Activities for Teaching Problem-Solving in Math
Mathematics is one of the oldest sciences in human history. In ancient times, Mathematics was defined while the science of numbers and shapes. Mathematics, like other branches of science, has evolved as time passes; it’s no more possible to spell it out it in several sentences. What I have to state now will undoubtedly be words that emphasize its various aspects, as opposed to describe mathematics. In taking care of, mathematics is a skill like painting and music. The vast majority of mathematicians perform it being an art. Using this standpoint, the truth that a work done, a developed theory works in one of the ways or another besides mathematics doesn’t concern them much. What matters to them could be the depth of the job done, the novelty of the techniques used, the aesthetic value and the usefulness of mathematics in itself. Mathematics, in another aspect, is really a language. If the objective of science is the universe; When it is to understand, rule and direct everything in the universe, we must have the ability to browse the book of nature. The book of nature is written in the language of mathematics, with the highly cited words of Galile; its letters are shapes of geometry. To be able to understand and interpret them, we must know the language of mathematics. In another aspect, mathematics is definitely an intellectual game like chess.
Some mathematicians also view it as a game. Mathematics is just a tool for its user. After entering it, we understand and perceive what mathematics is in your knowledge and in the direction of our interest. Mathematics has become far beyond the dimensions any human can rule. Therefore, I don’t believe that people who deal with mathematics tend to be more than we understand and perceive it from mathematics than the blind touched net understands and perceives the elephant. The term mathematics, for the very first time, BC. It absolutely was employed by the members of the Pythagorean school in the 550s. His entry to the written literature, with Plato BC. It was in the 380s. The term meaning is “what must be learned”, that’s, information. In the years before these dates, instead of the word mathematics, words that mean geometry, equal to it in geometry or old languages were used.
It’s extremely hard to express anything definite about where and how mathematics started. If we take documents which are not based on archaeological findings that need interpretation, but open enough to require interpretation, We could say so it started between 3000 and 2000 in Egypt and Mesopotamia. In accordance with Heredotus (485-415 BC), mathematics started in Egypt. As you know, 97% of the Egyptian lands aren’t suitable for agriculture; It is the 3% portion that offers life to Egypt and forms the Nile delta. Therefore, these lands are extremely valuable. However, by the end of the floods brought on by the Nile river every year, the boundaries of the landowners’lands become obscure. Considering that the landowners also pay taxes in proportion to the land they own, after each and every flood, the “geometricists” of their state, who are responsible for these works, should arrive at take the required measurements and give the landowners just as much land as they had in the last year. Herodotus says that geometry has begun to emerge consequently of those measurements and calculations. An additional opinion in regards to the birth of mathematics is the one put forward by Aristotle (384-322 BC). According to Aristotle, mathematics was born in Egypt. But it was created out of the boredom of clergymen and priests, not the requirement for measurement-calculation caused by Nile floods. At that time, the sole intellectual class of countries such as Egypt was the priest class. Since the livelihood with this class is provided by the public or the state, they’ve much time to share with intellectual pursuits. To help keep them busy, they invented geometry and arithmetic, the mathematics of the period, just like others invented games like chess, bridge, and go&hellip ;.Both of these views might be true; priests wished to simplify the work of the geometric, or they found out just how to calculate the regions of some geometric shapes such as for example triangular and trapezoidal to test that the distribution was fair, and this way led to the birth of geometry.
We will divide the written history of mathematics into five periods. The first period is going to be Egypt and Mesopotamia; this period BC In 2000s BC. It will cover an amount of 1500-2000 years between 500s. The second period, BC. 500-M.S. It’ll cover an amount of 1000 years, called the Greek Mathematics period, between 500 years. The third term, M.S. It will cover a 1200-year period from the 500’s until the start of calculus and will mainly cover European mathematics in the Hind, Islam and Renaissance era. The fourth semester will cover the classical mathematics era, referred to as the golden age of mathematics, dating from 1700-1900. The period we are surviving in, dating back once again to the early 1900s, called the age of modern mathematics, will be the fifth period. I will attempt to give details about the development of mathematics for the reason that period, contributing mathematicians, the spot of mathematics in social life and the fundamental top features of mathematics in that period.
We shall start the initial semester with Egyptian mathematics. Written documents about ancient Egyptian mathematics and generally Egyptian history – I don’t mean the remains of archaeological works – are almost nonexistent. There are two major causes for this. The very first is that the ancient Egyptians wrote the writing on papyrus; The 2nd reason could be the 3 big fires of the Alexandria libraries, the last of those fires happened through the conquest of Egypt by 641 Muslims, the written documents disappeared. Papyrus is the leaves of a reddish, reed type plant growing in the Nile delta, an average of 15-25 meters long and 30-50 inches wide. These leaves were used to write text as opposed to paper after cutting, joining, pressing and undergoing some simple operations. Words in western languages such as “Paper”, “papier” are based on the term papyrus. The common lifespan of a papyrus is 300 years; 300 years later, it’s flaky as a result of moisture, heat and similar reasons. Currently, two papyrus related to mathematics appear to possess been hidden under exceptional circumstances. The key sourced elements of our familiarity with Egyptian mathematics are both of these papyri. The very first of those papyrus is just a 6-meter long and 35-cm wide papyrus known as the Ahmes (or Rhind) papyrus. This papyrus, BC. You’re a puree written in 2000s, BC. It is just a copy compiled by a “mathematician” named Ahmes in the 1650s. This papyrus was bought by the Irish antiquarian H. Rhind in the 1850s, now in the British museum. This papyrus is a guide written to instruct math. In the introduction part, after having a few exercises given to instruct operations with fractional numbers, 87 questions are made using their solutions. They are the kind of questions people can encounter in everyday life, such as for example sharing account, interest calculation, or finding the location of some geometric shapes. This really is just about our 8th grade mathematics. The 2nd papyrus, called the Moscow papyrus and now in the Moscow museum, can also be BC. It is just a booklet written in the 1600s. This papyrus contains 25 questions. These questions are of the kind of questions in the Ahmes papyrus, except for the two. Are you aware that other two questions, one could be the calculation of the quantity and area of the surface of the sphere part cut by a plane. Another could be the question of finding the volume of a pyramid cut by a plane. Both questions were solved correctly. Both of these questions are accepted because the pinnacle of Egyptian mathematics. The Egyptians realized that the location of the circle was proportional to its diameter and found how many pi to be 4x (8/9) squared, ie 256/81 = 3.16. It is understood that Egyptian mathematics has remained at this level for 2000 years and hasn’t made any significant progress.
B.C. 600s would be the years once the Persians started to dominate the middle east. B.C. By the 550s, Persians are the sole rulers of the entire middle east, including Anatolia and Egypt. The Persians organize three trips to Greece between 500-480 BC; They captured Athens in 480, but burned it, a year later, in 479, Greeks expelled the Persians from Greece. This date BC. 479 could be the date that was accepted as the beginning of Greek civilization. This date is the beginning of a really bright period in science, art and literature. Greek mathematics actually started earlier than this period. Two different people, Tales (624-547 BC) and Pythagoras (569-475 BC), are regarded as being the father of Greek mathematics. Tales Milet (Aydın) was also born. It is famous that he visited Egypt, stayed there for a time and learned geometry in Egypt. During Egypt, it’s described in books where he calculates the height of the truly amazing pyramid by measuring the length of the shadow of the truly amazing pyramid, multiplying this number by the ratio of its length to the length of the current shadow. After returning to Tales Milet, he taught them geometry by forming friends around him to show what he learned. It’s assumed that abstract proof predicated on reasoning, that is not predicated on mathematics – experimental verification, entered into Tales. Additionally, Tales is the person who is known as the very first philosopher in human history. He was created on the island of Pythagoras Samos (Samos), another father of Greek mathematics. Pythagoras stayed with Tales for some time, visited Egypt following his advice, learned geometry there, visited Egyptian temples, learned religious information, and was taken fully to Babylon by capturing the Persians throughout the occupation of Egypt by the Persians. it’s known. During his 5 years in Babylon, he learned mathematics, music and religious information, and after time for Samos, he created a school and tried to show the folks he gathered around. For political reasons, BC. He left 518 Samos, settled in southern Italy, in the town of Crotone, where he created a semi-mystical-semi-scientific, cult-like school. The senior individuals of this school called “mathematics” live together and they are connected to each other with oath. The second group includes students attending school. Pythagoras school is based on number cult. According in their mind, everything could be reduced to numbers; It posseses an unusually perfect harmony among numbers, and harmony is a reflection of the divine harmony. Known numbers for that day are integers indicating the plurality such as 1,2,3,…; and kes, ¾,… would be the fractional numbers that indicate the ratio of the part to the whole. The emergence of irrational numbers with the theorem referred to as the Pythagorean theorem (the square of the best sides of the right triangle equals the square of the hypotenuse) put the Pythagorean school in a deep crisis. The discovery of irrational numbers is the initial major crisis of mathematics. Many of the members of the Pythagorean school were massacred by way of a raid led by a big cyber named Cylon. Pythagoras saved his life, but after many years he died. Pythagoras’thoughts, the Pythagorean school lived for many years under this or that name. As could be understood from these records, Egyptian and Mesopotamian mathematics are the cornerstone of Greek mathematics.