III. Draw your mood graph or graph with your marks showing changes.
Practice set 13
I. Use this mind-map to speak about advantages and disadvantages of computers. Add more information.
| has no intuition and follows instructions, one after another |
| is a part of our life used in all spheres of our life |
| is only a man-made machine which has no brain |
| must be directed and controlled by the programmer |
| solves problems by doing mathematical and decision – making operations |
| can solve only three types of logic problems |
| is fast and exact ; performs operations without mistakes, if there is a mistake it is a fault of a person but not a computer |
| performs more than million operations per second without becoming bored or tired |
| can have viruses which damage your information |
| COMPUTER |
| can repeat operations over and over again |
| ConsA. is a generalization of arithmetic. In arithmetic every number has a single definite value |
| ProsBut in algebra we use symbols, which usually don’t have a single definite value |
II. Draw a chart showing the main parts of the computer system. Follow these steps:
- at first draw the two main components: software and hardware
- then draw the software parts
- after that draw the hardware parts
- show your chart to your partner. Does s/he agree with the elements shown?
III. Work in pairs. Look at your chart and tell about the functions of each element.
Part III Reading and Speaking (Mathematics: History, Culture, Reality)
Text 1
Reading and Speaking
SOME FACTS FROM THE HISTORY OF MATHEMATICS EDUCATION
Elementary mathematics was a part of the education system in the most ancient civilizations, including ancient Greece, ancient Rome and ancient Egypt. In most cases, a formal education was only available to male children with a sufficiently high status, wealth or caste.
In Plato’s division of the liberal arts into the trivium (education) and the quadrivium (classical education), the quadrivium included the mathematical fields of arithmetic and geometry. This structure was continued in the structure of classical education that was developed in medieval Europe. Teaching geometry was based on Euclid‘s Elements. Apprentices to trades such as masons, merchants and money-lenders could expect to learn such practical mathematics as was relevant to their profession.
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The first mathematics textbooks to be written in English and French were published by Robert Recorde, beginning with ‘The Ground of Arts’ in 1540.
In the Renaissance the academic status of mathematics declined, because it was strongly associated with trade and commerce. Although it continued to be taught in European universities, it was seen as subservient to the study of Natural, Metaphysical and Moral Philosophy.
This trend was somewhat reversed in the seventeenth century, with the University of Aberdeen creating a Mathematics Chair in 1613, followed by the Chair in Geometry being set up in the University of Oxford in 1619 and the Lucasian Chair of Mathematics being established by the University of Cambridge in 1662. However, it was uncommon for mathematics to be taught outside of the universities. Isaac Newton, for example, received no formal mathematics teaching until he joined Trinity College, Cambridge in 1661.
In the eighteenth and nineteenth centuries the industrial revolution led to an enormous increase in urban populations. Basic numeracy skills, such as the ability to tell the time, count money and carry out simple arithmetic, became essential in this new urban lifestyle. Within the new public education systems, mathematics became a central part of the curriculum from an early age.
In the twentieth century mathematics became a part of the core curriculum in all developed countries.
During the twentieth century mathematics education was established as an independent field of research. Here are some of the main events in this development:
- A Chair in mathematics education was created at the University of Göttingen, under the administration of Felix Klein in 1893.
- The International Commission on Mathematical Instruction (ICMI) was founded in 1908, and Felix Klein became the first president of the organization.
- A new interest in mathematics education emerged in the 1960 s, and the commission was revitalized.
- In 1968, the Shell Centre for Mathematical Education was established in Nottingham.
- In 1969 the first International Congress on Mathematical Education (ICME) was held in Lyon. The second congress was in Exeter in 1972, and after that it has been held every four years.
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In the 20 th century the cultural impact of the ‘electric age’ was also taken up by educational theory and the teaching of mathematics. While previous approach focused on ‘working with specialized ‘problems’ in arithmetic’, the emerging structural approach to knowledge had ‘small children’ meditating about number theory and ‘sets’.
I. Match the words (1–7) with their definitions/explanations (a–g):
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