Teaching High School Math | Math

Teaching High School Math

This blog will give ideas for teaching middle and high school math.

MATHEMATIC HISTORY

Mathematics is one of many 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 longer possible to spell it out it in a couple of sentences. What I’ve to say now will be words that emphasize its various aspects, rather than describe mathematics. In taking care of, mathematics is an art like painting and music. The great majority of mathematicians perform it as an art. Out of this point of view, the fact that a work done, a developed theory works in one way or another besides mathematics doesn’t concern them much. What matters in their mind could be the depth of the task done, the novelty of the strategy 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; If it’s to know, 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. In order to understand and interpret them, we have to know the language of mathematics. In another aspect, mathematics can be an intellectual game like chess.

Some mathematicians also notice it as a game. Mathematics is only 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 do not genuinely believe that people who deal with mathematics tend to be more than we understand and perceive it from mathematics compared to the blind touched net understands and perceives the elephant. The phrase mathematics, for initially, BC. It absolutely was utilized 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 phrase meaning is “what must be learned”, that is, information. In the years before these dates, instead of the word mathematics, words which means that 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 are able to say so it started between 3000 and 2000 in Egypt and Mesopotamia. In accordance with Heredotus (485-415 BC), mathematics started in Egypt. You may already know, 97% of the Egyptian lands are not suited to agriculture; It’s the 3% portion that gives life to Egypt and forms the Nile delta. Therefore, these lands are extremely valuable. However, at the conclusion of the floods caused by the Nile river every year, the boundaries of the landowners’lands become obscure. Because the landowners also pay taxes in proportion to the land they own, after each flood, the “geometricists” of their state, that are responsible for these works, should come to take the required measurements and provide the landowners as much land as they had in the earlier year. Herodotus says that geometry has begun to emerge consequently of those measurements and calculations. Another opinion about the birth of mathematics is the one put forward by Aristotle (384-322 BC). According to Aristotle, mathematics was created in Egypt. Nonetheless it was created out from the boredom of clergymen and priests, not the necessity for measurement-calculation caused by Nile floods. In those days, the only real intellectual class of countries such as for example Egypt was the priest class. Because the livelihood of this class is provided by the public or their state, they have much time and energy to give to intellectual pursuits. To keep them busy, they invented geometry and arithmetic, the mathematics of that time, just as others invented games like chess, bridge, and go&hellip ;.These two views might be true; priests wanted to simplify the work of the geometric, or they learned just how to calculate the regions of some geometric shapes such as for instance triangular and trapezoidal to check that the distribution was fair, and this way generated the birth of geometry.

We will divide the written history of mathematics into five periods. The very first period is likely to be Egypt and Mesopotamia; this period BC In 2000s BC. It’ll cover a period of 1500-2000 years between 500s. The next period, BC. 500-M.S. It will cover an amount of 1000 years, referred to as the Greek Mathematics period, between 500 years. The next 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, known as the golden age of mathematics, dating from 1700-1900. The period we are residing in, dating back again to early 1900s, called age modern mathematics, would be the fifth period. I will attempt to give information about the development of mathematics because period, contributing mathematicians, the place of mathematics in social life and the basic options that come with mathematics in that period.

We will start the very first 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. You can find two major causes for this. The first is that the ancient Egyptians wrote the writing on papyrus; The next reason is the 3 big fires of the Alexandria libraries, the past of the fires happened during 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 create text instead of paper after cutting, joining, pressing and undergoing some simple operations. Words in western languages ​​such as “Paper”, “papier” are produced from the term papyrus. The typical lifespan of a papyrus is 300 years; 300 years later, it’s flaky as a result of moisture, heat and similar reasons. Up to now, two papyrus related to mathematics appear to have been hidden under exceptional circumstances. The key resources of our knowledge of Egyptian mathematics are these two papyri. The first of the papyrus is really a 6-meter long and 35-cm wide papyrus known as the Ahmes (or Rhind) papyrus. This papyrus, BC. You are a puree written in 2000s, BC. It is 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 book written to teach math. In the introduction part, after a few exercises given to show operations with fractional numbers, 87 questions get making use of their solutions. They’re the type of questions people can encounter in daily life, such as for instance sharing account, interest calculation, or finding the location of ​​some geometric shapes. This really is more or less our 8th grade mathematics. The next papyrus, called the Moscow papyrus and now in the Moscow museum, can also be BC. It is really a booklet written in the 1600s. This papyrus contains 25 questions. These questions are of the type of questions in the Ahmes papyrus, except for the two. Are you aware that other two questions, one could be the calculation of the volume and part of ​​the surface of the sphere part cut by way of a plane. One other could be the question of finding the volume of a pyramid cut with a plane. Both questions were solved correctly. These two questions are accepted whilst the pinnacle of Egyptian mathematics. The Egyptians seen that the area of ​​the circle was proportional to its diameter and found the amount of pi to be 4x (8/9) squared, ie 256/81 = 3.16. It is understood that Egyptian mathematics has remained as of this level for 2000 years and has not made any significant progress.

B.C. 600s will be the years once the Persians started to dominate the middle east. B.C. By the 550s, Persians are the only 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, annually later, in 479, Greeks expelled the Persians from Greece. This date BC. 479 may be the date which 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. A couple, Tales (624-547 BC) and Pythagoras (569-475 BC), are regarded as being the daddy of Greek mathematics. Tales Milet (Aydın) was also born. It is known that he went to Egypt, stayed there for a while and learned geometry in Egypt. Whilst in Egypt, it’s described in books where he calculates the height of the fantastic pyramid by measuring the size of the shadow of the fantastic pyramid, multiplying this number by the ratio of its length to along the existing shadow. After time for Tales Milet, he taught them geometry by forming an organization around him to show what he learned. It’s assumed that abstract proof predicated on reasoning, which is not centered on mathematics – experimental verification, entered into Tales. In addition, Tales is the one who is recognized as the initial philosopher in human history. He came to be on the island of Pythagoras Samos (Samos), another father of Greek mathematics. Pythagoras stayed with Tales for a while, went along to Egypt following his advice, learned geometry there, visited Egyptian temples, learned religious information, and was taken fully to Babylon by capturing the Persians during 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 college and tried to show individuals he gathered around. For political reasons, BC. He left 518 Samos, settled in southern Italy, in the city 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’re connected to one another with oath. The 2nd group contains students attending school. Pythagoras school is based on number cult. According for them, everything could be reduced to numbers; It has an unusually perfect harmony among numbers, and harmony is really a reflection of the divine harmony. Known numbers for that day are integers indicating the plurality such as for instance 1,2,3,…; and kes, ¾,… are 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. Most of the members of the Pythagorean school were massacred by a raid led by way of a big cyber named Cylon. Pythagoras saved his life, but after many years he died. Pythagoras’thoughts, the Pythagorean school lived for quite some time under this or that name. As may be understood from this information, Egyptian and Mesopotamian mathematics are the foundation of Greek mathematics.

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