Comparative policing systems Essay Example for Free

Comparative policing systems Essay Introduction Policing is not a recent issue in terms which duty of state as protecting both public and state still remains as a concept to focus on, yet, it is current enough to remember and to consider again. In this comparative study, policing systems of United Kingdom, Turkey and France will be controversially discussed in terms of policing related to its legitimacy, its structure, and its function. In the first section, the concepts of legitimacy, structure, and function will be defined. Afterwards, British policing system will be examined in terms of these three conceptions. Following British system, Turkish policing system which has been remarkably adapted to new policing concepts despite the fact that there are more to deal with will be following subject. Then, lastly, French system which has effectively been a model for some countries will be analyzed so as to understand The Continental Model. After analyzing three countries, the similarities and differences between British and The Continental System will be focused on, more particularly within a proposition that British Policing leads the way. Policing: Legitimacy, Structure, and Function Modern police was often seen as an instrument of progress, consistent with the idea of free enterprise, academic freedom, constitutional protection against arbitrary government (Liang, 2002, p: 4). Although there has been a common acceptance of policing recently, as Liang stated, there are different police systems all over the world. In order to be able to analyze and compare police systems, there are three terms by the help of which policing in different societies can be examined; legitimacy, structure, and function. In his early study, Bayley asserts that three characteristics of the police contemporarily exist in todays world and these as dichotomous are public/private, specialized/no specialized, professional/nonprofessional. Being public/private oriented refers to the nature of the police agency and can easily be confused with community authorization, specialization for a police agency, in opposite terms of that unspecialized police force is authorized to use force but do many other things as well, concentres on the application of force, and professionalism refers to explicit preparation to perform the unique police function (Bayley, 1990, p: 11-13). Using this triple explanation, Bayley originally emphasizes on legitimacy, structure and function of policing. Similarly, Mawby attempts to compare different police systems according to legitimacy, structure, and function. Moreover, he defines these terms. Legitimacy implies that the police are granted some degree of monopoly within society by those with the power to so authorize, be they an elite within the society, an occupying power, or the community as a whole.(1990, p: 3). Structure means specialization/non specialization, and function implies that the role of the police is concentrated on the maintenance of law and order prevention and detection of offences. Nevertheless, this is not only about these fixed concepts, but also the balance between law and order, or prevention and detection and being service-related, administrative, or concerned with political control (Mawby, 1990). United Kingdom; Policing System Police systems in England and Wales prior to the 19th century are portrayed private, non-professional, and unspecialized by authors such as Critchley (1978) and Radzinowicz (1956a). After creation of new police, The Metropolitan Police Force (1829), Londons first centralized, uniformed, wholly professional, centrally-controlled police force (Reynolds, 1998) and similar forces were established in other urban and rural areas between 1835 and 1888, so the nineteenth century was a breakpoint. After a dynamic duration in 20th century, now there are currently 43 police forces in England and Wales employing over 233,000 personnel, over 140,000 police officers, nearly 78,000 police staff and over 15,600 Police Community Support Officers. Additionally, there are currently in excess of 14,500 volunteer police officers known as Special Constables in England and Wales (Home Office, 2009). The 51 police forces those were over 100 prior to the Police Act of 1964 in England, Wales, and Scotland each headed by a Chief Constable who is accountable to a Police Authority (Tupman and Tupman, 1999). In Scotland, there are 8 constabularies corresponding to the 8 former regional governments of Scotland. Initially, in terms of function, the polices role is crime control and maintenance public order, more specifically crime prevention through uniformed patrol while, at the same time, fulfilling a welfare and service order public (Mawby, 2008). Secondly, in terms of structure, there is a balance between local and central control and organization. The modern police system in England and Wales is traced back to the early nineteenth century, this idea is reinforced by Bayley in such a way that he states that The modern English police constable is medieval Tythingman1, still acting under royal authority but now serving at public expense in a chosen career (1990, p: 29). The 1962 Royal Commission on the Police identified the protection of local police forces autonomy through the institution of the three partite structure of accountability: individual chief constables, police authorities and central government claims Mawby in his study dedicated to compare policing systems all over the world (2008). From a more general perspective, in UK structure is decentralized compared to continental system, and there are local police forces with the help of these information, but Northern Ireland has a different system based on colonial system (Mawby, 1992). It is possible, in terms of structure, to say that police is decentralized, unarmed, and civilian force (Mawby, 1990). Afterwards, in terms of legitimacy there is a tendency to do what public want. It is possible to see on the green paper that the police are in attempts to improve the connection between public and the police: This Green Paper sets out proposals for a new policing pledge which will be developed in partnership between the police and local people (Green Paper, July 2008). In his recent study, Mawby states that there at least four attempts to allay public concern by providing public access to local police management: Crime and Disorder Reduction Partnerships (CDRPs), the formation of police consultative committees, the establishment of lay visitors schemes, and the introduction of Independent Advisory Groups to monitor police racism following the Stephen Lawrence Inquiry (Mawby, 2008, p: 21). Turkey; Policing System The history of the police in Turkey derives from Ottoman Empire in 19th century like public administration through adapting to French prefecture model (Mercedes and Newburn, 2008, p: 34). Moreover, Turkish civilian administration system is influenced by the French civilian administration system and its domestic security approach (Celador, Gemma Collantes et al 2008). Security function is provided by both public and private sector, and there are three public law enforcement institutions: the police, the jandarma (gendarmerie) and the coast guard command. The jandarma and the coast guard command are responsible to the Minister of Interior as well as the police; yet, the jandarma and the coast guard command are military institutions. In terms of promotions, appointments, personnel administration, disciplinary and judiciary procedures, the jandarma corps is located within the military structure headed by the Office of the Chief of General Staff, who, in turn, responds to the Office of the Prime Minister, instead of to the Ministry of National Defence. Additionally, the national police force and the jandarma are different in terms of their respective jurisdictions and responsibilities vis-à ¯Ã‚ ¿Ã‚ ½-vis the civilian government authorities (Celador, Gemma Collantes et al 2008, p: 8). Jurisdiction of the police geographically differs from the jandarmas jurisdiction; the police provide security in urban areas rather whereas the jandarma are responsible for rural areas. In terms of structure, the police force is centralized, thus, compared to western central administration models, this structure is excessively central (Cerrah, 2005).In terms of function, there is obviously a higher number of the jandarma compared to the police, although urban areas contain more population than rural areas. There are some 193,000 police whereas the jandarma are between 280,000 and 300,000 (Mercedes and Newburn, 2008). According to Mercedes and Newburns study which is one of the last studies about Turkey and policing system, number of the jandarma is highly more than the polices. There are several reasons but, eventually, as a result of disproportional allocation, the priority is not welfare but the continuity of order in terms of administrative and political tasks in addition to crime prevention. Last of all, in terms of legitimacy, police legitimacy derives from law rather than public. After legislation through the EU twinning projects, for example with amendments and modifications on Law on Powers and Tasks of Police (1936), the government has aimed at changing consideration of police as a service rather than power. Nevertheless, in practice, this is not easily possible. Despite all the time that has passed since then, the Turkish police organisation has been unable to establish systemic institutional civilian participation and a satisfactory control mechanism. On both national and regional level, security policies and practices are only run and supervised by appointed civilian administration authorities and police administrators. claims Cerrah (2005) and as he adds the police still have to do more to be more accountable. Unless the police are more accountable and open to be controlled by civilian mechanism, legitimacy of the police will be discussed as well as its function. However, community policing is a new issue in Turkey with a pilot practicing in ten big cities including Istanbul, Ankara, Izmir, and Bursa (Directorate General of Security, 2009). There is a tendency to be more people-oriented. France; Policing System French police system is arguably the first modern system in Europe whereas The London Metropolitan Police is known to be the first modern police (Mawby 1990, p: 34, Bowden, 1978, p: 140). Bowden also adds that 615 is the year first peace and police existed in France, but, ironically, French is the nation who has frequently experienced the discontinuity in a nations political life despite the fact that they developed the most sophisticated police in Europe (1978). The police function in France is rooted to Roman law tradition, and since the French Revolution (1789), historically, there are significant processes but it is not going to be discussed because of lack of space. Today, police system in French can be analyzed through being distinguished as the police nationale and gendarmerie nationale. The gendarmerie are accountable to three different authorities: to Minister of Justice for criminal investigations, to the Ministry of Interior for public order, or administrative matters, and to the Ministry of Defence for all other aspects of their work whereas the police nationale are responsible to the Minister of Justice for criminal investigations, and to the Ministry of Interior for public order, or administrative matters (Hodgson, 2005). According to Hodgsons account, which compares French criminal justice system to British systems and includes an extensive investigation, the police nationale is composed of some 120,000 officers now according to Interpol 126,000 whereas the Gendarmerie comprises some 85,000 officers now according to Interpol 90,000 (2009) (2005). Moreover, there are some 3000 small municipal police forces. In terms of structure French police system is centralized as it is seen from this portray, the police forces are armed and not exactly- militaristic. France is typically an example of continental European system and in terms of function police system in France is putting emphasises on administrative and political tasks rather than welfare (Mawby, 2008, p: 22). As a consequence of being centrally organized, France has more centralized policing system with two main forces the police nationale and the gendarmerie compared to British policing system and less centralized compared to Turkish police system. Compared with UK, the availability of other community initiatives involving polis-public cooperation such as neighbourhood watch or volunteer police auxiliaries are relatively unknown (Mawby, 1990). As a continental European country, in terms of legitimacy the police and the gendarmerie are closely tied to government rather than public or law. United Kingdom (Excluding Northern Ireland) Turkey France Legitimacy Local government Central government Central government Function Welfare Crime prevention, emphasis on administrative tasks Crime prevention, emphasis on administrative tasks Structure Decentralized Centralized (More excessively) Centralized It is possible to infer from whole information that United Kingdom, excluding Northern Ireland, has community-oriented policing system where as France and Turkey have continental and highly centralized and government oriented policing systems. Mawby who has a range of comparative police studies since early 1990s sees continental police systems in the past as being distinguished in terms of their lack of accountability, being directly responsible to the head of state, and he adds in another study that While this less easily reconciled with the liberal democracies of post-war Europe, it is still the case that public accountability is more restricted in countries where the police are more centralized and militaristic (2008, p: 23). Also in Turkey, more recently, with the increased quality of the police training and education, the rising numbers of commissioners and officers receiving masters and doctorates (some on topics including human rights law, technologically more advanced crime-fighting methods, etc.) and the positive impact of EU twinning projects, a younger reformist wing seems to have emerged within the police. This wing is also psychologically supported by civil societal demands for the establishment of more professional, accountable and transparent police structures. (Celador, Gemma Collantes et al, 2008, p: 9) From a historical perspective; between 1804 and 1810 in France, during Napoleons dictatorship Fouchà ¯Ã‚ ¿Ã‚ ½ was his strong right arm and was commanding French police. Fouchà ¯Ã‚ ¿Ã‚ ½, Duc dOtranto, had an army consisting of spies and agent provocateurs spreading insidious terror and repression throughout France (Manwaring-White, 1993). As Manwaring-White states, there was a very real fear in Britain that any sort police force like in France would result the same fearful invasion of privacy and liberty. On the other, while Robert peel was introducing his Metropolis Police Improvement Bill, he had figures to show a population increase of 19 per cent in London and Middlesex, but an increase in crime of 55 per cent between the periods of seven years from 1811 to 1818 and from 1821-1828 (Emsley, 1991). The bill passed through the parliament and The Metropolitan Police of London was established contrast to French militaristic system. However, contentiously, despite the horror of the Fouchà ¯Ã‚ ¿Ã‚ ½ regime in France, the British government did employ spies and agents to try and uncover hints of treasonable activity or political unrest and despite anathema to French style spies, a detective department was reorganised in Scotland in 1842 (Manwaring-White, 1993). There several attempts contrast to thought because of which the Met was established. Furthermore, during the 70s the developments in police riot brought the English police closer in their riot tactics and equipments, yet, unlike continental neighbours, employers were not specialized riot squads (Emsley, 1991). Finally, the men, responsible for creation the English police during the 19th century, wanted to restrict the political and military nature of the new police, but Emsley states that despite these reasons of creation of English police, the economic, political and social nature of Victorian England was instrumental in helping some people to achieve their aim (1991). By contrast with whom see centralized system as incorporating problems of non-accountability and partisanship, Mawby critically examines this idea. Firstly, one should not assume that locally, community-oriented systems are necessarily panaceas; they may incorporate problems of non-accountability, elite control and partisanship. Secondly, however, although political policing has been more a future of policing systems in countries where the police are militaristic, there is no clear relationship between the presence of one, central police system and these features. Nor is a central system necessarily incompatible with local accountability. Last of all, as illustrated in his study, the presence of absence of a single, centralized police is no more evidence of a police state than is the presence or absence of the jury system (Mawby, 1992, p: 125-126). Today, in terms of function, structure, and legitimacy, community-oriented systems are seen more advantageous, but privacy and liberty of individuals are threatened by the surveillance, bugging and file-keeping methods of modern police (Manwaring-White, 1993). Bibliography Books Bayley, David H. (1990) Patterns of Policing: A Comparative International Analysis, Rutgers University Press. Bowden, T. (1978), Beyond the Limits of Law, Harmondsworth: Penguin Cerrah, Ibrahim, Police, in Cizre, Umit (ed.), Almanac Turkey 2005: Security Sector and Democratic Oversight, Istanbul: TESEV Publications, 2006, pp. 86-99. Critchley, T.A. (1978), The History of Police in England and Wales in Mawby, Rob I. (1990), Comparative Police Issues: The British and American system in international perspective, London: Unwin Hyman. Celador, Gemma Collantes et al (2008), Fostering an EU Strategy for Security Sector Reform in the Mediterranean: Learning from Turkish and Palestinian Police Reform Experiences, EuroMeSCo Paper 66 (January 2008) Emsley, Clive (1991), the English Police, a Political and Social History, Second Edition, Addison Wesley: Longman Hin, Mercedes S and Newburn, Tim (2008) Policing Developing Democracies, Taylor Francis Hodgson, Jacqueline (2005), French Criminal Justice: A Comparative Account of the Investigation and Prosecution of Crime in France, Hart, University of Michigan Lambert, John L. (1986) Police Powers and Accountability, Taylor Francis Manwaring-White, Sarah (1983) the Policing Revolution, Police Technology, Democracy and Liberty in Britain, the Harvester Press Mawby, Rob I. (1990), Comparative Police Issues: The British and American system in international perspective, London: Unwin Hyman. Mawby, RI (1992) Comparative police systems: searching for a continental model, pp: 108-132 in K. Bottomley, T. Fowles and R. Reiner (eds.) (1992) Criminal Justice: Theory and Practice, British Criminology Conference 1991, London: British Society of Criminology. Mawby Rob I. (2008), Models of Policing, in Newburn, Tim (ed.) (2008) Handbook of Policing, 2nd Edition, Cullompton: Willan, pp: 17-46. Radzinowicz, L. (1956a), A history of English Criminal Law and its administration from 1750, Volume 1: The Movement for Reform in Mawby, Rob I. (1990), Comparative Police Issues: The British and American system in international perspective, London: Unwin Hyman. Reynolds, Elaine A. (1998), Before the Bobbies, Stanford University Press. Liang, Hsi-Huey (2002), The Rise of Modern Police and the European State System from Metternich to the Second World War, Cambridge University Press, pp: 11-13. Tupman, Bill and Tupman, Alison (1999), Policing in Europe, Intellect Books. Websites Home office (2009) About Us, available: http://police.homeoffice.gov.uk/about-us/ last accessed 18 March 2009. Directorate General of Security (2009) Community Policing, available: http://www.asayis.pol.tr/tdpyapilanmasunumu_dosyalar/frame.htm. Last accessed 18 March 2009. Interpol (2009) France: Police system, available: http://www.interpol.int/Public/Region/Europe/pjsystems/France.asp. Last accessed 18 March 2009 Additional Source Green Paper (2008), From the Neighbourhood to the National: Policing Our Communities Together, Green Paper, Home Office, July 2008 1 Tythingman was of Saxon times and he was elected by his peers in the local community and exercised wide responsibilities for all aspects of local government on heir behalf He was not , however, a royal officer, as his authority derived from the community he served rather than from the sovereign (Lambert, 1986, p: 21)

Contribution Of Indian Mathematics History Essay

Contribution Of Indian Mathematics History Essay Mathematics is the study of numbers, and counting, and measuring, but that is only the beginning. Mathematics involves the study of number patterns and relationships, too. It is also a way to communicate ideas, and perhaps more than anything, it is a way of reasoning that is unique to human beings. Mathematics plays a vital role in the modernization of this civilization. It is everywhere and affects the everyday lives of people. Although it is abstract and theoretical knowledge, it emerges from the real world. It is also a way to communicate and analyze ideas, a tool for organizing and interpreting data and above all, perhaps a method of logical reasoning unique to man. Mathematics is a necessary part of other sciences. In the words of Physicist Richard Feynan (2002) Nature talks to us in the language of mathematics that is numbers, mathematical rules and equations help us to make sense of the world around us (The Book of Popular Science). Mathematics in some form or other has been s ince the early age of human civilization. But its use in todays world has assumed great importance, since without its application higher technology cannot be mastered and harnessed for increasing production of goods and services and promoting human welfare. Over the centuries there has been spectacular progress in the development of mathematics as a branch of knowledge. And without the application of mathematics on a wide scale no country can march forward in line with the general progress of human knowledge and thought. Therefore learning of mathematics and promoting the horizons of knowledge by advanced researches in mathematics should be over emphasized. Thus, mathematics is an important and inseparable part of human life. It has been existed and developed since the ancient era and the aim of this article is to give a brief review of a few of the outstanding innovations introduced by Indian mathematics from ancient times to modern as Indias contribution in the field of mathematic s is immense and it should always be studied from a thoughtful perspective. Key Words: INTRODUCTION: India was the motherland of our race and Sanskrit the mother of Europes languages. India was the mother of our philosophy, of much of our mathematics, of the ideals embodied in Christianity of self-government and democracy. In many ways, Mother India is the mother of us all. Will Durant, American Historian 1885-1981 Mathematics is an important field of study. Mathematics is vital as it helps in developing lots of practical skills, in fact study of mathematics itself include the concepts related to the routine lives of human. It not only develops mathematical skills and concepts, it also helps in developing the attitudes, interest, and appreciation and provides opportunities to develop ones own thinking. So, mathematics is undoubtedly a discipline which is imperative to know and study. Fig. 1, Importance of MathematicsC:UsersnaveenDesktopUntitled.png Mathematics has played a very significant role in the development of Indian culture for millennia. Mathematical ideas that originated in the Indian subcontinent have had a thoughtful impact on the world. In ancient time, mathematics was mainly used in an auxiliary or applied role. Thus mathematical methods were used to solve problems in architecture and construction (as in the public works of the Harrappan civilization) in astronomy and astrology (as in the Jain mathematicians) and in the construction of Vedic altars (as in the case of the Shulba Sutras of Baudhayana and his successors). By the sixth or fifth century BCE, mathematics was studied for its own sake, as well as for its application in other fields of knowledge. In fact there does not seem to have been a time in Indian history when mathematics was not being developed. Recent work has unearthed many manuscripts, and what were previously regarded as inactive periods in Indian mathematics are now known to have been very activ e. The picture is yet not complete, and it seems that there is much more to do in the field of the history of Indian mathematics. The challenges are twofold. First, there is the task of locating and identifying manuscripts and of translating them into a language that is more familiar to modern scholars. Second there is the task of interpreting the significance of the work that was done. The time is ripe to make a major effort to develop as complete a picture as possible of Indian mathematics. The importance of mathematics in India can be seen by a well-known verse in Sanskrit of VedangJyotish (written 1000 BC) as: This verse means that As the crown on the head of a peacock and as the gem on the hood of a snake, so stands Mathematics crowned above all disciplines of knowledge. This fact was well known to intellectuals of India that is why they gave special importance to the development of mathematics, right from the beginning. Indian mathematicians made great strides in developing arithmetic, algebra, geometry, infinite series expansions and calculus. Indian works, through a variety of translations, have had significant influence throughout the world. Mathematics in ancient times (3000 to 600 BCE) The oldest evidence of mathematical knowledge to Indians is being found in Indus Valley Civilization. The metallic seals found in the excavations of Mohan-Jo-Daro and Harrapan indicates that the people of this civilization had the knowledge of numbers. It is also clear from the pottery and other archaeological remains that they had the knowledge of measurement and geometry even in crude form. The Indus valley civilization is considered to have existed around 3000 BCE. Two of its most famous cities, Harappa and Mohenjo-Daro, provide evidence that construction of buildings followed a standardized measurement which was decimal in nature. Here, we see mathematical ideas developed for the purpose of construction. This civilization had an advanced brick-making technology (having invented the kiln). Bricks were used in the construction of buildings and embankments for flood control. The study of astronomy is considered to be even older, and there must have been mathematical theories on which it was based. Even in later times, we find that astronomy motivated considerable mathematical development, especially in the field of trigonometry. Much has been written about the mathematical constructions that are to be found in Vedic literature. In particular, the Shatapatha Brahmana, which is a part of the Shukla Yajur Veda, contains detailed descriptions of the geometric construction of altars for yajnas. Here, the brick-making technology of the Indus valley civilization was put to a new use. Supplementary to the Vedas are the Shulba Sutras. These texts are considered to date from 800 to 200 BCE. Four in number, they are named after their authors: Baudhayana (600 BCE), Manava (750 BCE), Apastamba (600 BCE), and Katyayana (200 BCE). The sutras contain the famous theorem commonly attributed to Pythagoras. The Shulba Sutras introduce the concept of irrational numbers, numbers that are not the ratio of two whole numbers. It is interesting that the mathematics of this period seems to have been developed for solving practical geometric problems, especially the construction of religious altars. However, the study of the series expansion for certain functions already hints at the development of an algebraic perspective. In later times, we find a shift towards algebra, with simplification of algebraic formulate and summation of series acting as catalysts for mathematical discovery. Jain Mathematics (600 BCE to 500 CE) Just as Vedic philosophy and theology inspired the development of certain aspects of mathematics, so too did the rise of Jainism. Jain cosmology led to ideas of the infinite. This in turn, led to the development of the notion of orders of infinity as a mathematical concept. By orders of infinity, we mean a theory by which one set could be deemed to be more infinite than another. In modern language, this corresponds to the notion of cardinality. For a finite set, its cardinality is the number of elements it contains. However, we need a more sophisticated notion to measure the size of an infinite set. In Europe, it was not until Cantors work in the nineteenth century that a proper concept of cardinality was established. Besides the investigations into infinity, this period saw developments in several other fields such as number theory, geometry, computing, with fractions. In particular, the recursion formula for binomial coefficients and the Pascals triangle were already known in this period. The period 600 CE coincides with the rise and dominance of Buddhism. In the Lalitavistara, a biography of the Buddha which may have been written around the first century CE, there is an incident about Gautama being asked to state the name of large powers of 10 starting with 10. He is able to give names to numbers up to 10 (tallaksana). The very fact that such large numbers had names suggests that the mathematicians of the day were comfortable thinking about very large numbers. It is hard to imagine calculating with such numbers without some form of place value system. Brahmi Numerals, The place-value system and Zero No account of Indian mathematics would be complete without a discussion of Indian numerals, the place-value system, and the concept of zero. The numerals that we use even today can be traced to the Brahmi numerals that seem to have made their appearance in 300 BCE. But Brahmi numerals were not part of a place value system. They evolved into the Gupta numerals around 400 CE and subsequently into the Devnagari numerals, which developed slowly between 600 and 1000 CE. By 600 CE, a place-value decimal system was well in use in India. This means that when a number is written down, each symbol that is used has an absolute value, but also a value relative to its position. For example, the numbers 1 and 5 have a value on their own, but also have a value relative to their position in the number 15. The importance of a place-value system need hardly be emphasized. It would suffice to cite an often-quoted remark by La-place: It is India that gave us the ingenious method of expressing all numbers by means of ten symbols, each symbol receiving a value of position as well as an absolute value; a profound and important idea which appears so simple to us now that we ignore its true merit. But its very simplicity and the great ease which it has lent to computations put our arithmetic in the first rank of useful inventions; and we shall appreciate the magnificence of the achievement the more when we remember that it escaped the genius of Archimedes and Apolloniu s, two of the greatest men produced by ancient times. A place-value system of numerals was apparently known in other cultures; for example, the Babylonians used a sexagesimal place-value system as early as 1700 BCE, but the Indian system was the first decimal system. Moreover, until 400 BCE, The Babylonian system had an inherent ambiguity as there was no symbol for zero. Thus it was not a complete place-value system in the way we think of it today. The elevation of zero to the same status as other numbers involved difficulties that many brilliant mathematicians struggled with. The main problem was that the rules of arithmetic had to be formulated so as to include zero. While addition, subtraction, and multiplication with zero were mastered, division was a more subtle question. Today, we know that division by zero is not well-defined and so has to be excluded from the rules of arithmetic. But this understanding did not come all at once, and took the combined efforts of many minds. It is interesting to note that it was not until the seventeenth century that zero was being used in Europe. The Classical Era of Indian Mathematics (500 to 1200 CE) The most famous names of Indian mathematics belong to what is known as the classical era. This includes Aryabhata I (500 CE) Brahmagupta (700 CE), Bhaskara I (900 CE), Mahavira (900 CE), Aryabhatta II (1000 CE) and Bhaskarachrya or Bhaskara II (1200 CE). During this period, two centers of mathematical research emerged, one at Kusumapura near Pataliputra and the other at Ujjain. Aryabhata I was the dominant figure at Kusumapura. One of Aryabhatas discoveries was a method for solving linear equations of the form ax + by = c. Aryabhata devised a general method for solving such equations, and he called it the kuttaka (or pulverizer) method. It should be noted that Aryabhatas studied linear equations because of his interest in astronomy. Amongst other important contributions of Aryabhata is his approximation of Pie to four decimal places (3.14146) and work on trigonometry. The other major centre of mathematical learning during this period was Ujjain, which was home to Varahamihira, Brahmagupta and Bhaskaracharya. The text Brahma-sphuta-siddhanta by Brahmagupta, published in 628 CE, dealt with arithmetic involving zero and negative numbers. As with Aryabhata, Brahmagupta was an astronomer, and much of his work was motivated by problems that arose in astronomy. He gave the famous formula for a solution to the quadratic equation. Brahmagupta also studied quadratic equation in two variables and sought solutions in whole numbers. This period closes with Bhaskaracharya (1200 CE). In his fundamental work on arithmetic (titled Lilavati) he refined the kuttaka method of Aryabhata and Brahmagupta. The Lilavati is impressive for its originality and diversity of topics. Brahmagupta discovered a method, which he called samasa, by which; given two solutions of the equation a third solution could be found. Brahmaguptas lemma was known one thousand years before it was rediscovered in Europe by Fermat, Legendre, and others. This method appears now in most standard text books and courses in number theory. The name of the equation is a historical accident. Mathematics in South India Mahavira is a mathematician belonging to the ninth century who was most likely from modern day Karnataka. He studied the problem of cubic and quartic equations and solved them for some families of equations. His work had a significant impact on the development of mathematics in South India. His book Ganita- sara- sangraha amplifies the work of Brahmagulpta and provides a very useful reference for the state of mathematics in his day. Another notable mathematician of South India was Madhava from Kerala. Madhava belongs to the fourteenth century. He discovered series expansions for some trigonometric functions such as the sine, cosine and arctangent that were not known in Europe until after Newton. In modern terminology, these expansions are the Taylor series of the functions in question. Madhava gave an approximation to Pie of 3.14159265359, which goes far beyond the four decimal places computed by Aryabhata. Madhavas work with series expansions suggests that he either discovered elements of the differential calculus or nearly did so. Mathematics in the Modern Age In more recent times there have been many important discoveries made by mathematicians of Indian origin. We shall mention the work of three of them: Srinivasa Ramanujan, Harish-Chandra, and Manjul Bhargava. Ramanujan (1887- 1920) is perhaps the most famous of modern Indian mathematicians. Though he produced significant and beautiful results in many aspects of number theory, his most lasting discovery may be the arithmetic theory of modular forms. In an important paper published in 1916, he initiated the study of the Pie function. Ramanujan proved some properties of the function and conjectured many more. As a result of his work, the modern arithmetic theory of modular forms, which occupies a central place in number theory and algebraic geometry, was developed by Hecke. Harish-Chandra (1923- 83) is perhaps the least known Indian mathematician outside of mathematical circles. He began his career as a physicist, working under Dirac. In his thesis, he worked on the representation theory of the group SL2 (C). This work convinced him that he was really a mathematician, and he spent the remainder of his academic life working on the representation theory of semi-simple groups. For most of that period, he was a professor at the Institute for Advanced Study in Princeton, New Jersey. His Collected Papers published in four volumes contain more than 2,000 pages. His style is known as meticulous and thorough and his published work tends to treat the most general case at the very outset. This is in contrast to many other mathematicians, whose published work tends to evolve through special cases. Interestingly, the work of Harish-Chandra formed the basis of Langlandss theory of automorphic forms, which are a vast generalization of the modular forms considered by R amanujan. CONCLUSION: The present mathematical knowledge has not dropped as a bolt from the blue, nor a product of some magical tricks. The apparently ready-made knowledge and results have been achieved after centuries of efforts, often painful, by hundreds of mathematicians and historians through the ages. Lots of discoveries and inventers contributed to the fruits, facilities and luxuries which we enjoy today were the contribution of Indian mathematicians. From the notion of zero to the modern concept of computational number theory, their contribution is significant. It is without doubt that mathematics today owes a huge debt to the outstanding contributions made by Indian mathematicians over many hundreds of years. What is quite surprising is that there has been a reluctance to recognize this and one has to conclude that many famous historians of mathematics found what they expected to find, or perhaps even what they hoped to find, rather than to realize what was so clear in front of them. Kim Plofker from Netherland says that Indian mathematical science is extremely important and has a significant effect on the worlds knowledge as it is today. The lack of available resources has kept us under informed about the developments that have taken place in India. It is the need of the hour to carry forward the legacy of great mathematicians so as to encourage and nurture the glorious tradition of the country in mathematics. The ingenious method of expressing every possible number using a set of ten symbols (each symbol having a place value and an absolute value) emerged in India. The idea seems so simple nowadays that its significance and profound importance is no longer appreciated. Its simplicity lies in the way it facilitated calculation and placed arithmetic foremost amongst useful inventions. The importance of this invention is more readily appreciated when one considers that it was beyond the two greatest men of ancient times, Archimedes and Apollonius.

Propaganda Theories and Models: The MH370 Incident

Propaganda Theories and Models: The MH370 Incident PROPAGANDA THEORY ON THE MH370 INCIDENT Contents (Jump to) INTRODUCTION PROPAGANDA THEORY RELATING TO MH370 INCIDENT COUNTER PROPAGANDA BY THE GOVERNMENT REFERENCES INTRODUCTION Mystery continues to surround the fate of Malaysia Airlines flight MH370, which disappeared en route from Kuala Lumpur to Beijing on 8 March. Malaysian authorities, assisted by international aviation and satellite experts, are now battling to piece together the planes final hours in the hope that they can find its wreckage and explain what happened to its 239 passengers and crew. Some preliminary details were released on 1 May in a short report. Accordingly, many propaganda arises on this issue. Some of propaganda emanating from the local media and not to forget from abroad. If we look from the point of propaganda theory itself, there is some good propaganda that led to the issue of loss MH370, but there also resulting in a negative impact on public perception towards the way the government is dealing with the issue. To deal with the propaganda that apply to this incident, we will analyze whether the form of propaganda, the propaganda perspective itself and how the government to overcome this problem. Merriam Webster Dictionary gives the definition of propaganda as ideas or statements that are often false or exaggerated and that are spread in order to help a cause, a political leader, a government, etc. the spreading of ideas, information, or rumor for the purpose of helping or injuring an institution, a cause, or a person, ideas, facts, or allegations spread deliberately to further ones cause or to damage an opposing cause; also : a public action having such an effect First introduced by Edward S. Herman and Noam Chomsky (1988), Manufacturing Consent: The Political Economy of the Mass Media, the propaganda model argues that the material news through five filters, which in turn form the audience received the news. This filter determines what is considered newsworthy events, how they are covered, where they were placed in the media and how much coverage they receive. Propaganda model of media control that was introduced by Edward. S. Herman and Noam Chomsky (1988) states how propaganda works in the media. This model tries to understand how populations are manipulated, and how social, economic, political attitudes are formed in the minds of the people through propaganda. Herman and Chomsky are mostly concentrated in the American population and the media for their research, but the theory applies universally. Propaganda model seeks to explain the behavior of the media by examining the institutional pressures that limit and influence the news content in a profit-driven system. In contrast to liberal theories that argue that journalism is defined hostility power, the propaganda model predicts that the company-owned news media will consistently produce news content that serves the interests of established power (Herman Chomsky, 1988). PROPAGANDA THEORY RELATING TO MH370 INCIDENT Among the propaganda that exists from within Malaysia itself mostly spread through social media on the internet, given the sophistication of the current information age, there are blogs and websites questioned the credibility of the government and even spread propaganda relating to this issue of MH370. Among the widely disseminated propaganda on the website saying that Malaysia experienced a bad media Especially from the Western press and especially CNN and Extension of this, of good journalistic practice for hazardous and agenda driven, further lead to more conspiracy theories especially the involvement of CNN.The Mole reproduces an article written by Matthias Chang, the profession as a lawyer, social activist, author and political analyst. He reveals how the MH370 is a multi-dimensional, and why the Zionist hands should not be overlooked. Although somewhat lengthy, is worth reading every word printed: Before proceeding with Expose of Zionist propaganda Insidious Dastardly and Israel on the Cessation of MH 370, let me take this opportunity to convey my personal condolences and that of my family to a family who loves Ones have been killed in this tragedy and we hope ur strength to overcome the disadvantage pint them.† He would also commend the Malaysian governments efforts in the SAR Mission involved 26 countries that had never happened before. Allegations of unfair and unfounded against the Malaysian government made by many people in social media who do not have a clue and or expertise to comment on the operation of the Standard and Poors scale. Another propaganda that there is involvement from the United States, which was propagated that where Maldives island Residents reported sighting of low flying jet on the morning of the planes Disappearance thats was finally Reported on twelve days after the fact. The pilot of the missing plane had a home flight simulator, Which was been Reported twelve days later to contain the landing simulation program of the Diego Garcia runway along with four other Approaches in the region. Whether any, all, or none of this information is true is still a matter of Conjecture. What Remains thats a fact is not a trace of the Malaysian 777-200ER has been found. At his daily news briefing on 3-18-14, WH spokesperson Jay Carney has denied any Involvement of the Diego Garcia facility with the Disappearance of flight MH370. In addition to conspiracy theories involving the United States, one side is highly spoken of as real mastermind behind the MH370 is a tribe of lost Jewish or Israeli. It is the act of buying and Israel has a Boeing 777 2H6 (ER) long owned Malaysian Airline (MAS). Aircraft twin MH370 has been recorded at a small airport in Tarbes-Lourdes-Pyrà ©nà ©es, France on October 4, 2013 before he was taken to Ben Gurion Airport, Tel Aviv, Israel on 4 November 2013. Understandable, MAS Boeing 777 aircraft with serial number 28 416 and registered as 9M-MRI has been sold to GA Telesis, LLC in Fort Lauderdale, Florida on October 21, 2013 before the N105GT.Pesawat registered as recorded in Tarbes Lourdes Pyrenees on October 4, 2014 before taken to Tel Aviv a month later. The question is, why would Israel want to buy and have a long plane MAS this? If referred back Israeli reactions associated loss MH370, a security expert of the country, Isaac Yeffet relate it to the theory that MH370 have been captured by the terrorists and taken to Iran to be used for a series of terror will come. Yeffet reportedly gave a statement to the Times of Israel: What happened to this aircraft, nobody knows. My guess is based upon the stolen passports, and I believe Iran was INVOLVED. They hijacked the aircraft and they landed it in a place that nobody can see or find it. (There is no case what has happened to the aircraft. Based on reported cases of stolen passports, I believe Iran is involved in this case. They had seized the plane and fly it into a place that cannot be found). Another propaganda that arises during the incident came from the opposition parties, where they claim that the incident crated by the government was to create a diversion to the voter, as coincidently at that time Kajang by-election was taking place. The propaganda was that by showing the great effort towards the search and rescue operations, the government will the heart of the voters. Actually, there was so many propaganda arises during the incident even until now, people are still fed with various elements of propaganda for the positive and negative as well. If we examine this theory from the angle of propaganda, the government should also take the opportunity by using this incident as their leverage in building up the government credibility. COUNTER PROPAGANDA BY THE GOVERNMENT According to brownpoliticalreview.org in its reports, the recent disappearance of Malaysian Airlines Flight MH370 and the resulting media spotlight has revealed Malaysia’s fundamental shortcomings and glaring political issues. While the plane’s disappearance itself is horrendous – in particular for the many families left in limbo – the Malaysian government’s handling of the situation has drawn considerable international disapproval which leads to the dissemination of the propaganda. In order to deal with the issue of propaganda in connection with the issue of MH370, the government shall be wise to use methods and tactics namely through counter propaganda. Counterpropaganda is a structure of communication consisting of method in use and messages relayed to resist propaganda which seeks to manipulate action or perspectives among a targeted audience. It is closely linked to propaganda as the two often utilize the same methods to transmit methods to a targeted audience. Counterpropaganda differs from propaganda as it is defensive and responsive to identified propaganda. in addition, counterpropaganda consists of several elements that further differentiate it from propaganda and ensure its efficiency in opposing propaganda messages. While propaganda messages may not always be straightforward, efficient counterpropaganda commonly only broadcast the truth. Without a doubt, counterpropaganda is generally understood to be the truthful, honest opposition to an adversarys propaganda. Counterpropaganda communicates honest messages for ethical and realistic reasons. Looking though reporting of the event, the government from the beginning should report the facts related to this incident. Counter propaganda elements should be applied to achieve the best effect. Reporting matters of fact, although filtered, to some extent can relieve speculations made by the public, especially from the families involved. This can create a deficiency or weakness in reporting which leads to the dissemination of wild propaganda, even more so from the opposition. References: Chomsky, Noam and Herman, Edward. (1988) Manufacturing Consent: The Political Economy of the Mass Media. New York: Pantheon Books. Cole, Robert. (1996)Propaganda in Twentieth Century War and Politics Lasswell, Harold D.. (1971)Propaganda Technique in World War I. Cambridge, Mass: The M.I.T. Press. Garth Jowett and Victoria ODonnell, Propaganda and Persuassion, 4th ed. Sage Publications, 7 Herbert Romerstein, Counterpropaganda: We Cant Do Without It,] in Waller, ed., Strategic Influence: Public Diplomacy, Counterpropaganda and Political Warfare (IWP Press, 2008), 135. [Frontpost, Nachrichten fà ¼r Deutsche Soldaten, Herausgeber: Die Amerikanischen Truppen in Westeuropa,] No. 1(March 1945), 3 in Waller, ed., Strategic Influence: Public Diplomacy, Counterpropaganda and Political Warfare (IWP Press, 2008), 144-145.

Dress Codes :: essays research papers

It is in the middle of summer and very hot and humid. You are in complete uniform, wearing the long wool pants with the shirt, tie and sweater. Your whole body is uncontrollably sweating. Instead of paying attention in class, you wipe yourself down every second.   Ã‚  Ã‚  Ã‚  Ã‚  Uniforms are uncomfortable, cause distractions and are expensive. They serve no purpose in getting the proper knowledge that one is in school to earn. One that is not comfortable, may not concentrate in class. He/she will move around their seat impatiently trying to get comfortable. Uniforms always cause problems in the summer and winter. The girls complain about wearing short dresses in the winter, arguing that it gets too cold to have their bare legs showing outside in the freezing weather conditions. The boys complain about wearing the hot long pants in the summer.   Ã‚  Ã‚  Ã‚  Ã‚  I attended a school that required a uniform. I wear boxers longer than the girls’ skirts. Although my values were strongly set on education, my mind wondered, trying to get a glimpse of a girl bending over. Some girls deny it, they wear their dresses too short. This causes a distraction. The guys will not pay attention in class, instead they will stare at the short dresses. This causes the boys to do work at a lower level. The schools should make a rule on the skirt lengths and enforce it with severe punishments such as detentions, suspensions, and expulsions. This rule should make the lengths below the knees.   Ã‚  Ã‚  Ã‚  Ã‚  Most uniforms are very expensive. The whole uniform may cost about $250.00. This is expensive for a normal family. Since some schools require uniforms, the family is forced to buy the uniform. This puts the family back financially. This might force the family to live on bread and water due to the fact that they have spent all the food money on ties dressshoes and dress pants.   Ã‚  Ã‚  Ã‚  Ã‚  How can uniforms change the way people act? They can not. No matter what the opposing argument may be, it can not be logically correct.

Kofi Annans effects on Canada trip :: essays research papers fc

Introduction Mr. Kofi Annan is, I feel, one of the most important people in mankind today. He is the Secretary-General of The United Nations. Last March, he came to deliver a speech on Canada’s position in the world. He thanked and congratulated us on what we have done in the world. He also admits that more needs to be done by rich nations like us. This I feel will spark some controversy because I feel Canada has done enough for the world and the UN should be satisfied with their efforts. I feel Mr. Kofi Annan’s speech will inspire and motivate the rest of The United Nations (it’s countries) and even us to keep committing or even add even more to what each and every one of us do. The proposal by Mr. Kofi Annan may bring many different advantages in helping our mixed up world. First, I feel it may get countries like the USA to get up off their stubborn behinds to start helping other nations instead of calling war on every one of them. The USA may feel that they are slowing or stopping terrorist activities worldwide, but they are only increasing the number of terrorist activities since they declared war on terrorism. They decide to concentrate places where there isn’t very much terrorist activity or even any hostility. Places like Afghanistan or Iraq may have had militants but they were not an immediate threat to anyone. They should have occupied places where help is needed most like in the Middle East where clashes between Palestinians and Israel h ave been numerous and brutal to this day. Maybe by listening to the speech the USA will see that there are other ways of helping the world besides bombing anyone they don’t like.   Ã‚  Ã‚  Ã‚  Ã‚  This speech may let Canada know that they’re role in the world is greatly appreciated which may lead to a greater participation with The United Nations and other poorer nations. We have been an outstanding part of the development of many developing nations such as Afghanistan, Iraq and some African nations. When we realize that we had not been just making our selves look good politically, we were making a huge difference. I can just see in the future Canada getting world support in the event of a crisis just as we have aided many others. I can just see the Chinese, the Russians the Germans, the French and the English running to our aid in the event of a disaster of any kind.

Causes And Solutions Of Juvenile Delinquency EDIT

I agree with this statement because if children are born in a family where they are not able to eat, or have to go to bed hungry, of course here is going to be some problems. When they are starving, they are going to be less focused on school. The growing rate of unemployment makes it difficult for parents to provide for their children. It also makes it easy for people to turn to a life of crime. One of these crimes is drug dealing and buying. When they live in an environment that has a supply of drugs and guns more than new textbook there is going be some problems.In a violent environment you are going to be more prone to be violent or a victim of violence. Whatever resources are more readily available in their neighborhood is the one they are more likely to pick up. So, if they have new guns and old textbooks, they might just pick up the new gun. When they are living in substandard housing, they might just feel substandard and depressed. They also are prone to have more environment al hazards in or near their neighborhood. All these previous things can have an effect on people's genetics or them personally.Psychological The author in this section wants his audience to know author problems can be passed on by parents and siblings through mental illness or behavior. There is a long list of people in jail right now that have some type of mental illness. It is probably over 50% of the jail population. The question that isn't asked in this article is: does the chicken come first or do the egg? In other words does the environment cause the mental illness or does the mental illness cause the environment. I think in a poor neighborhood it is a little bit of both.There are hazards and mental stress as well as trauma that come with living in a bad neighborhood. Believe that having to worry about safety and security can lead to mental stress, just as the article mentions. Bad neighborhoods also consist of many crimes, many of which are seen by nouns children. This causes trauma to innocent people and if trauma is left untreated, it can cause mental problems in the long run, although it may not be evident in the beginning. Furthermore, mental illness funding for the poor and general health funding for the poor has been on a steady cut over the last several decades.This leads to less and worst treatments for those that sometime need it the most. So, this becomes part of a contributing factor of the poor- having a higher crime rate across the board. This can lead to generations of mental illness that could have been prevented or at least Essen the problem. Social This part of the article talks about how you are treated in the family; whether a child is the first born, middle, or last child. This will all make a difference in how they are treated in the family and how they might be discriminate against.An example is that the oldest child usually has more responsibilities than their siblings. Therefore, they have more stress and may feel the need to do whatever they can to help the family- including turning to illegal work. The middle child is usually ignored, with most of the attention focused on the older and younger siblings. The younger sibling usually gets the most attention because they are the â€Å"baby' of the family. Parenting Styles Regardless of the social factors in a family, it can all come back to how parents raise their children.Some questions can determine aspects in a child's life such as: Does the child do what is asked of them with no reward or are they rewarded? Are actions (bad or good) explained by the parent when punishment is issued? Are parents holding their children accountable for their actions? Do parents take an active role in their children's lives, such as education? All this will make a difference in a child's behavior in the future. These very things can make a difference in whether a child becomes a juvenile delinquent or not.I believe that if parents are inconsistent with their children, punish them for minor issues, never give positive feedback, or do not take an active role in their children's lives, then they are negatively impacting their children and setting them up for failure. Personal: Sometimes, despite how great a child's family life is, there are still internal problems that a child can face. Though they may receive all the praise and eve from family, school, and friends, children can still become juvenile delinquents. One reason for this social problem is their personality.Everyone has a different set of personality and sometimes children are born naturally aggressive. Sometimes being easily angered or naturally irritable can cause problems in a child's life. No amount of tenderness or love from anyone can change this, in some cases. It is my opinion that natural aggression can cause violence and therefore make them commit crimes that other people who don't have the same similar problem would not do. Psychological The article states, â€Å"Statistics show tha t mental illnesses are one of the biggest reasons behind juvenile delinquency in America and other developed countries. To me, this is very believable because of how mental illnesses can affect a person. People with mental disabilities sometimes do not have the capacity to learn morals or empathy. An example is people who are psychopaths. This is not a learned disability. The English dictionary defines psychopath as: â€Å"a person with a psychopathic personality, which manifests as amoral and antisocial behavior, lack of ability to love or establish meaningful arsenal relationships, extreme egocentricity, failure to learn from experience, etc. This means that when a person lacks the ability to love, then they also are not able to form personal relationships. As humans, we are born with the need for companionship- it is a vital part of everyone's lives. Also, the lack of empathy will cause people to do bad things without feeling bad. An example is stealing. It is morally wrong and when someone steals, they should feel guilt. But a mentally ill person without empathy will not feel guilt. Peer Groups: This type of influence can greatly affect a child.The article states that parents should make sure their children hang out with people who belong to their â€Å"class† because it prevents jealousy. Jealousy between friends can cause several crimes in adolescents. This can be a good thing because if middle class children are hanging out with other middle class children, there is no one to be jealous of from a friend who has a richer family or a poor friend to be jealous of everyone else. However, this can also be a bad thing because if poor children are hanging out with other poor children, they may acquire bad habits those other poor children may have.One evident problem among families in the poverty line is the formations of gangs. These gangs can have negative effects in a child's life. They consist of negative and abusive behavior. Another peer group inf luence is peer rejection which can cause children to commit crimes because they feel they do not belong anywhere. I believe that a large part of an adolescence life is finding out who they are and where they belong. Society: Society affects what children see and also their environment. Social media is a powerful tool that society uses, and sometimes has negative impacts on teenagers. An example is bullying.Though bullying is extremely frowned upon, it still happens because many teenagers see more of this in the media than they do of people being kind and helping others. The news is always so quick to put out bad news than good news. Other things can spawn from something, like bullying, into labeling. An example of labeling is a child who is involved in bullying just by being there, though they actually never harmed anyone. This child may be labeled as criminal by circumstance and poor decision on who they hung out with. It will follow the child through the rest of heir lives and may even make them become an actual criminal.

Calls for Change in High School Mathematics Essay

Mathematic educators, parents and students are calling for proper changes in approaches to learning mathematics in high schools. The need to improve learning of mathematics in schools is highly recognized and underlined. Thus, the National Council of Teachers of Mathematics published the Curriculum and Evaluation Standards for School Mathematics that offered recommendations for high school mathematics reform. In addition, the Conference Board of the Mathematical Sciences in their official report ‘The Mathematical Sciences Curriculum K–12: What Is Still Fundamental and What Is Not’ stresses the importance of new topics and techniques in the secondary schools. New approaches should develop new learning techniques that would be discrete from statistics, mathematics, and emphasis on algebra and geometry should be properly re-assessed according to different abilities and needs of students who are taking mathematics course in the secondary school and high school respectively. The need for change and innovation is generally driven by emergence of advanced computing technologies that offers excellent opportunities for school educators to replace manipulative traditional techniques with more complex realistic problem-solving techniques. In its turn, the National Science Board Commission issued a report ‘Educating Americans for the 21st Century’ challenging courses in algebra and pre-calculus and stressing the importance of developing integrated mathematical sciences curriculum in the secondary school. Researchers argue that new curriculum will positively affect students’ achievement outcomes in the secondary and high schools. To make changes more effective teachers are required to understand the advantage of curriculum’s full scope and its consequences; students are required to support the expectations of classroom environment. The Core-Plus Mathematic Project is newly developed curriculum for high school mathematics. Of course, the Core-Plus Mathematic Project or CPMP curriculum is a matter of debates and controversies as not everyone admits the need of high school mathematics reforms. Nonetheless, the CPMP curriculum is worked out with assistance of mathematics education researchers, instructional specialists and classroom teachers. Moreover, the curriculum is shaped by empirical evidence gathered from students and teachers who are willing to participate in field testing. In particular, organization of mathematics curriculum should be interpreted in terms of teaching and assessment recommendations and should follow the standards set in the above-mentioned reports. New mathematics curriculum is a three-year mathematics course for high-school students who are allowed to take the fourth year to prepare for college mathematics. Newly designed curriculum differs from more traditional approaches as new curriculum encourages students’ understanding of mathematics – statistics, probability, algebra, geometry, trigonometry and discrete mathematics. Learning mathematics is developed in focused units that combine fundamental ideas with mathematical habits of mind. It means that new curriculum stresses the need to connect function, data analysis and symmetry with recursive and visual thinking. In contrast to traditional approaches to mathematics, new curriculum emphasizes the role of mathematical modeling and problem-solving instead of simple calculus. Researchers say the primary goal of curriculum improvement is to enhance students’ understanding and comprehension of key mathematical processes and concepts, to enhance student’s ability to use mathematical concepts in real-world problem-solving. Graphic calculators should enhance students’ understanding and abilities to solve authentic problems. Improved instructional materials encourage active teaching and learning processes that will primarily focus on problem situations, abstraction and analysis. Oral and written communication, reasoning with ability to represent, and conceptual understanding are highly appreciated and encouraged. All courses centre on mathematical reasoning and thinking with abilities to develop formal proof. Additional fourth year course will allow to keep students, who prepare for college mathematics, despite whether their undergraduate program is based on calculus. Students interested in mathematics are encouraged to be accelerated into the fourth course year. Today, many researches are focus on identifying whether new curriculum meets its specific goals. In particular, they try to reveal whether the learning outcomes based on new patterns of mathematics learning process differ from outcomes based on more traditional curriculum. During the past eight years researchers conducted various studies to examine mathematical achievement in classroom with CPMP curricula. Research studies have revealed that performance of CPMP students is much better than that of students with traditional interpretation of mathematical representation. It means that problem-solving and recursive thinking appear to be more effective in learning mathematics than simple understanding of key concepts of processes. Further, CPMP students are characterized by higher grade results at the end of the years than students with traditional approach to mathematics. Summing up, recent researches have indicated that CPMP students perform better than students with traditional curriculum. CPMP students are characterized by better abilities to interpret mathematical representation and calculation, to measure conceptual understanding and to recognize the importance of problem-solving. CPMP students are better in probability and statistics, algebraic manipulative skills, etc. Nonetheless, researchers argue that student’s success in college mathematics doesn’t fully depend on CPMP curriculum. Other factors, as, for example, student’s attentiveness, readiness to participate in learning process, self-awareness, classroom environment, play their important role in student’s high school mathematics performance. With guidance from educators, researchers and teachers, curriculum developers will be able to build on stronger patters of student outcomes. References Schoen, H. L. , & Hirsch, Ch. R. (2003). Responding to Calls for Change in High School Mathematics: Implications for Collegiate Mathematics. The Mathematical Association of America Monthly, February, pp. 109-123. Available on-line from http://www. jstor. org/stable/3647770 .