1.
Divisor
–
In mathematics, a divisor of an integer n, also called a factor of n, is an integer m that may be multiplied by some other integer to produce n. In this case one says also that n is a multiple of m, an integer n is divisible by another integer m if m is a divisor of n, this implies dividing n by m leaves no remainder. Under this definition, the statement m ∣0 holds for every m, as before, but with the additional constraint k ≠0. Under this definition, the statement m ∣0 does not hold for m ≠0, in the remainder of this article, which definition is applied is indicated where this is significant. Divisors can be negative as well as positive, although sometimes the term is restricted to positive divisors. For example, there are six divisors of 4, they are 1,2,4, −1, −2, and −4,1 and −1 divide every integer. Every integer is a divisor of itself, every integer is a divisor of 0. Integers divisible by 2 are called even, and numbers not divisible by 2 are called odd,1, −1, n and −n are known as the trivial divisors of n. A divisor of n that is not a divisor is known as a non-trivial divisor. A non-zero integer with at least one divisor is known as a composite number, while the units −1 and 1. There are divisibility rules which allow one to recognize certain divisors of a number from the numbers digits, the generalization can be said to be the concept of divisibility in any integral domain. 7 is a divisor of 42 because 7 ×6 =42 and it can also be said that 42 is divisible by 7,42 is a multiple of 7,7 divides 42, or 7 is a factor of 42. The non-trivial divisors of 6 are 2, −2,3, the positive divisors of 42 are 1,2,3,6,7,14,21,42. 5 ∣0, because 5 ×0 =0, if a ∣ b and b ∣ a, then a = b or a = − b. If a ∣ b and a ∣ c, then a ∣ holds, however, if a ∣ b and c ∣ b, then ∣ b does not always hold. If a ∣ b c, and gcd =1, then a ∣ c, if p is a prime number and p ∣ a b then p ∣ a or p ∣ b. A positive divisor of n which is different from n is called a proper divisor or a part of n. A number that does not evenly divide n but leaves a remainder is called an aliquant part of n, an integer n >1 whose only proper divisor is 1 is called a prime number
Divisor
–
The divisors of 10 illustrated with
Cuisenaire rods: 1, 2, 5, and 10
2.
Arithmetic
–
Arithmetic is a branch of mathematics that consists of the study of numbers, especially the properties of the traditional operations between them—addition, subtraction, multiplication and division. Arithmetic is an part of number theory, and number theory is considered to be one of the top-level divisions of modern mathematics, along with algebra, geometry. The terms arithmetic and higher arithmetic were used until the beginning of the 20th century as synonyms for number theory and are still used to refer to a wider part of number theory. The earliest written records indicate the Egyptians and Babylonians used all the elementary arithmetic operations as early as 2000 BC and these artifacts do not always reveal the specific process used for solving problems, but the characteristics of the particular numeral system strongly influence the complexity of the methods. The hieroglyphic system for Egyptian numerals, like the later Roman numerals, in both cases, this origin resulted in values that used a decimal base but did not include positional notation. Complex calculations with Roman numerals required the assistance of a board or the Roman abacus to obtain the results. Early number systems that included positional notation were not decimal, including the system for Babylonian numerals. Because of this concept, the ability to reuse the same digits for different values contributed to simpler. The continuous historical development of modern arithmetic starts with the Hellenistic civilization of ancient Greece, prior to the works of Euclid around 300 BC, Greek studies in mathematics overlapped with philosophical and mystical beliefs. For example, Nicomachus summarized the viewpoint of the earlier Pythagorean approach to numbers, Greek numerals were used by Archimedes, Diophantus and others in a positional notation not very different from ours. Because the ancient Greeks lacked a symbol for zero, they used three separate sets of symbols, one set for the units place, one for the tens place, and one for the hundreds. Then for the place they would reuse the symbols for the units place. Their addition algorithm was identical to ours, and their multiplication algorithm was very slightly different. Their long division algorithm was the same, and the square root algorithm that was taught in school was known to Archimedes. He preferred it to Heros method of successive approximation because, once computed, a digit doesnt change, and the square roots of perfect squares, such as 7485696, terminate immediately as 2736. For numbers with a part, such as 546.934. The ancient Chinese used a positional notation. Because they also lacked a symbol for zero, they had one set of symbols for the place
Arithmetic
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Arithmetic tables for children, Lausanne, 1835
Arithmetic
–
A scale calibrated in imperial units with an associated cost display.
3.
Divisors
–
In mathematics, a divisor of an integer n, also called a factor of n, is an integer m that may be multiplied by some other integer to produce n. In this case one says also that n is a multiple of m, an integer n is divisible by another integer m if m is a divisor of n, this implies dividing n by m leaves no remainder. Under this definition, the statement m ∣0 holds for every m, as before, but with the additional constraint k ≠0. Under this definition, the statement m ∣0 does not hold for m ≠0, in the remainder of this article, which definition is applied is indicated where this is significant. Divisors can be negative as well as positive, although sometimes the term is restricted to positive divisors. For example, there are six divisors of 4, they are 1,2,4, −1, −2, and −4,1 and −1 divide every integer. Every integer is a divisor of itself, every integer is a divisor of 0. Integers divisible by 2 are called even, and numbers not divisible by 2 are called odd,1, −1, n and −n are known as the trivial divisors of n. A divisor of n that is not a divisor is known as a non-trivial divisor. A non-zero integer with at least one divisor is known as a composite number, while the units −1 and 1. There are divisibility rules which allow one to recognize certain divisors of a number from the numbers digits, the generalization can be said to be the concept of divisibility in any integral domain. 7 is a divisor of 42 because 7 ×6 =42 and it can also be said that 42 is divisible by 7,42 is a multiple of 7,7 divides 42, or 7 is a factor of 42. The non-trivial divisors of 6 are 2, −2,3, the positive divisors of 42 are 1,2,3,6,7,14,21,42. 5 ∣0, because 5 ×0 =0, if a ∣ b and b ∣ a, then a = b or a = − b. If a ∣ b and a ∣ c, then a ∣ holds, however, if a ∣ b and c ∣ b, then ∣ b does not always hold. If a ∣ b c, and gcd =1, then a ∣ c, if p is a prime number and p ∣ a b then p ∣ a or p ∣ b. A positive divisor of n which is different from n is called a proper divisor or a part of n. A number that does not evenly divide n but leaves a remainder is called an aliquant part of n, an integer n >1 whose only proper divisor is 1 is called a prime number
Divisors
–
The divisors of 10 illustrated with
Cuisenaire rods: 1, 2, 5, and 10
4.
Caleb Gattegno
–
Caleb Gattegno was one of the most influential and prolific mathematics educators of the twentieth century. He is best known for his approaches to teaching and learning mathematics, foreign languages. He is also the inventor of pedagogical materials for each of these approaches, Caleb Gattegno’s pedagogical approach is characterised by propositions based on the observation of human learning in many and varied situations. This is a description of three of these propositions, Gattegno noticed that there is an “energy budget” for learning. Human beings have a developed sense of the economics of their own energy and are very sensitive to the cost involved in using it. It is therefore essential to teach in ways that are efficient in terms of the amount of energy spent by learners, to be able to mathematically determine whether one method was more efficient than another, he created a unit of measurement for the effort used to learn. He called that unit an ogden, and one can say an ogden has been spent if the learning was done outside of ordinary functionings. For example, learning one word in a foreign language costs one ogden, but if the word cannot be recalled, gattegnos teaching materials and techniques were designed to be economical with ogdens, so that the most information can be recalled with the least sense of effort. Certain kinds of learning are very expensive in terms of energy, i. e. ogdens, memorization is a very expensive way to learn. The energy cost can be high when the content is of no particular interest to the learner. Memorizing dates in history or major exports of foreign countries is like that, school is not the only place where that kind of learning is found. Learning somebodys name or telephone number is equally arbitrary and we have to use our own energy to make such arbitrary items stick in our memories. The “mental glue” necessary is expensive, since that type of learning uses up a lot of energy, not only is that type of learning expensive, it tends also to be fragile. It is typically difficult to remember those kinds of items, even when we make a great effort, we do not always succeed. We often recognise a face without being able to remember the name of the person, not to mention all that almost all of us have forgotten much of what we learned at school. It is not unusual for us to forget much of what we memorize, however, there is another way of functioning, which Gattegno called retention. An example of retention is the reception of sensory images, when we look at something – a street, a film, a person, a fine view – photons move from what we are contemplating and enter our eyes to strike the retina. When we listen to something, we create auditory images in a similar way, to retain an auditory or visual image, we have to use perhaps only an insignificant amount of our own to retain it, the amount is so small we are not aware of any effort
Caleb Gattegno
–
Caleb Gattegno
5.
Belgium
–
Belgium, officially the Kingdom of Belgium, is a sovereign state in Western Europe bordered by France, the Netherlands, Germany, Luxembourg, and the North Sea. It is a small, densely populated country which covers an area of 30,528 square kilometres and has a population of about 11 million people. Additionally, there is a group of German-speakers who live in the East Cantons located around the High Fens area. Historically, Belgium, the Netherlands and Luxembourg were known as the Low Countries, the region was called Belgica in Latin, after the Roman province of Gallia Belgica. From the end of the Middle Ages until the 17th century, today, Belgium is a federal constitutional monarchy with a parliamentary system of governance. It is divided into three regions and three communities, that exist next to each other and its two largest regions are the Dutch-speaking region of Flanders in the north and the French-speaking southern region of Wallonia. The Brussels-Capital Region is a bilingual enclave within the Flemish Region. A German-speaking Community exists in eastern Wallonia, Belgiums linguistic diversity and related political conflicts are reflected in its political history and complex system of governance, made up of six different governments. Upon its independence, declared in 1830, Belgium participated in the Industrial Revolution and, during the course of the 20th century, possessed a number of colonies in Africa. This continuing antagonism has led to several far-reaching reforms, resulting in a transition from a unitary to a federal arrangement during the period from 1970 to 1993. Belgium is also a member of the Eurozone, NATO, OECD and WTO. Its capital, Brussels, hosts several of the EUs official seats as well as the headquarters of major international organizations such as NATO. Belgium is also a part of the Schengen Area, Belgium is a developed country, with an advanced high-income economy and is categorized as very high in the Human Development Index. A gradual immigration by Germanic Frankish tribes during the 5th century brought the area under the rule of the Merovingian kings, a gradual shift of power during the 8th century led the kingdom of the Franks to evolve into the Carolingian Empire. Many of these fiefdoms were united in the Burgundian Netherlands of the 14th and 15th centuries, the Eighty Years War divided the Low Countries into the northern United Provinces and the Southern Netherlands. The latter were ruled successively by the Spanish and the Austrian Habsburgs and this was the theatre of most Franco-Spanish and Franco-Austrian wars during the 17th and 18th centuries. The reunification of the Low Countries as the United Kingdom of the Netherlands occurred at the dissolution of the First French Empire in 1815, although the franchise was initially restricted, universal suffrage for men was introduced after the general strike of 1893 and for women in 1949. The main political parties of the 19th century were the Catholic Party, French was originally the single official language adopted by the nobility and the bourgeoisie
Belgium
–
Charlemagne and
Charles V
Belgium
–
Flaga
Belgium
Belgium
–
Episode of the
Belgian Revolution of 1830 (1834), by
Egide Charles Gustave Wappers
6.
Primary school
–
A primary school or elementary school is a school in which children receive primary or elementary education from the age of about five to twelve, coming after preschool and before secondary school. In most parts of the world, primary education is the first stage of education, and is normally available without charge. The term grade school is used in the US though this term may refer to both primary education and secondary education. The term primary school is derived from the French école primaire, primary school is the preferred term in the United Kingdom and many Commonwealth Nations, and in most publications of the United Nations Educational, Scientific, and Cultural Organization. Elementary school is preferred in some countries, especially in the United States, in the United States, primary school may refer to a school with grades Kindergarten through second grade or third grade. In these municipalities, the school includes grade three through five or grades four to six
Primary school
–
A primary school in
Český Těšín,
Czech Republic
Primary school
–
A small primary school in
Norfolk,
England
Primary school
–
An elementary school in
Višňové (
Slovakia)
Primary school
–
"Michlal" Elementary school in
Ramat Gan (
Israel)
7.
Teacher
–
A teacher is a person who helps others to acquire knowledge, competences or values. Informally the role of teacher may be taken on by anyone, in some countries, teaching young people of school age may be carried out in an informal setting, such as within the family, rather than in a formal setting such as a school or college. Some other professions may involve a significant amount of teaching, in most countries, formal teaching is usually carried out by paid professional teachers. This article focuses on those who are employed, as their role, to teach others in a formal education context. A teachers role may vary among cultures, Teachers may provide instruction in literacy and numeracy, craftsmanship or vocational training, the arts, religion, civics, community roles, or life skills. Formal teaching tasks include preparing lessons according to agreed curricula, giving lessons, a teachers professional duties may extend beyond formal teaching. In some education systems, teachers may have responsibility for student discipline, Teaching is a highly complex activity. This is in part because teaching is a practice, that takes place in a specific context. Factors that influence what is expected of teachers include history and tradition, social views about the purpose of education, so the competences required by a teacher are affected by the different ways in which the role is understood around the world. Broadly, there seem to be four models, the teacher as manager of instruction, the teacher as caring person, the teacher as expert learner, some evidence-based international discussions have tried to reach such a common understanding. Scholarly consensus is emerging that what is required of teachers can be grouped under three headings, knowledge craft skills and dispositions and it has been found that teachers who showed enthusiasm towards the course materials and students can create a positive learning experience. These teachers do not teach by rote but attempt to find new invigoration for the materials on a daily basis. One of the challenges facing teachers is that they may have covered a curriculum until they begin to feel bored with the subject. Students who had enthusiastic teachers tend to rate them higher than teachers who didnt show much enthusiasm for the course materials, Teachers that exhibit enthusiasm can lead to students who are more likely to be engaged, interested, energetic, and curious about learning the subject matter. Recent research has found a correlation between teacher enthusiasm and students intrinsic motivation to learn and vitality in the classroom, students who experienced a very enthusiastic teacher were more likely to read lecture material outside of the classroom. There are various mechanisms by which teacher enthusiasm may facilitate higher levels of intrinsic motivation, teacher enthusiasm may contribute to a classroom atmosphere of energy and enthusiasm which feeds student interest and excitement in learning the subject matter. Enthusiastic teachers may also lead to becoming more self-determined in their own learning process. The concept of mere exposure indicates that the teachers enthusiasm may contribute to the expectations about intrinsic motivation in the context of learning
Teacher
–
A teacher in a classroom at a secondary school in
Pendembu,
Sierra Leone.
Teacher
–
Jewish children with their teacher in
Samarkand, the beginning of the 20th century.
Teacher
–
A teacher of a Latin school and two students, 1487
Teacher
–
Dutch schoolmaster and children, 1662
8.
Maria Montessori
–
Maria Tecla Artemisia Montessori was an Italian physician and educator best known for the philosophy of education that bears her name, and her writing on scientific pedagogy. Her educational method is in use today in public and private schools throughout the world. Montessori was born on August 31,1870 in Chiaravalle, Italy and her father, Alessandro Montessori,33 years old at the time, was an official of the Ministry of Finance working in the local state-run tobacco factory. Her mother, Renilde Stoppani,25 years old, was educated for the times and was the great-niece of Italian geologist and paleontologist Antonio Stoppani. While she did not have any particular mentor, she was close to her mother who readily encouraged her. She also had a relationship with her father, although he disagreed with her choice to continue her education. The Montessori family moved to Florence in 1873 and then to Rome in 1875 because of her fathers work, Montessori entered a public elementary school at the age of 6 in 1876. Her early school record was not particularly noteworthy, although she was awarded certificates for good behavior in the 1st grade and for lavori donneschi, or womens work and she graduated in 1886 with good grades and examination results. She did well in the sciences and especially in mathematics and she initially intended to pursue the study of engineering upon graduation, an unusual aspiration for a woman in her time and place. Montessori moved forward with her intention to study medicine and she appealed to Guido Baccelli, the professor of clinical medicine at the University of Rome, but was strongly discouraged. This degree, along with studies in Italian and Latin. She was met with hostility and harassment from some medical students, because her attendance of classes with men in the presence of a naked body was deemed inappropriate, she was required to perform her dissections of cadavers alone, after hours. She resorted to smoking tobacco to mask the odor of formaldehyde. Montessori won a prize in her first year, and in 1895 secured a position as a hospital assistant. In her last two years she studied pediatrics and psychiatry, and worked in the consulting room and emergency service. Montessori graduated from the University of Rome in 1896 as a doctor of medicine and her thesis was published in 1897 in the journal Policlinico. She found employment as an assistant at the University hospital and started a private practice. )From 1896 to 1901, Montessori worked with and researched so-called phrenasthenic children—in modern terms, children experiencing some form of mental retardation, illness, or disability. She also began to travel, study, speak, and publish nationally and internationally, coming to prominence as an advocate for womens rights, on 31 March 1898, her only child – a son named Mario Montessori was born
Maria Montessori
–
Maria Montessori
Maria Montessori
–
Italian 1000 Lire banknote (approx. 0.52 €) representing Maria Montessori.
9.
Thuin
–
Thuin or ) is a Walloon municipality located in the Belgian province of Hainaut. The Thuin municipality includes the old communes of Leers-et-Fosteau, Biesme-sous-Thuin, Ragnies, Biercée, Gozée, Donstiennes and this area was already used as a burial place in Gallo-Roman times, around the 2nd and 3rd century. The village was a possession of the abbey of Lobbes and, together with the abbey, the neighbouring Aulne Abbey, reputedly founded in the 7th century by Landelin, a repentant robber, was also made part of the Bishopric of Liège. A century later, Prince-Bishop Notger had a wall built in Thuin. In the following centuries, several took place in this frontier area. In 1048, Adalbert, Duke of Lorraine was killed at the Battle of Thuin by Godfrey III, many more battles followed between the County of Hainaut and the Bishopric of Liège, with Thuin caught in between. Despite the stronger defensive walls that were built in the 12th century and in the 15th century, the Aulne Abbey, which had been given to Saint Bernard of Clairvaux in 1147 fared better and was even expanded several times in the 16th and 18th century. In 1654, the Spanish army under the Prince of Condé tried in vain to take Thuin, the good fortunes of the city were attributed to the intercession of Saint Roch, who is still commemorated in the annual St-Roch procession. Several 17th-century buildings, including the belfry, can still be today in the upper city. In 1675, the troops of Louis XIV took and occupied Thuin until the Treaty of Nijmegen in 1678, like its neighbour Charleroi, Thuin went in turn to Spain and Austria. On May 10,1794, during the French Revolutionary Wars, General Marceau expelled the Austrians, the Aulne Abbey was burned to the ground. In 1829, on the eve of the Belgian Revolution, William II of the Netherlands was welcomed in Thuin, to no avail. The last major fighting around Thuin occurred on August 23,1914, at the onset of World War I. The Belfry of Thuin, dating from the 17th century, has named a World Heritage Site by UNESCO. A splendid view on the Thuin area can be seen from the top, Thuin is the location of the ASVi museum, specialising in the history of the Belgian Vicinal tramway system. This includes a museum tramway that runs through the streets of the town, the charming “hanging gardens” on the southern flank of the Thuin hill can be visited on foot, following a path enhanced by several explanation signs. The 7th-century Aulne Abbey, now in ruins, and its setting are well worth a visit. The neighbouring village of Ragnies, also mentioned in the Lobbes offering, is a member of the most beautiful villages of Wallonia association, the Château du Fosteau dates from the 14th and 15th century
Thuin
–
The old city and the belfry
10.
Student-centred learning
–
Student-centered learning, also known as learner-centered education, broadly encompasses methods of teaching that shift the focus of instruction from the teacher to the student. In original usage, student-centered learning aims to develop learner autonomy, student-centered instruction focuses on skills and practices that enable lifelong learning and independent problem-solving. Student-centered learning puts students interests first, acknowledging student voice as central to the learning experience, in a student-centered learning space, students choose what they will learn, how they will learn, and how they will assess their own learning. This is in contrast to education, also dubbed teacher-centered learning. In a teacher-centered classroom, teachers choose what the students learn, how the students will learn. In contrast, student-centered learning requires students to be active, responsible participants in their own learning, usage of the term student-centered learning may also simply refer to educational mindsets or instructional methods that recognize individual differences in learners. Theorists like John Dewey, Jean Piaget, and Lev Vygotsky, carl Rogers ideas about the formation of the individual also contributed to student-centered learning. Rogers wrote that the only learning which significantly influences behavior is self discovered, maria Montessori was also a forerunner of student-centered learning, where preschool children learn through independent self-directed interaction with previously presented activities. Self-determination theory focuses on the degree to which a behavior is self-motivated and self-determined. When students are given the opportunity to gauge their learning, learning becomes an incentive, student-centered learning means inverting the traditional teacher-centered understanding of the learning process and putting students at the centre of the learning process. In the teacher-centered classroom, teachers are the source for knowledge. On the other hand, in student-centered classrooms, active learning is strongly encouraged, armstrong claimed that traditional education ignores or suppresses learner responsibility. A further distinction from a classroom to that of a student-centered classroom is when the teacher acts as a facilitator. Through peer-to-peer interaction, collaborative thinking can lead to an abundance of knowledge, in placing a teacher closer to a peer level, knowledge and learning is enhanced, benefitting the student and classroom overall. According to Lev Vygotskys theory of the zone of proximal development, scaffolding is important when fostering independent thinking skills. Vygotsky proclaims, Learning which is oriented toward developmental levels that have already been reached is ineffective from the viewpoint of the overall development. It does not aim for a new stage of the developmental process, one of the most critical differences between student-centered learning and teacher-centered learning is in assessment. Student-centered learning typically involves more formative assessment and less summative assessment than teacher-centered learning, in student-centered learning, students participate in the evaluation of their learning
Student-centred learning
–
Student-centered learning theorist Carl Rogers
Student-centred learning
–
A student-centered class at
Shimer College
11.
Reading, England
–
Reading is a large, historically important town in Berkshire, England, of which it is the county town. The 19th century saw the coming of the Great Western Railway, Today Reading is a major commercial centre, with involvement in information technology and insurance, and, despite its proximity to London, has a net inward commuter flow. The first evidence for Reading as a settlement dates from the 8th century, by 1525, Reading was the largest town in Berkshire, and tax returns show that Reading was the 10th largest town in England when measured by taxable wealth. By 1611, it had a population of over 5000 and had grown rich on its trade in cloth, the 18th century saw the beginning of a major iron works in the town and the growth of the brewing trade for which Reading was to become famous. During the 19th century, the town rapidly as a manufacturing centre. It is ranked the UKs top economic area for economic success and wellbeing, according to such as employment, health, income. Reading is also a regional retail centre serving a large area of the Thames Valley. Every year it hosts the Reading Festival, one of Englands biggest music festivals, sporting teams based in Reading include Reading Football Club and the London Irish rugby union team, and over 15,000 runners annually compete in the Reading Half Marathon. In 2015, Reading had an population of 232,662. The town is represented in Parliament by two members, and has been continuously represented there since 1295, for ceremonial purposes the town is in the county of Berkshire and has served as its county town since 1867, previously sharing this status with Abingdon-on-Thames. It is in the Thames Valley at the confluence of the River Thames and River Kennet, and on both the Great Western Main Line railway and the M4 motorway. Reading is 75 miles east of Bristol,25 miles south of Oxford,42 miles west of London,17 miles north of Basingstoke,13 miles south-west of Maidenhead and 20 miles east of Newbury. Reading may date back to the Roman occupation of Britain, possibly as a port for Calleva Atrebatum. However the first clear evidence for Reading as a settlement dates from the 8th century, the name probably comes from the Readingas, an Anglo-Saxon tribe whose name means Readas People in Old English, or less probably the Celtic Rhydd-Inge, meaning Ford over the River. In late 870, an army of Danes invaded the kingdom of Wessex, on 4 January 871, in the first Battle of Reading, King Ethelred and his brother Alfred the Great attempted unsuccessfully to breach the Danes defences. The battle is described in the Anglo-Saxon Chronicle, and that account provides the earliest known record of the existence of Reading. The Danes remained in Reading until late in 871, when they retreated to their quarters in London. After the Battle of Hastings and the Norman conquest of England, William the Conqueror gave land in, in its 1086 Domesday Book listing, the town was explicitly described as a borough
Reading, England
–
From top left: the
Town Hall and
St Laurence's Church, the
Maiwand Lion, the Town Centre skyline from the
Royal Berkshire Hospital,
Reading Abbey and
The Oracle
Reading, England
–
The earliest map of Reading, published in 1611 by
John Speed
Reading, England
–
View of Reading from
Caversham by
Joseph Farington in 1793
Reading, England
–
Reading
Crown Court
12.
New Zealand
–
New Zealand /njuːˈziːlənd/ is an island nation in the southwestern Pacific Ocean. The country geographically comprises two main landmasses—the North Island, or Te Ika-a-Māui, and the South Island, or Te Waipounamu—and around 600 smaller islands. New Zealand is situated some 1,500 kilometres east of Australia across the Tasman Sea and roughly 1,000 kilometres south of the Pacific island areas of New Caledonia, Fiji, because of its remoteness, it was one of the last lands to be settled by humans. During its long period of isolation, New Zealand developed a distinct biodiversity of animal, fungal, the countrys varied topography and its sharp mountain peaks, such as the Southern Alps, owe much to the tectonic uplift of land and volcanic eruptions. New Zealands capital city is Wellington, while its most populous city is Auckland, sometime between 1250 and 1300 CE, Polynesians settled in the islands that later were named New Zealand and developed a distinctive Māori culture. In 1642, Dutch explorer Abel Tasman became the first European to sight New Zealand, in 1840, representatives of Britain and Māori chiefs signed the Treaty of Waitangi, which declared British sovereignty over the islands. In 1841, New Zealand became a colony within the British Empire, today, the majority of New Zealands population of 4.7 million is of European descent, the indigenous Māori are the largest minority, followed by Asians and Pacific Islanders. Reflecting this, New Zealands culture is derived from Māori and early British settlers. The official languages are English, Māori and New Zealand Sign Language, New Zealand is a developed country and ranks highly in international comparisons of national performance, such as health, education, economic freedom and quality of life. Since the 1980s, New Zealand has transformed from an agrarian, Queen Elizabeth II is the countrys head of state and is represented by a governor-general. In addition, New Zealand is organised into 11 regional councils and 67 territorial authorities for local government purposes, the Realm of New Zealand also includes Tokelau, the Cook Islands and Niue, and the Ross Dependency, which is New Zealands territorial claim in Antarctica. New Zealand is a member of the United Nations, Commonwealth of Nations, ANZUS, Organisation for Economic Co-operation and Development, Pacific Islands Forum, and Asia-Pacific Economic Cooperation. Dutch explorer Abel Tasman sighted New Zealand in 1642 and called it Staten Landt, in 1645, Dutch cartographers renamed the land Nova Zeelandia after the Dutch province of Zeeland. British explorer James Cook subsequently anglicised the name to New Zealand, Aotearoa is the current Māori name for New Zealand. It is unknown whether Māori had a name for the country before the arrival of Europeans. Māori had several names for the two main islands, including Te Ika-a-Māui for the North Island and Te Waipounamu or Te Waka o Aoraki for the South Island. Early European maps labelled the islands North, Middle and South, in 1830, maps began to use North and South to distinguish the two largest islands and by 1907, this was the accepted norm. The New Zealand Geographic Board discovered in 2009 that the names of the North Island and South Island had never been formalised and this set the names as North Island or Te Ika-a-Māui, and South Island or Te Waipounamu
New Zealand
–
The Waitangi sheet from the
Treaty of Waitangi
New Zealand
–
Flag
New Zealand
–
Painting of
Mount Earnslaw by John Turnbull Thomson, oil on canvas, 1888
New Zealand
–
John Key,
Prime Minister of New Zealand since 2008
13.
Michael Parekowhai
–
Michael Te Rakato Parekowhai is a New Zealand sculptor and a professor at University of Aucklands Elam School of Fine Arts. He is of Ngā Ariki Kaiputahi, Ngāti Whakarongo and Pākehā descent, Parekowhai was awarded an Arts Foundation of New Zealand Laureate Award in 2001. In 2011 he represented New Zealand at the Venice Biennale and he spent his childhood and attended school in Aucklands North Shore suburbs. After leaving high school, Parekowhai worked as an assistant before commencing his BFA at University of Aucklands Elam School of Fine Arts. He trained as an art teacher, before returning to Elam to complete his MFA. With the diligence of a cultural props person, he appropriates the already appropriated in a manner that is often humorous, despite the range of Parekowhais output, his practice is linked throughout, both stylistically – a characteristic gloss of high production value – and thematically. Curator Justin Paton writes of Parekowhai, They have a way of sneaking up on you, pick-up sticks swollen to the size of spears. A photograph of a rabbit who has you in his sights. A silky bouquet that rustles with politics, seemingly serene beneath their gleaming, factory-finished surfaces, Michael Parekowhais sculptures and photographs are in fact supremely artful objects. Artful not just because theyre beautifully made. but also because they manage, with a combination of slyness, charm and audacity, the World Turns – a life-sized bronze elephant tipped on its head and eye-to-eye with a kuril, commissioned by the Queensland Gallery of Modern Art. He Kōrero Pūrākau mo Te Awanui o Te Motu, story of a New Zealand river – an original Steinway grand piano covered in glossy red carvings. The piano is played at each of the exhibitions that it features in, for example in the 2012 Te Papa exhibition with works from Colin McCahon and Jim Allen. 2013 The Past in the Present, Michael Lett at the Auckland Art Fair, Auckland 2012 On First Looking into Chapman’s Homer, Christchurch Art Gallery Te Puna o Waiwhetu, also at Museum of New Zealand Te Papa Tongarewa 2011 54th Venice Biennale New Zealand Pavilion. Also at Waikato Museum of Art and History, Hamilton,1994 A Capella, Greg Flint Gallery, Auckland 1990 Choice. Premier of Queensland Sculpture Commission, Queensland, Australia,2011, nga Toa Whahaihuwaka, Māori of the Year for Arts,2011. Barfoot & Thompson, 90th Anniversary Gift to Auckland City, Waterfront Commission,2013. ‘Top 50 Public Art Project’ awarded by Americans for the Arts, Public Art Network,2013 Year in Review, for Blue Stratus, Phoenix Sky Harbor International Airport, Arizona, Parekowhais work is held in most New Zealand public gallery collections and a number of international museums. Michael Parekowhai, the land, Brisbane, Queensland Art Gallery,2015
Michael Parekowhai
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On First Looking into Chapmans Homer
Michael Parekowhai
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The World Turns
14.
Foreign language teaching
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Language education refers to the process and practice of acquiring a second or foreign language. It primarily is a branch of applied linguistics, however can be considered an interdisciplinary field, there are four main learning categories for language education, communicative competencies, proficiencies, cross-cultural experiences, and multiple literacies. Increasing globalization has created a large need for people in the workforce who can communicate in multiple languages, the uses of common languages are in areas such as trade, tourism, international relations, technology, media, and science. Many countries such as Korea, Japan and China frame education policies to teach at least one language at the primary and secondary school levels. However, some such as India, Singapore, Malaysia, Pakistan. According to GAO, China has recently been putting enormous importance on foreign language learning, although the need to learn foreign languages is older than human history itself, the origins of modern language education are in the study and teaching of Latin in the 17th century. John Amos Comenius was one of people who tried to reverse this trend. He composed a complete course for learning Latin, covering the school curriculum. In this work, Comenius also outlined his theory of language acquisition and he is one of the first theorists to write systematically about how languages are learned and about pedagogical methodology for language acquisition. He held that language acquisition must be allied with sensation and experience, the schoolroom should have models of things, and failing that, pictures of them. As a result, he published the worlds first illustrated childrens book. The study of Latin diminished from the study of a language to be used in the real world to a subject in the school curriculum. Such decline brought about a new justification for its study and it was then claimed that its study developed intellectual abilities, and the study of Latin grammar became an end in and of itself. Grammar schools from the 16th to 18th centuries focused on teaching the grammatical aspects of Classical Latin, advanced students continued grammar study with the addition of rhetoric. The study of modern languages did not become part of the curriculum of European schools until the 18th century, based on the purely academic study of Latin, students of modern languages did much of the same exercises, studying grammatical rules and translating abstract sentences. Oral work was minimal, and students were required to memorize grammatical rules. This tradition-inspired method became known as the grammar-translation method, innovation in foreign language teaching began in the 19th century and became very rapid in the 20th century. It led to a number of different and sometimes conflicting methods, the earliest applied linguists included Jean Manesca, Heinrich Gottfried Ollendorff, Henry Sweet, Otto Jespersen, and Harold Palmer
Foreign language teaching
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Henry Sweet was a key figure in establishing the
applied linguistics tradition in language teaching
Foreign language teaching
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High school Spanish taught as a second
language to a class of native
English speakers at an
American private school in
Massachusetts.
15.
The Silent Way
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The Silent Way is a language-teaching method created by Caleb Gattegno that makes extensive use of silence as a teaching method. Gattegno introduced the method in 1963, in his book Teaching Foreign Languages in Schools, Gattegno was critical of mainstream language education at the time, and he based the method on his general theories of education rather than on existing language pedagogy. The method emphasizes learner autonomy and active student participation, pronunciation is seen as fundamental to the method, with a great deal of time spent on it each lesson. The Silent Way uses a structural syllabus and concentrates on teaching a number of functional. Translation and rote repetition are avoided, and the language is usually practiced in meaningful contexts, evaluation is carried out by observation, and the teacher may never set a formal test. One of the hallmarks of the Silent Way is the use of Cuisenaire rods, while the Silent Way is not widely used in its original form, its ideas have been influential, especially in the teaching of pronunciation. Gattegno was an outsider to language education when Teaching Foreign Languages in Schools was first published in 1963 and he was previously a designer of mathematics and reading programmes, and the use of color charts and colored Cuisenaire rods in the Silent Way grew directly out of this experience. Gattegno was openly sceptical of the role the linguistic theory of his time had in language teaching and he felt that linguistic studies may be a specialization, carry with them a narrow opening of ones sensitivity and perhaps serve very little towards the broad end in mind. The general goal of the Silent Way is to help students gain basic fluency in the target language, with the ultimate aim being near-native language proficiency. An important part of this ability is being able to use the language for self-expression, students should be able to express their thoughts, feelings, in order to help them achieve this, teachers emphasize self-reliance. Students are encouraged to explore the language, and to develop their own inner criteria as to what is linguistically acceptable. The role of the teacher is that of technician or engineer, as Gattegno says, The teacher works with the student, the student works on the language. For example, teachers will give students time to correct their own mistakes before giving them the answer to a question. Teachers also avoid praise or criticism, as it can discourage students from developing self-reliance, in the Silent Way students are seen as bringing a vast amount of experience and knowledge with them to the classroom, namely, their first language. The teacher capitalizes on this knowledge when introducing new material, always building from the known to the unknown, the students begin their study of the language by studying its sound system. The sounds are associated to different colors using a chart that is specific to the language being learned. The teacher first elicits sounds that are present in the students native language. These sound-color associations are later used to help the students with spelling, reading, the Silent Way uses a structural syllabus
The Silent Way
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A Spanish lesson in
Guadalajara, Mexico, taught using the Silent Way.
The Silent Way
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Caleb Gattegno, creator of the Silent Way.
The Silent Way
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Gattegno's original sound-color chart for English. This type of chart is used right from the beginning stages to teach pronunciation and
word stress.
The Silent Way
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A set of Cuisenaire rods
16.
Preposition
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Prepositions and postpositions, together called adpositions, are a class of words that express spatial or temporal relations or mark various semantic roles. A preposition or postposition typically combines with a noun or pronoun, or more generally a noun phrase, a preposition comes before its complement, a postposition comes after its complement. Some languages, which use a different word order, have postpositions instead, the phrase formed by a preposition or postposition together with its complement is called a prepositional phrase – such phrases usually play an adverbial role in a sentence. A less common type of adposition is the circumposition, which consists of two parts that appear on side of the complement. Other terms sometimes used for types of adposition include ambiposition, inposition and interposition. Some linguists use the preposition in place of adposition regardless of the applicable word order. The word preposition comes from Latin, prae and Latin, ponere and this refers to the situation in Latin and Greek, where such words are placed before their complement, and are hence pre-positioned. In some languages, including Sindhi, Urdu, Turkish, Hindi, Korean, and Japanese, to indicate this, they are called postpositions. There are also cases where the function is performed by two parts coming before and after the complement, this is called a circumposition. Prepositions, postpositions and circumpositions are collectively known as adpositions, however, some linguists prefer to use the well-known and longer established term preposition in place of adposition, irrespective of position relative to the complement. An adposition typically combines with exactly one complement, most often a noun phrase, in English, this is generally a noun, together with its specifier and modifiers such as articles, adjectives, etc. The complement is called the object of the adposition. The resulting phrase, formed by the adposition together with its complement, is called a phrase or prepositional phrase. An adposition establishes a relationship that links its complement to another word or phrase in the context. It also generally establishes a relationship, which may be spatial, temporal. Some examples of the use of English prepositions are given below, in each case, the prepositional phrase appears in italics, and the preposition within it appears in bold. The word to which the phrase expresses a relation – that is, in some of the examples, the same word has two prepositional phrases as adjuncts. As an adjunct to a noun, the weather in March cheese from France with live bacteria As a predicative expression The key is under the stone, prepositional phrases themselves are sometimes nominalized, In the cellar was chosen as the best place to hide the bodies
Preposition
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Adjectives
17.
Number line
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In basic mathematics, a number line is a picture of a graduated straight line that serves as abstraction for real numbers, denoted by R. Every point of a line is assumed to correspond to a real number. Often the integers are shown as specially-marked points evenly spaced on the line, although this image only shows the integers from −9 to 9, the line includes all real numbers, continuing forever in each direction, and also numbers not marked that are between the integers. It is often used as an aid in teaching simple addition and subtraction, a number line is usually represented as being horizontal, but in a Cartesian coordinate plane the vertical axis is also a number line. Another convention uses only one arrowhead which indicates the direction in which numbers grow, if a particular number is farther to the right on the number line than is another number, then the first number is greater than the second. The distance between them is the magnitude of their difference—that is, it measures the first number minus the second one, taking this difference is the process of subtraction. Thus, for example, the length of a segment between 0 and some other number represents the magnitude of the latter number. Two numbers can be added by picking up the length from 0 to one of the numbers and this gives a result that is 3 combined lengths of 5 each, since the process ends at 15, we find that 5 ×3 =15. This puts the right end of the length 2 at the end of the length from 0 to 6. Since three lengths of 2 filled the length 6,2 goes into 6 three times, the section of the number line between two numbers is called an interval. If the section includes both numbers it is said to be an interval, while if it excludes both numbers it is called an open interval. If it includes one of the numbers but not the other one, all the points extending forever in one direction from a particular point are together known as a ray. If the ray includes the point, it is a closed ray. Sometimes it is convenient to scale the numbers on the line with a logarithmic scale. This approach is useful, for example, in illustrating a sequence of events in the history of the universe or of evolution, a line drawn through the origin at right angles to the real number line can be used to represent the imaginary numbers. This line, called line, extends the number line to a complex number plane. Together these lines form what is known as the Cartesian coordinate system, further, the Cartesian coordinate system can itself be extended by visualizing a third number line coming out of the screen, measuring a third variable called z. Positive numbers are closer to the eyes than the screen is, while negative numbers are behind the screen
Number line
18.
International Standard Book Number
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The International Standard Book Number is a unique numeric commercial book identifier. An ISBN is assigned to each edition and variation of a book, for example, an e-book, a paperback and a hardcover edition of the same book would each have a different ISBN. The ISBN is 13 digits long if assigned on or after 1 January 2007, the method of assigning an ISBN is nation-based and varies from country to country, often depending on how large the publishing industry is within a country. The initial ISBN configuration of recognition was generated in 1967 based upon the 9-digit Standard Book Numbering created in 1966, the 10-digit ISBN format was developed by the International Organization for Standardization and was published in 1970 as international standard ISO2108. Occasionally, a book may appear without a printed ISBN if it is printed privately or the author does not follow the usual ISBN procedure, however, this can be rectified later. Another identifier, the International Standard Serial Number, identifies periodical publications such as magazines, the ISBN configuration of recognition was generated in 1967 in the United Kingdom by David Whitaker and in 1968 in the US by Emery Koltay. The 10-digit ISBN format was developed by the International Organization for Standardization and was published in 1970 as international standard ISO2108, the United Kingdom continued to use the 9-digit SBN code until 1974. The ISO on-line facility only refers back to 1978, an SBN may be converted to an ISBN by prefixing the digit 0. For example, the edition of Mr. J. G. Reeder Returns, published by Hodder in 1965, has SBN340013818 -340 indicating the publisher,01381 their serial number. This can be converted to ISBN 0-340-01381-8, the check digit does not need to be re-calculated, since 1 January 2007, ISBNs have contained 13 digits, a format that is compatible with Bookland European Article Number EAN-13s. An ISBN is assigned to each edition and variation of a book, for example, an ebook, a paperback, and a hardcover edition of the same book would each have a different ISBN. The ISBN is 13 digits long if assigned on or after 1 January 2007, a 13-digit ISBN can be separated into its parts, and when this is done it is customary to separate the parts with hyphens or spaces. Separating the parts of a 10-digit ISBN is also done with either hyphens or spaces, figuring out how to correctly separate a given ISBN number is complicated, because most of the parts do not use a fixed number of digits. ISBN issuance is country-specific, in that ISBNs are issued by the ISBN registration agency that is responsible for country or territory regardless of the publication language. Some ISBN registration agencies are based in national libraries or within ministries of culture, in other cases, the ISBN registration service is provided by organisations such as bibliographic data providers that are not government funded. In Canada, ISBNs are issued at no cost with the purpose of encouraging Canadian culture. In the United Kingdom, United States, and some countries, where the service is provided by non-government-funded organisations. Australia, ISBNs are issued by the library services agency Thorpe-Bowker
International Standard Book Number
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A 13-digit ISBN, 978-3-16-148410-0, as represented by an
EAN-13 bar code
19.
Associated Press
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The Associated Press is an American multinational nonprofit news agency headquartered in New York City that operates as a cooperative, unincorporated association. The AP is owned by its contributing newspapers and radio and television stations in the United States, all of which stories to the AP. Most of the AP staff are members and are represented by the Newspaper Guild, which operates under the Communications Workers of America. As of 2007, news collected by the AP was published and republished by more than 1,700 newspapers, in addition to more than 5,000 television, the photograph library of the AP consists of over 10 million images. The AP operates 243 news bureaus in 120 countries and it also operates the AP Radio Network, which provides newscasts twice hourly for broadcast and satellite radio and television stations. Many newspapers and broadcasters outside the United States are AP subscribers, as part of their cooperative agreement with the AP, most member news organizations grant automatic permission for the AP to distribute their local news reports. The AP employs the inverted pyramid formula for writing that enables the news outlets to edit a story to fit its available publication area without losing the storys essentials. Cutbacks at rival United Press International in 1993 left the AP as the United States primary news service, although UPI still produces and distributes stories and photos daily. Other English-language news services, such as the BBC, Reuters, some historians believe that the Tribune joined at this time, documents show it was a member in 1849. The New York Times became a member shortly after its founding in September 1851, initially known as the New York Associated Press, the organization faced competition from the Western Associated Press, which criticized its monopolistic news gathering and price setting practices. The revelations led to the demise of the NYAP and in December 1892, when the AP was founded, news became a salable commodity. The invention of the press allowed the New York Tribune in the 1870s to print 18,000 papers per hour. During the Civil War and Spanish–American War, there was a new incentive to print vivid, Melville Stone, who had founded the Chicago Daily News in 1875, served as AP General Manager from 1893 to 1921. He embraced the standards of accuracy, impartiality, and integrity, the cooperative grew rapidly under the leadership of Kent Cooper, who built up bureau staff in South America, Europe and, the Middle East. He introduced the telegraph typewriter or teletypewriter into newsrooms in 1914, in 1935, AP launched the Wirephoto network, which allowed transmission of news photographs over leased private telephone lines on the day they were taken. This gave AP a major advantage over other media outlets. While the first network was only between New York, Chicago, and San Francisco, eventually AP had its network across the whole United States, in 1945, the Supreme Court of the United States held in Associated Press v. The decision facilitated the growth of its main rival United Press International, AP entered the broadcast field in 1941 when it began distributing news to radio stations, it created its own radio network in 1974
Associated Press
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The AP headquarters in October 2008, located at
450 West 33rd Street, in
New York City.
Associated Press
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Associated Press
Associated Press
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Logo on the former AP Building in New York City
Associated Press
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The APTN Building in London
