed and reemployed, by integrating new materials and rituals. Historically, appropriations of the Qur’an for esoteric purposes have been widespread in Muslim West Africa. These esoteric appropriations are at the basis of the considerable continuities, overlaps and crossovers, between scripture-related esoteric practices on one side, and the treatment by Sharif Haidara’s followers of audio taped sermons as vessels of his spiritual power, on the other.


Author(s):  
Iryna Rusnak

The author of the article analyses the problem of the female emancipation in the little-known feuilleton “Amazonia: A Very Inept Story” (1924) by Mykola Chirsky. The author determines the genre affiliation of the work and examines its compositional structure. Three parts are distinguished in the architectonics of associative feuilleton: associative conception; deployment of a “small” topic; conclusion. The author of the article clarifies the role of intertextual elements and the method of constantly switching the tone from serious to comic to reveal the thematic direction of the work. Mykola Chirsky’s interest in the problem of female emancipation is corresponded to the general mood of the era. The subject of ridicule in provocative feuilleton is the woman’s radical metamorphoses, since repulsive manifestations of emancipation becomes commonplace. At the same time, the writer shows respect for the woman, appreciates her femininity, internal and external beauty, personality. He associates the positive in women with the functions of a faithful wife, a caring mother, and a skilled housewife. In feuilleton, the writer does not bypass the problem of the modern man role in a family, but analyses the value and moral and ethical guidelines of his character. The husband’s bad habits receive a caricatured interpretation in the strange behaviour of relatives. On the one hand, the writer does not perceive the extremes brought by female emancipation, and on the other, he mercilessly criticises the male “virtues” of contemporaries far from the standard. The artistic heritage of Mykola Chirsky remains little studied. The urgent task of modern literary studies is the introduction of Mykola Chirsky’s unknown works into the scientific circulation and their thorough scientific understanding.


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