How to Teach Math with Interactive Notebooks | Math

How to Teach Math with Interactive Notebooks

Read more about the 5 components I’ve found so important in my students’ math notebooks and my favorite tips for getting the most out of math interactive notebooks.

MATHEMATIC HISTORY

Mathematics is one of many oldest sciences in human history. In ancient times, Mathematics was defined because the science of numbers and shapes. Mathematics, like other branches of science, has evolved over time; it is no more possible to describe it in several sentences. What I have to state now will soon 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 as an art. Out of this standpoint, the fact a work done, a developed theory works in one way or another other than mathematics doesn’t concern them much. What matters for them may be the depth of the work 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 goal of science could be the universe; If it’s to understand, rule and direct everything in the universe, we must have the ability to see 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 have to know the language of mathematics. In another aspect, mathematics is definitely an intellectual game like chess.

Some mathematicians also see it as a game. Mathematics is just a tool because of its user. After entering it, we understand and perceive what mathematics is in your knowledge and in the direction of our interest. Mathematics is currently far beyond the dimensions any human can rule. Therefore, I do not believe that people who handle 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 word mathematics, for the very first time, BC. It absolutely was used by the members of the Pythagorean school in the 550s. His entry into the written literature, with Plato BC. It was in the 380s. The phrase meaning is “what needs to be learned”, that is, information. In the years before these dates, rather than the word mathematics, words which means that geometry, equal to it in geometry or old languages ​​were used.

It is not possible to say anything definite about where and how mathematics started. When we take documents which are not centered on archaeological findings that require interpretation, but open enough to require interpretation, We can say that it started between 3000 and 2000 in Egypt and Mesopotamia. Based on Heredotus (485-415 BC), mathematics were only available in Egypt. As you know, 97% of the Egyptian lands aren’t suited to agriculture; It’s the 3% portion that provides 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 annually, the boundaries of the landowners’lands become obscure. Because the landowners also pay taxes in proportion to the land they own, after each and every flood, the “geometricists” of the state, who’re accountable for these works, should arrived at take the necessary measurements and provide the landowners the maximum amount of land as they’d in the last year. Herodotus says that geometry has begun to emerge consequently of the measurements and calculations. An additional opinion about the birth of mathematics is the main one put forward by Aristotle (384-322 BC). Based on Aristotle, mathematics came to be in Egypt. However it was created from the boredom of clergymen and priests, not the need for measurement-calculation caused by Nile floods. During those times, the only intellectual class of countries such as Egypt was the priest class. Since the livelihood of the class is given by the public or their state, they have much time for you to give intellectual pursuits. To keep them busy, they invented geometry and arithmetic, the mathematics of that point, in the same way others invented games like chess, bridge, and go&hellip ;.Both these views might be true; priests wished to simplify the job of the geometric, or they learned how exactly to calculate the aspects of some geometric shapes such as for example triangular and trapezoidal to check on that the distribution was fair, and in this way led to the birth of geometry.

We will divide the written history of mathematics into five periods. The very first period is going 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’ll cover a period of 1000 years, known as the Greek Mathematics period, between 500 years. The 3rd term, M.S. It’ll 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’re surviving in, dating back to the early 1900s, called age modern mathematics, will be the fifth period. I will endeavour to give information about the development of mathematics because period, contributing mathematicians, the area of mathematics in social life and the fundamental top features of mathematics in that period.

We shall 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. There are two significant reasons for this. The first is that the ancient Egyptians wrote the writing on papyrus; The 2nd reason is the 3 big fires of the Alexandria libraries, the final of these fires happened through the conquest of Egypt by 641 Muslims, the written documents disappeared. Papyrus could be the leaves of a reddish, reed type plant growing in the Nile delta, on average 15-25 meters long and 30-50 inches wide. These leaves were used to publish 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 common lifespan of a papyrus is 300 years; 300 years later, it is flaky because of moisture, heat and similar reasons. To date, two papyrus linked to mathematics appear to own been hidden under exceptional circumstances. The main resources of our understanding of Egyptian mathematics are those two papyri. The initial of those papyrus is just a 6-meter long and 35-cm wide papyrus referred to as the Ahmes (or Rhind) papyrus. This papyrus, BC. You’re a puree written in 2000s, BC. It is just a copy published 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 show math. In the introduction part, following a few exercises given to teach operations with fractional numbers, 87 questions get with their solutions. These are the kind of questions people can encounter in lifestyle, such as for example sharing account, interest calculation, or finding the area of ​​some geometric shapes. That is just about our 8th grade mathematics. The next papyrus, called the Moscow papyrus and now in the Moscow museum, is also 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, with the exception of the two. As for the other two questions, one of them is the calculation of the volume and area of ​​the surface of the sphere part cut with a plane. The other may be the question of finding the volume of a pyramid cut with a plane. Both questions were solved correctly. Those two questions are accepted while the pinnacle of Egyptian mathematics. The Egyptians realized that the region 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’s understood that Egyptian mathematics has remained as of this level for 2000 years and hasn’t made any significant progress.

B.C. 600s are the years once the Persians began to dominate the middle east. B.C. By the 550s, Persians are the only real rulers of the whole 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, per year later, in 479, Greeks expelled the Persians from Greece. This date BC. 479 may be the date that was accepted as the start of Greek civilization. This date is the start of a really bright period in science, art and literature. Greek mathematics actually started prior to when this period. Two different people, Tales (624-547 BC) and Pythagoras (569-475 BC), are considered to be 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 great 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 a group around him to teach what he learned. It’s assumed that abstract proof centered on reasoning, which is not predicated on mathematics – experimental verification, entered into Tales. In addition, Tales is the person who is known as the first 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, visited Egypt following his advice, learned geometry there, visited Egyptian temples, learned religious information, and was taken to Babylon by capturing the Persians throughout the occupation of Egypt by the Persians. it is known. During his 5 years in Babylon, he learned mathematics, music and religious information, and after returning to Samos, he created a school and tried to teach 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 folks of this school called “mathematics” live together and they are connected together with oath. The second group consists of 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 just 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,… will be the fractional numbers that indicate the ratio of the part to the whole. The emergence of irrational numbers with the theorem called the Pythagorean theorem (the square of the right sides of a right triangle equals the square of the hypotenuse) put the Pythagorean school in a heavy 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 with a big cyber named Cylon. Pythagoras saved his life, but after a couple of years he died. Pythagoras’thoughts, the Pythagorean school lived for quite some time under this or that name. As could be understood from these details, Egyptian and Mesopotamian mathematics are the basis of Greek mathematics.

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