Учебно-методическое пособие для студентов I-II курсов заочного отделения неязыковых факультетов (стр. 6 из 12)

Needless to say, those children who have attended better schools, or who come from families with better-educated parents, often have an advantage over those who don't. This remains a problem in the U.S., where equality of opportunity is a central cultural goal. Not surprisingly, the members of racial minorities are the most deprived in this respect - with the notable exception of the Asian-Americans.

In 1990, for instance, 23 percent of all Americans 25 years and older had completed four years of college or more. However, the figure for Blacks was 12 percent and for Hispanics 10 percent. Compared with the figures from 1970, when the national average was only 10.7 percent (with 11.3 percent for whites, 4.4 percent for Blacks, and 7.6 percent for students of Hispanic origin), this does reveal a considerable improvement within two decades. The number of students who fail to complete high school, too, is much larger among minority groups. The national average of all 14 to 24-year-olds who did not graduate from high school was 10.5 percent in 1991. For white students it was 10.5 percent, for Blacks 11.3 percent, and for Hispanics the figure was as much as 29.5 percent. Yet, it is still a fact today, as the ВВС commentator Alistair Cooke pointed out in 1972, that "a Black boy has a better chance of going to college here than practically any boy in Western Europe." Today it would also be true of a Black girl.

The educational level is still relatively lower for women than for men. While 24.5 percent of male Americans had four years of college or more in 1989, only 18 percent of women had. But as indicated in the table above, there have been some recent improvements.

A large number of different programs aimed at improving educational opportunities among minority groups exist at all levels - local, state, and federal. They have met with some, even if moderate, success. These programs along with the figures above point to one aspect, which is critical to understanding American education (and, for that matter, American society in general). Americans could conclude that they have been more successful than most other nations in including large proportions of their minorities at all levels of education. And they could conclude that enormous progress has been made in the past decades. But, in fact, few Americans do either. Rather, they concentrate on the fact that within the United States, minorities are still not equally represented in the number of high school graduates, or the numbers of engineers, doctors, lawyers, and university professors.

Elementary and Secondary Education

Because of the great variety of schools and colleges, and the many differences among them, no one institution can be singled out as typical or even representative. Yet there are enough basic similarities in structure among the various schools and systems to permit some general comments.

Most schools start at the kindergarten level. There are some school districts that do not have this beginning phase and others which have an additional "pre-school" one. There are almost always required subjects at each level. In some areas and at more advanced levels, students can choose some subjects. Pupils who do not do well often have to repeat courses, or have to have special tutoring, usually done in and by the schools. Many schools also support summer classes, where students can make up for failed courses or even take extra courses.

In addition to bilingual and bicultural education programs, many schools have special programs for those with learning and reading difficulties. These and other programs repeat the emphasis of American education on trying to increase equality of opportunity. They also attempt to integrate students with varying abilities and backgrounds into an educational system shared by all. At the same time, many high school students are given special advanced coursework in mathematics and the sciences. Nation-wide talent searches for minority group children with special abilities and academic promise began on a large scale in the 1960s. These programs have helped to bring more minority children into advanced levels of university education and into the professions.

Like schools in Britain and other English-speaking countries, those in the U.S. have also always stressed "character" or "social skills" through extracurricular activities, including organised sports. Because most schools start at around 8 o'clock every morning and classes often do not finish until 3 or 4 o'clock in the afternoon, such activities mean that many students do not return home until the early evening. There is usually a very broad range of extracurricular activities available. Most schools, for instance, publish their own student newspapers, and some have their own radio stations. Almost all have student orchestras, bands, and choirs, which give public performances. There are theater and drama groups, chess and debating clubs, Latin, French, Spanish, or German clubs, groups which meet after school to discuss computers, or chemistry, or amateur radio, or the raising of prize horses and cows. Students can learn flying, skin-diving, and mountain climbing. They can act as volunteers in hospitals and homes for the aged and do other public-service work.

Many different sports are also available, and most schools share their facilities - swimming pools, tennis courts, tracks, and stadiums - with the public. Many sports that in other countries are normally offered by private clubs are available to students at no cost in American schools. Often the students themselves organise and support school activities and raise money through car washes, baby-sitting, bake sales, or by mowing lawns. Parents and local businesses often also help a group that, for example, has a chance to go to a state music competition, to compete in some sports championship, or take a camping trip. Such activities not only give pupils a chance to be together outside of normal classes, they also help develop a feeling of "school spirit" among the students and in the community.

Adult and Continuing Education

The concept of continuing (or lifelong) education is of great importance to Americans. In 1991, 57 million Americans 17 years and older furthered their education through participation in part-time instruction, taking courses in universities, colleges, professional associations, government organisations or even churches and synagogues. Most participants in continuing or adult education have a practical goal: they want to update and upgrade their job skills. As a result of economic changes and the rapid advance of the "information age," the necessity to acquire new occupational skills has increased. Adult education thus fills a need of many Americans who want to improve their chances in a changing job market. This is one explanation for the continuing growth of adult education classes over the past several years. Of course, not all people who take courses in adult education do this for job-related purposes. Many simply want to broaden their knowledge or learn something they would enjoy doing such as printmaking, dancing, or photography.

Continuing education courses are provided mainly by community or junior colleges and mostly take place in the evenings. The types of courses adults enrol in range from hobby and recreational activities to highly specialised technical skills. Courses in business, health care and health sciences, engineering, and education are most popular. Most of these courses are taken by employees because the employer provided major support for educational programs, either by paying part of the fees, giving time off, or providing other incentives. While some 50 percent of all people in adult education are enrolled in programs sponsored by educational institutions, about 15 percent were sponsored directly by business and industry. Over 80 percent of all companies today conduct their own training programs. Many large corporations offer complete degree programs, and some even support their own technical and business colleges and universities.

In the 1980s about 5 million students took industry-sponsored university programs and roughly twice that number were involved in corporate education of some kind. A great many universities and colleges, public and private, also admit part-time students to their programs. Many offer evening courses so those who work can attend, and most institutions have summer semesters, as well. This way many American are able to earn a university degree, bit by bit, and year by year. State universities have long "taken education to the people" by setting up extension campuses in small towns, or largely rural areas. Therefore, someone at home in Stevens Point, Wisconsin, for example, will be able to take courses taught by professors from the University of Wisconsin’s main campus in Madison.

THE FACULTY OF MATHEMATICS

The Whole Numbers

Generally when numbers are written the numerals are grouped by threes so that it becomes easy for the eye to distinguish them. Thus five million six hundred seventy-five thousand four hundred ninety two is written as 5 675 492. The groups of threes are often separated from one another by commas, that is: 5,675,492.

Numbers, when written, are often described by the number of numerals they contain, the number of places. Thus 72 is a two place number and 4895 is a four place number. Four place numbers, especially dates, are often written without commas or spaces, as 1905, 1943.

Addition of Whole Numbers

The addition of two or more numbers is an arithmetic operation by means of which a new number is obtained. This new number contains as many units as are contained in all added numbers taken together. The numbers that are added are known as the addends. The number resulting from addition of two or more numbers is known as the sum. The sign for addition is + (plus).

Addition is best performed when the numbers are written in columns so that units, tens, hundreds, and so forth are written vertically. For example, the sum of 1,562 and 1,891 is obtained, as follows:

1,562

+1,891

3,453

Addition is performed from right to left. We can easily observe that addition of 8 to 35 gives the same result when 35 is added to 8. In either of the operations of addition the sum is 43. So the sum of two or more numbers does not change when the order, in which the numbers are added, is changed.

Subtraction of Whole Numbers

Subtraction is an arithmetic operation by means of which one of the addends is obtained, when the sum and another addend are given. The result is known as the difference of the two given numbers. The number from which another number is to be subtracted is known as the minuend. The number that is subtracted is known as the subtrahend. Subtraction is an operation opposite to addition. The sign is - (minus).

Subtraction of many-place numbers is performed as follows:

986

-354

632

We begin subtraction from the right and we subtract the numbers in the same column. Thus: 6 – 4 = 2; 8 – 5 = 3, etc.

Multiplication of Whole Numbers

Multiplication is an arithmetic operation by means of which one number is repeated as an addend until it occurs as many times as it is indicated by another number. There are two numbers involved in multiplication. The result of the operation of multiplication is known as the product. The number which is repeated is known as the multiplicand. The number by which the multiplicand is multiplied is known as the multiplier. The sign is “x“or “×”.

Division of Whole Numbers

The operation by means of which a factor is obtained when the product and the other factor are given is called division. The arithmetic operation is performed on the number, which we take as the given product. In division this number is called the dividend. The given factor is known as the number by which the dividend or the product is to be divided. This number is called the divisor. The result of the division of the dividend by the divisor is called the quotient. The sign of division is “:” or “/“ in England.

Fractions

A fraction is a part of a unit, such as ½; ¼; etc. A fraction has a numerator and a denominator. For example in the fraction ¾ - 3 is the numerator, and 4 is the denominator. In the fraction the numerator is divided by the denominator. The fraction 2/7; indicates that 2 is being divided by 7.

A mixed number is an integer together with a fraction, such as 2 3/5; 7 3/8 etc. An integer is the integral part and a fraction is the fractional part. An improper fraction is one in which the numerator is greater than the denominator, such as 19/6; 23/4 etc.

To change a mixed number to an improper fraction you must:

a) multiply the denominator of the fraction by the integer;

b) add the numerator to this product;

c) place the sum over the denominator of the fraction.

For example let’s change 3 4/7 to a fraction.

The solution is: 7 x 3 = 21; 21 + 4 = 25; 3 4/7 = 25/7 .

Addition of Fractions

Fractions cannot be added unless the denominators are all the same. If they are, add all the numerators and place this sum over the common denominator. Add up the integers, if any.

If the denominators are not the same, the fractions in order to be added must be converted into fractions having the same denominators. In order to do this; it is first necessary to find the Lowest Common Denominator (L.C.D.). The L.C.D. is the lowest number, which can be divided by all the given denominators.

For example L.C.D. of ½, 1/3, and 1/5 is 2 x 3 x 5 = 30.

Subtraction of Fractions

More than two numbers may be added at the same time. In subtraction, however, only two numbers are involved. In subtraction, as in addition, the denominators must be the same. One must be careful to determine which term is the first. The second term is always subtracted from the first, which should be of a larger quantity.

To subtract fractions you must:

a) change the mixed numbers, if any, to improper fractions;

b) find the L.C.D.;

c) change both fractions to fractions having the L.C.D. as the denominator;

d) subtract the numerator of the second fraction from the numerator of the first, and place this difference over the L.C.D.;

e) reduce if possible.

Multiplication of Fractions

To be multiplied, fractions need not have the same denominator.

To multiply fractions you must:

a) change the mixed numbers, if any, to improper fractions;

b) multiply all the numerators and place this product over the product

of denominators;

c) reduce the fraction if possible.

Illustration: multiply 2/3 x 2 4/7 x 5/9; 2 4/7=18/7;

2/3 x 18/7 x 5/9 = 180/189 = 20/21.

Division of Fractions

In division as in subtraction only two terms are involved. It is very important to determine which term is the first. If the problem reads 2/3 divided by 5, then 2/3 is the first term and 5 is the second. If it reads “How many times is ½ contained in1/3?”, then 1/3 is the first and ½ is the second.

To divide fractions you must:

a) change the mixed numbers, if any, to improper fractions;

b) invert the second fraction and multiply;

c) reduce the fraction if possible.

Illustration: divide 2/3 by 2 1/4 ; 2 1/4 =9/4; 2/3: 9/4=2/3x4/9=8/27

Addition and Subtraction of Decimal Fractions

Addition and subtraction of decimal fractions are performed in the same manner as addition and subtraction of whole numbers.

1. When we add two or several decimal fractions, all of these numbers should have the same number of places to the right of the decimal point.

2. If we subtract one decimal fraction from another both should have the same number of places to the right of the decimal point.

3. We shall refer to places to the right of the decimal point as decimal places.

In a set of addends or in a minuend or subtrahend one or several numbers may have more decimal places than the others. In such situations we note the number having the fewest decimal places and discard the digits, which are to the right of these decimal places in the other numbers, for example, in adding