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The economy in most of Europe was agrarian and the children of serfs started work as soon as they were able. It was accepted as a truth by Christians that man was created by God in the image of Adam with his share of original sin and that a boy was...
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Alcuin — developed teaching material that were based on the catechetical method - repeating and memorizing questions and answers, although often understanding the information was not important. These skills were also needed in the great abbeys such as Cluny. There was a divergence between the needs of town and monasteries and we see the development of parish, chantry, monastic and cathedral schools. With the entry of women into church life, convents were established and with them convent schools. Girls entered at the age of eight and were taught Latin grammar, religious doctrine and music, and the women's arts of spinning, weaving, tapestry, painting and embroidery. Chantry schools were the result of charitable donations and educated the poor. Beginning in , parishes were obliged to have a school from , and cathedrals had to establish schools after the Lateran Council of Elementary education was mainly to teach sufficient Latin for the trivium and the quadrivium that formed the basis of the secondary curriculum.
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Renaissance boys from the age of five learned Latin grammar using the same books as the Roman child. Others were educated in schools attached to the parishes, cathedrals or abbeys. From the 13th century, wealthy merchants endowed money for priests to "establish as school to teach grammar". These early grammar schools were to teach basic, or elementary grammar, to boys. No age limit was specified. The Reformation and the Dissolution of the Monasteries disrupted the funding of many schools. The schools petitioned the King, Edward VI , for an endowment. Paupers and the poor[ edit ] Though the Grammar schools which were set up to deliver elementary education, they did require their entrants to already have certain skills. In particular, they expected them to be able to read and write in the vernacular. There was a need for something more basic.
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Martin Isaacs Book Summary: One of the challenges many mathematics students face occurs after they complete their study of basic calculus and linear algebra, and they start taking courses where they are expected to write proofs. Historically, students have been learning to think mathematically and to write proofs by studying Euclidean geometry. In the author's opinion, geometry is still the best way to make the transition from elementary to advanced mathematics.
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The book begins with a thorough review of high school geometry, then goes on to discuss special points associated with triangles, circles and certain associated lines, Ceva's theorem, vector techniques of proof, and compass-and-straightedge constructions. There is also some emphasis on proving numerical formulas like the laws of sines, cosines, and tangents, Stewart's theorem, Ptolemy's theorem, and the area formula of Heron. An important difference of this book from the majority of modern college geometry texts is that it avoids axiomatics. The students using this book have had very little experience with formal mathematics. Instead, the focus of the course and the book is on interesting theorems and on the techniques that can be used to prove them. This makes the book suitable to second- or third-year mathematics majors and also to secondary mathematics education majors, allowing the students to learn how to write proofs of mathematical results and, at the end, showing them what mathematics is really all about.
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