Учебно-методическое пособие для студентов I-II курсов заочного отделения неязыковых факультетов (стр. 9 из 12)
Others simply conclude that Americans simply like sports activities and always have. They like to play a friendly game of softball at family picnics, and "touch football" (no tackling!) games can get started on beaches and in parks whenever a few young people come together. "Shooting baskets" with friends is a favourite way to pass the time, either in a friend's driveway (the basket is over the garage door) or on some city or neighbourhood court. And on a beautiful autumn afternoon - the sun shining in a clear blue sky, the maple trees turning scarlet and the oaks a golden yellow - it is fun to go with friends to a football game. And go they do.
An average of more than 100,000 people attend each of the University of Michigan's football games. Ohio State University, located only about 150 miles away, has had its Saturday games sold out for years (an average of almost 90,000 per game). Back East, Harvard and Yale "only" attract an average of about 20,000 fans each. Altogether, there are over 600 university and college football teams playing most Saturdays across the nation.
Among the 30 (as of 1995) professional National Football League (NFL) teams, the average number of fans attending each game is over 62,000. And, of course, there are the millions watching the game on TV By tradition there are always many parties which follow football games, win or lose, and these are especially popular at universities. Some critics say that among the millions of those attending football games there are many who think it's the first part of the party (and our research shows that this might be correct). Friends and relatives often come together to spend a Sunday having drinks, barbecuing, and, yes, watching a game or two. But with or without parties, Americans do like their sports, for whatever reason you care to choose.
The money earned by some professional athletes does not seem so impressive when one thinks that only a very few of the best will ever make it to a professional team. And once there, at best they will only have a few years to play, even in baseball and basketball. They know that they will soon be replaced by someone who is younger, faster, bigger, or better. Professional players’ organisations are therefore very concerned with such things as retirement benefits and pensions. More and more, they are also concerned with getting a good education, with acquiring university-level skills that will allow them to find good jobs when their playing days are over". Increasingly, universities and sports officials have enforced rules which require athletes to be properly enrolled in academic programs in order to qualify for a university team. Rules which state that all college athletes must meet set academic standards have long been accepted. If the students do not meet them, they are not allowed to take part in sports.
TERM IY
THE FACULTY OF PRIMARY SCHOOLING
THE FACULTY OF PRE-SCHOOL PSYCHOLOGY AND PEDAGOGICS
Standards
Those who believe that American schools are more play than work overlook an important fact: a high school diploma is not a ticket that allows someone to automatically enter a university. Standardised examinations play a decisive role at almost every level of education, especially in the admission to colleges and universities. Students who wish to go to a good university but only took high school courses that were a "snap," or who spent too much time on extracurricular activities, will have to compete with those who worked hard and took demanding courses.
There are two widely used and nationally administered standardised tests for high school students who wish to attend a college or university. One is the SAT (Scholastic Aptitude Test), which attempts to measure aptitudes in verbal and mathematical fields necessary for college work. The other is the ACT (American College Testing program), which attempts to measure skills in English, mathematics, and the social and natural sciences. Both tests are given at specific dates and locations throughout the U.S. by nongovernmental organisations. The tests are used by universities as standards for comparison, but are not in any way "official."
Each year, the SAT is taken by some two million high school students. One million of these students are in their last year of high school. Another million are in their next-to-last year. The ACT, more commonly used in the western part of the U.S., is taken each year by another million high school students. With so many different types of high schools and programs, with so many differences in subjects and standards, these tests provide common, nation-wide measuring sticks. Many universities publish the average scores achieved on these tests by the students they admit. This indicates the "quality" or level of ability expected of those who apply.Similar testing programs exist at higher levels, as well. Someone who has already finished four years of university and wishes to go to a law or medical school is also required to take standardised tests. These tests have been agreed upon by the various law and medical schools and are administered nation-wide at scheduled times. Like the SAT or ACT, these tests are not official or governmentally controlled. Other examinations, however, are official and usually quite difficult. For example, even after someone has studied for many years and earned a medical degree from a university, this still does not mean that he or she can begin to practice in the U.S. The individual states require still further examinations.
The United States Educational Structure
Other pressures also operate at the university level. Most universities require mid-semester and final (end-of-semester) examinations. It is possible, as a great many students have learned, to "flunk out" of a university that is to be asked to leave because of poor grades. And most students who have scholarships must maintain a certain grade average to keep their scholarships.
Since tuition fees alone can be rather high (ranging from some $20,000 for an academic year at Harvard, Yale or Stanford to under $ 1,000 at small public institutions) at most colleges and universities, a large number of students hold jobs besides studying. These part-time jobs may be either "on campus" (in the dormitories, cafeterias, students services, in research, and in teaching and tutoring jobs) or "off campus" (with local firms and businesses, in offices, etc.). In this way, for example, more than half of all students at Stanford University earn a significant part of their college expenses during the school year. In addition, there are work-study programs at a number of universities, and financial assistance programs, which are provided by the states and the federal government. At Michigan State University, for instance, 50 percent of all students receive some form of financial aid through the university, and 85 percent of undergraduate students worked part-time on campus during the academic year 1991-92. At Harvard, 74 percent of beginning students ("freshmen") and 61 percent of continuing students received financial aid in the 1991 -92 academic year. The average award for the 66 percent of beginning students receiving aid at Stanford was $13,600 per year. Students who must work as well as study are the rule rather than the exception. Students also cannot simply move from one university to another, or trade places with other students. Before changing to another university, students must first have been accepted by the new university and have met that university's admission requirements.
The competition and pressures at many universities, especially at the higher, graduate levels, are not pleasant. Nor are they evident in the popular picture of campus life. However, this system has been highly successful in producing scholars who are consistently at the top or near the top of their fields internationally. One indication of this can be seen by looking at the textbooks or professional journals used and read in foreign universities and noting the authors, where they teach and where they were trained. Another indication, less precise perhaps, is the number of Americans who have won Nobel Prizes. Americans have won 168 Nobel Prizes in the science alone-physics, chemistry, and physiology or medicine - since the awards were first given in 1901. This represents over 40 percent of all recipients. The next closest country is Great Britain, with 69 Nobel Prizes. If most Americans are very critical of their educational system at the elementary and secondary school levels, many will also admit that their higher education system is "in many respects, the best in the world."
Reform and Progress
A major conflict has always existed between two goals of American education. One is the comprehensive, egalitarian education with the goal of providing equal opportunity. The other is the highly selective educational emphasis that aims at excellence and the training of academic and scientific elite. Some Americans feel that more money and efforts should be spent on improving comprehensive education. Others think that more money should be provided for increasing scientific knowledge and maintaining America's position in technology and research. And some people, of course, demand that more money be spent on both.
A series of studies in the 1980s criticised American public schools. As a result, better training and payment for teachers has been advocated and more stress has been placed on academic subjects. But striking a balance between a comprehensive, egalitarian education and one of specialisation and excellence has always been a difficult task, and is likely to remain so.
Schools and universities have also been asked to do more and more to help with, or even cure, certain social and economic problems, from the effects of divorce to drug problems, from learning disabilities to malnutrition. Most school systems not only have lunchrooms or cafeterias, they also offer to give free or low-cost meals, sometimes including breakfast, to needy pupils. They also employ psychologists, nurses, staff trained to teach the handicapped, reading specialists, and academic as well as guidance and employment counsellors. Because of their traditional ties with the communities, schools are expected to be involved in many such areas. There is a growing belief among some Americans that the public schools cannot really handle all such social problems, even if enough money were available where it is most needed.
Examining Schools
One of the major markers of education in America - and one that is often noted by observers abroad - is the degree of constant self-examination. In the U.S. today, when pupils and students are tested, so, in effect, are their teachers, the curricula, the schools and universities, and the entire set of systems.
Each year hundreds of research studies are published which critically examine the nation's schools. Most of the large school districts employ full-time educational researchers. Almost all of the universities have departments for educational research and measurement. And, of course, there are many public and private institutes, educational commissions, think tanks, foundations, and professional organisations, which publish their reports and studies and voice their opinions. Newspapers publicly report the test results of local schools each year. These are compared with those of other cities, states, or countries. How do our schools "measure up?" What are the weaknesses? What can be done? This evaluation process is constant and continuing across the country.
In certain periods this examination is more intense. When the Soviet Union launched its Sputnik satellite in 1957, a great debate across the United States started. Was America "falling behind" in science and technology and in "the space race?" How did American school children compare in mathematics and foreign languages? This led to a massive investment in science education as well as to a search for, and support of, gifted pupils. The Civil Rights movement, too, had a shock effect on American education, all the way from pre-school programs to post-doctoral studies. Billions of dollars were made available for special programs for the educationally disadvantaged, for bilingual education, and for seeing minority students better represented in higher education. In the 1980s and into the '90s, again, America was swept by a great public debate over the quality, content, and goals of education.
Summing up results is extremely difficult. There are, for instance, literally thousands of special programs and hundreds of experimental schools across the nation. Since 1968 alone, Native American tribes have established 24 colleges of their own, mostly two-year institutions. In 1991, a survey of programs offering literacy instruction to linguistic minority students had 600 different programs return a questionnaire. Of these programs, all but 10 had been started since 1980. School "choice" approaches - allowing parents more freedom in determining which public, or, in some cases, private schools their children can attend - have been started in many districts. And, as another example, many areas have started "magnet" schools. These offer special curricula, perhaps an emphasis on science, mathematics, or even dance, and attract, and motivate, students.
Given America’s history and that of its people, their many backgrounds, needs, and desires, the fact that American education is sensitive to its weaknesses (and aware of its strengths) speaks well for the future.
THE FACULTY OF MATHEMATICS
Numbers
It has been customary ever since Euclid’s time to present geometry in the form of an axiomatic system. Some other, different approaches to geometry have been developed by modern mathematicians, but this axiomatic approach has continued to be widely used and presented to beginners.
Our mathematics of numbers, however, has not traditionally been organized in axiomatic form. Arithmetic, school algebra, and such subjects as the differential and integral calculus (which go under the heading of analysis) have customarily been presented as collections of rules of calculation, rather than in the form of axiomatized systems of laws.
This difference arises from the fact that our modern mathematics of numbers has its origins more in the mathematics of the Babylonians, Hindus, and Arabs than in that of the Greeks. The Greeks did treat some numerical problems, to be sure, but in doing so their method was to give geometrical interpretations to numbers; that is, when dealing with a problem about the comparative size of two numbers, they would treat it as a problem about the comparative lengths of two lines or the comparative areas of two figures.
But the Babylonians, Hindus, and Arabs (to whom we owe the word “algebra”) gradually developed symbols and rules of calculation that made it possible to deal with numerical problems more abstractly and more powerfully than could the Greeks. As was typical in Eastern mathematics, however, the Babylonians, Hindus, and Arabs did not much concern themselves with giving proofs, let alone with organizing their knowledge of numbers into axiomatic form.
Thus it happened that while geometry was being handed down1 through medieval and early modern times in the axiomatized form which Euclid had given it, the mathematics of number was passed along2 as a collection of comparatively unconnected laws and rules of calculation. This situation is finally changing; one of the striking features of twentieth-century mathematics is its greatly increased use of the axiomatic approach in mathematical studies besides geometry.
From very early times, the development of the mathematics of number must have given rise to philosophical puzzlement. The whole numbers 1, 2, 3, etc. are not too disturbing, to be sure, for their legitimacy seems clear to us as we count the number of beasts in a herd or of kings in a dynasty. The fractions also are not too disturbing, for we can regard them clients of whole numbers, useful for comparing the sizes of fields or lengths of time.
But one can imagine that there have been difficulties when the Babylonians, wishing to express the result of subtracting a number from itself, introduced a symbol for zero, and eventually began to treat it just as through zero were one of the whole numbers. Zero seems like an emptiness, like nothing; how then can we legitimately refer to zero as though it were something, a genuine number? No doubt this uneasiness was gradually soothed 3 as people came to realize that zero is just for “counting”, the number of beasts in an empty field, or the number of kings during a republican era.