- •Contents
- •Передмова
- •We are students at donetsk national university
- •Vocabulary
- •1. Guess the meaning of these international words. Check with your teacher or a dictionary
- •2. Key words
- •Student Dima Loboda
- •Student Dasha Klimova
- •Student Nastya Savchuk
- •Student profile
- •L earn mathematics in English Cardinal and ordinal numbers
- •1. Read the text about two arithmetical operations and do the exercises that follow it Basic arithmetical operations. (Addition & subtraction)
- •What’s your best friend like?
- •Vocabulary
- •1. Guess the meaning of these international words. Check with your teacher or a dictionary
- •2. Key words
- •Who’s their ideal partner?
- •L earn mathematics in English
- •1. Read the text and do the exercises below it Basic arithmetical operations (Multiplication & division)
- •A day in the life of a student
- •Vocabulary
- •1. Guess the meaning of these international words. Check with your teacher or a dictionary
- •2. Key words
- •I. Look through the text and do the tasks
- •Learn mathematics in English
- •I. Read the text and do the exercises below it. Advanced arithmetical operations
- •What’s your university like?
- •Vocabulary
- •1. Guess the meaning of these international words. Check with your teacher or a dictionary
- •2. Key words:
- •Donetsk national university
- •The University of Sheffield
- •1. Find a partner from the other group. Tell each other the information you read about one of the universities
- •Fractions
- •The city I live and study in
- •Vocabulary
- •1. Guess the meaning of these international words. Check with your teacher or a dictionary
- •2. Key words:
- •Learn mathematics in English
- •Mixed numbers
- •Mathematics is the queen of scienses
- •Vocabulary
- •1. Guess the meaning of these international words. Check with your teacher or a dictionary
- •Key words:
- •“`A mathematician is a machine for converting coffee into theorems”. /Paul Erdos/
- •L earn mathematics in English
- •Equivalent fractions
- •Reciprocals and the "invisible denominator"
- •The language of mathematics
- •Vocabulary
- •1. Guess the meaning of these international words. Check with your teacher or a dictionary
- •Key words
- •L earn mathematics in English
- •Statistics is very serious!
- •Vocabulary
- •1. Guess the meaning of these international words. Check with your teacher or a dictionary
- •Key words:
- •Statistics is very serious!
- •Get to know a typical computer
- •Vocabulary
- •1. Guess the meaning of these international words. Check with your teacher or a dictionary
- •2. Key words:
- •Get to know a typical computer
- •Computer without a program is just a heap of metal!
- •Vocabulary
- •1. Guess the meaning of these international words. Check with your teacher or a dictionary.
- •2. Key words
- •We can’t imagine modern computing without them
- •Vocabulary
- •1. Guess the meaning of these international words. Check with your teacher or a dictionary
- •2. Key words
- •I. Read the following texts and do the tasks Alan Turing
- •Tim Berners-Lee
- •He has left mathematicians enough to keep them busy for five hundred years
- •Vocabulary
- •1. Guess the meaning of these international words. Check with your teacher or a dictionary.
- •2. Key words
- •I. Read the text and do the tasks niels henric abel
- •Getting to know each other better
- •II. Swap charts with b. Ask a to explain the information in his/her chart. Ask for more information
- •III. Explain your answers to b
- •Mood graph
- •A time for everything
- •Expert opinion
- •Vocabulary
- •Vocabulary
- •What’s your body age?
- •I. Read the questionnaire and answer the questions below, adding or subtracting the numbers after your answer from your actual age
- •How many friends can you share problems with?
- •15. Have you taken antibiotics in the past five years?
- •II. Check your score
- •If you're younger than your years
- •I. Look at your partner’s answers. Ask for more information, for example: What is your worst diet habit? How much time do you have for yourself?
- •II. Some ways to lower our body age are given below. Read it and give your partner some good advice starting with the following words: I think you should…
- •Donetsk national university
- •Inspires students’ enthusiasm for learning
- •An ideal teacher
- •Is a well-educated person has a good sense of humor is a polite and a punctual person delivers interesting lectures
- •Numbers
- •I. Mind–map’ numbers’. When you read this ‘mind-map’, you’ll meet words that are new to you. First try to guess their meaning and then look them up in a dictionary.
- •II. Answering and explaining
- •III. Playing a trick with numbers
- •IV. The ‘Terribly Stressed‘ game
- •I. Use this mind-map ‘Four basic operations in Mathematics’ as a topic activator to speak about the basic operations in Arithmetic
- •III. Reading, writing and saying numerical expressions
- •3. Look at each numerical expression written in symbols and signs. Then say it in words. Your partner will listen to see if you repeat correctly and correct your incorrect answers
- •I. Use this mind-map ‘Algebra’ as a topic activator to speak about Algebra (its origin and some facts from its history)
- •II. Match each numerical expression in the left column with the equivalent expression in the right column
- •Look at the expressions written in words and write them in mathematical notation (in symbols)
- •III. Read the following inequalities aloud. Your partner will check your answers
- •I. Mind-map ‘Geometry’. Use this map to speak about geometry (its meaning, the history of its development, its application). Add more information you know
- •II. Working with geometric terms. Demonstrate your knowledge of geometric terms. Work in pairs (a/b)
- •The language of mathematics
- •Practice set 12
- •III. Draw your mood graph or graph with your marks showing changes during the week or a month (semester). Explain it to your partner
- •Some facts from the history of mathematics education
- •I. Read the article and mark the sentences t (true), f (false) or ng (not given)
- •Do you know that…
- •II. Search for some information about one of these mathematics teachers and share it with other students. Make a table of the most important facts of his/her biography
- •Ancient sources of information
- •I. Choose from (a-j) the one which best fits each of (1-7). There are two choices you do not need to use.
- •II. Tell your partner about these famous papyri
- •III. Find some information about Mathematics of ancient civilizations and share it with other students (e.G. The Maya calendar, the ancient numeration systems)
- •The history of the symbols for plus and minus
- •I. Read the article. Guess the meaning of the highlighted words. Check with the teacher or your dictionary
- •II. Read the article again. Say what events the following years refer to:
- •III. Tick (√) the things the article says
- •IV. Read the facts listed below. In pairs, discuss which one is the most surprising do you know that...
- •V. Find some information on the history of the mathematical symbols. Give a presentation to the students of your group
- •Statistics
- •I. Match the words with their definitions:
- •II. Decide if the given statements are true (t) or false (f) according to the text
- •III. Search for information about one of the scientists listed below and then give a presentation
- •Important contributors to statistics
- •Degrees and diplomas in statistics
- •III. Do you know anything about awards in Statistics in your country or abroad?
- •Why is there no nobel prize in mathematics?
- •I. Read the text. Seven sentences have been removed from it. Choose from the choices (a- I) the one which fits each gap (1-7). There are two choices you do not need to use
- •III. Work in pairs. Tell your partner why Nobel decided against a Nobel Prize in mathematics
- •Major awards in mathematics
- •The obverse of the Fields Medal
- •The reverse of the Fields Medal
- •A. Fields medal
- •III. Look at these words. Why are they important in this text?
- •B. Abel prize
- •IV. Focus on these words. Why are they important in the text?
- •VI. Compare the major awards in Mathematics with the Nobel Prize by using like (similar to) or unlike (different from) in the sentences
- •V. Search for more information on the following topics on the Internet and share it with other students
- •Abel Prize Laureates
- •Fields medalist
- •I. Decide if the given statement is true (t) according to the text, if it is false (f) or if the information is not given (ng) in the text (Work in pairs)
- •II. Number these events in the order they happened. Look at the Reading
- •III. Interview your partner about this great mathematician (Work in pairs)
- •IV. Ask and answer the following questions in pairs
- •II. Match the number with its symbolic meaning:
- •III. Answer the questions below and then ask for more information (Work in pairs)
- •Do you know that…
- •IV. Find information on the Internet and give a presentation of the number you are interested in (brings you good or bad luck)
- •Text 10
- •Reading and Speaking
- •Number and reality
- •I. Match the word with its meaning:
- •II. Work in pairs. Decide if the sentences 1- 7 are t (true) or f (false)
- •A strong mathematical component
- •I. Choose from (a-j) the one which best fits each of (1-6). There is one choice you do not need to use
- •II. Match choices (a-d) to (1-4)
- •III. In pairs, find and then say what events the following years refer to:
- •IV. Do you know an artist (a writer) having a strong mathematical component in his/her creative work? Search for information on the Internet and give a presentation on the subject
- •Reading and Speaking fractal
- •I. Match the words with their meanings:
- •II. Choose from (a-f) the one which best fits each of (1-5). There is one choice you do not need to use
- •III. Work in pairs. Tell your partner about fractal
- •IV. On the Internet search for information about applications of fractals and then share your information with other students
- •Healthy computer work
- •Match the words with their meanings:
- •I I. Read the article once and then decide if the following guidelines are true, false or are not mentioned in the text above
- •III. Team work. Work out the main rules for operating the computer. The winner is to give clear recommendations for young people working on the computer. The first one is given for you
- •IV. Ask and answer the questions (Work in pairs)
- •Computers can do wonders
- •I. Match the words with their meanings
- •II. Decide if the following statements are true or false (t/f) by referring to the information in the text
- •III. Work in pairs. Tell your partner about the most surprising facts from the article
- •IV. Search for information about ‘computer wonders’ on the Internet and give a presentation about new computer developments (e.G. Robots)
- •Watching ‘how did mathematics begin? (a cartoon)
- •I. Answer the following questions:
- •II. Tell the class about the most interesting facts you have learned from the cartoon. Do you agree with the information mentioned in the cartoon? Add more information about the development of numbers
- •Recommendations and some useful phrases for giving presentations
- •Introduction
- •Introducing your subject
- •If you make a mistake, start your sentence again.
- •If you can’t remember a word, use another one.
- •Conclusion
- •Inviting questions
- •Questions
- •Wording mathematical signs, symbols and formulae
- •Answer keys
- •References
The language of mathematics
Vocabulary
1. Guess the meaning of these international words. Check with your teacher or a dictionary
Symbol-symbolic-symbolism, universal, civilized, numeral, alphabet, mechanically, characteristic, modern, reason-reasoning, design-designed, confusing, to perfect-perfection, general, theorem, construct, cathetus, hypotenuse,, economy, verbal-verbally, abbreviation.
Key words
Reasoning |
Міркування, логічний хід думки |
To grasp |
Зрозуміти, схопити (основну ідею) |
Custom |
Звичай, традиція |
Purposefully |
Цілеспрямовано |
Ingeniously |
Уміло, майстерно |
To design |
Розробляти, проектувати |
Precise |
Точний |
Concise |
Короткий, стислий |
Unaccustomed to |
Який не звик до … |
To distinguish |
Розрізняти |
Brevity |
Стислість |
To make for something |
Сприяти чомусь |
Remarkable |
Чудовий |
To encompass |
Містити, охоплювати |
Convenience |
Зручність |
Reading
Task 1. Read the text and decide if the statements below it are true or false.
The language of mathematics may be called the language of science. It consists mostly of signs and symbols, and, in a sense, it is an unspoken language. There can be no more universal or simple language. It is the same throughout the civilized world, though the people of each country translate it into their own particular spoken language. For example, the symbol 5 means the same to a person in the UK, Germany, Ukraine or any other country, but in each country it is called by a different spoken word. Some of the best known symbols in maths are the numerals 1, 2, 3, 4, 5, 6, 7, 8, 9, 0 and the signs of addition (), subtraction (), multiplication (×), division (:), equality (=) and the letters of the Greek and Latin alphabets.
Symbolic language is one of the basic characteristics of modern mathematics. With the help of symbolism mathematicians can make transition in reasoning almost mechanically by the eye and leave their mind free to grasp the fundamental ideas of the subject matter. Unlike the common language which is the product of custom, social and political movements, the language of maths is carefully, purposefully and often ingeniously designed.
Maths language is precise and concise, so people unaccustomed to its forms find it confusing. The symbolism used in maths language is essential to distinguish meanings often confused in common speech. Maths style aims at brevity and formal perfection. Let us suppose we wish to express in general terms the Pythagorian theorem known to every pupil at school. We can say, ‘We have a right triangle. If we construct two squares each having a leg (cathetus) of the triangle as a side and if we construct a square having the hypotenuse of the triangle for its side, then the area of the third square is equal to the sum of the areas of the first two’. But no mathematician expresses himself that way. He prefers, ‘The sum of the squares on the legs (catheti) of a right triangle equals the square on the hypotenuse’. In symbols it can be stated as follows: c2 = a2 + b2. This economy of words makes for conciseness of presentation, and maths writing is remarkable because it encompasses much in a few words. So maths language expresses verbally stated facts in signs and symbols of maths. We use signs and symbols for convenience. In some cases symbols are abbreviations of words, but they often don’t have such relations to the things they stand for. We define their meaning by common agreement.
The student must always remember that understanding any subject in maths presupposes clear knowledge of the previous material. This is the reason why ‘there is no royal road to mathematics’ and why the study of maths is discouraging to weak minds.
The language of mathematics is mainly made up of words.
Symbolism used in maths facilitates efficiency of thought.
Symbols help mathematicians to avoid ambiguity of the common language.
Symbols are always abbreviations of words.
Task 2. Find the following information in the text
a. Characteristics of the mathematical language.
b. The effects of symbolism.
c. The difference between forming the language of maths and common language.