Innovative Ways to Teach Math

Believe it or not, math can be taught in some very innovative ways, and private schools are some of the top educational institutions pioneering new ways to master a traditional subject. A case study in this unique approach to teaching math can be found at one of the top boarding schools in the US, the Phillips Exeter Academy. Years ago, teachers at Exeter developed a series of math books containing problems, techniques, and strategies that are now being used at other private day and boarding schools. This technique has become known as Exeter Math.   The Process of Exeter Math What makes Exeter Math truly innovative, is that the traditional classes and course progression of Algebra 1, Algebra 2, Geometry, etc., is done away with in favor of students learning the skills and computations necessary to solve problems. Every homework assignment contains elements of each traditional math course, rather than separating them out into segmented annual learning.  The math courses at Exeter are centered on the math problems  written by the teachers. The entire course is different from traditional math classes in that it is problem-centered rather than topic-centered. For many, the traditional middle or high school math class generally presents a topic within the class time with the teacher and then asks students to complete lengthy assignments at home that consist of repetitive problem-solving exercises, intended to help students better master the procedures for homework. However, the process is altered in Exeters math classes, which involve little direct instruction drills. Instead, students are given a small number of word problems to complete each night independently. There is little direct instruction about how to complete the problems, but there is a glossary to help students, and the problems tend to build on each other. The students direct the learning process themselves. Each night, students work on the problems, doing the best they can, and log their work. In these problems, the learning  process  is just as important as the answer, and teachers want to see all of the students’ work, even if it is done on their calculators. What If a Student Struggles With Math? Teachers suggest that if students are stuck on a problem, they make an educated guess and then check their work. They do this by making up an easier problem with the same principle as the given problem. Since Exeter is a boarding school, students can visit their teachers, other students, or the math help center if they are stuck while doing their homework in their dorms at night. They are expected to carry out 50 minutes of concentrated work per night and to work persistently, even if the work is very difficult for them. The next day, students bring their work to class where they discuss it in a seminar-like style around a Harkness table, an oval-shaped table that was designed at Exeter and is used in most of their classes to facilitate conversation. The idea is not to just present the right answer but for each student to have a turn presenting his or her work to facilitate conversation, share methods, work out problems, communicate about ideas, and support other students. What Is the Purpose of the Exeter Method? While traditional math courses emphasize rote learning that does not connect to everyday issues, the purpose of the Exeter word problems is to help students really understand math by working out the equations and algorithms themselves rather than just being given them. They also come to understand the applications of the problems. While this process can be very difficult, particularly for students new to the program, students learn traditional math areas such as algebra, geometry, and others by working out the ideas themselves. As a result, they really understand them and how they relate to mathematical issues and problems they could encounter outside of the classroom. Many private schools across the country are adopting the Exeter math class materials and procedures, particularly for honors math class. Teachers at schools using Exeter math state that the program helps students own their work and take responsibility for learning it—rather than simply having it handed to them. Perhaps the most important aspect of Exeter math is that it teaches students that being stuck on a problem is acceptable. Instead, students realize that it’s all right not to know the answers right away and that discovery and even frustration are in fact essential to real learning. Updated by Stacy Jagodowski.

The Medieval Islamic Attitude Towards Christianity

The medieval Islamic attitude towards Christianity varied quite considerably; often Christians would be considered as either ‘People of the Book’, or as heretics. There was a common belief among Muslims that, while Muslims tolerated Christians and accepted them, Christians had a tendency to pre-condemn Muslims. On the other hand, although Christians did undeniably attempt to convert Muhammad, and many other Muslims, to Christianity, as well as refer to them repeatedly as pagans within their literature, it is almost understandable; within a century of the death of Muhammad in 632, Islam had spread across much of the known world, a dilemma that was unfathomable, theologically incomprehensible and simply terrifying for most Christians. The†¦show more content†¦It is clear that the East was a place that filled many European Christians with both fear and fascination, but the very nature of the Christian holy places being largely ruled by Muslims meant that the Christian West could not help but come into repeated contact with the East. The Islamic world was generally associated with relentless stereotypes, such as the character of the oppressive Oriental ruler, as well as the persistent idea of sexual immorality within Eastern customs. Some Christian doctrines, for example the thirteenth century Franciscan friars, strongly identifies Islam with the coming of the anti-Christ, and many medieval Christian writers displayed resentment towards Islam through attacking the basis of the religion in an attempt to undermine its validity. Muslims in Christian literature were ultimately not Muslims at all, but the fictional, projected Western archetype; as Matsushita states, the ‘medieval Christian literary repres entation of the Muslim was no

Primary Sourse Free Essays

Erin Gaudette AP Prep History Block 2 Primary Sources ‘Governor Berkeley Reports,’ American Spirit, pages 33-34 (#A2) LAST QUESTION ANSWER ONLY (#23) ‘A Contract for Indentured Service,’ American Spirit, pages 62-63 (#A1) ‘A Servant Girl Pays the Wages of Sin,’ American Spirit, page 69 (#A4) In the late 1600s Virginia was governed by Sir William Berkeley. In 1671, London asked Berkeley a series of questions including a question about the teachings of Christianity. He responded by saying, â€Å"our ministers are well paid, and by my consent should be better if they would pray more often and preach less. We will write a custom essay sample on Primary Sourse or any similar topic only for you Order Now † Governor Berkeley also believed that children ought to be taught religion by their parents. He said, â€Å"But, I thank God, there are neither free schools nor printing, and I hope we shall not have these hundred years. For learning has brought disobedience, and heresy. † I don’t agree with what Governor Berkeley believed. He contradicted his own beliefs. He talked about how he was against new ways of thinking or new ideas. He wanted everyone to believe in the Christian religion. If Berkeley wanted everyone to stay with traditional ideas, why would he have wanted individual families to teach religion? Wouldn’t it be less likely to create free thinkers if one minister taught the children the religion instead of individual families? Berkeley wants to prevent any form of heresy, yet he is provoking it. Indentured servants were often lower class people in England who would work for a number of years and would then be set free. In return for their work they would be given free passage to America by their owner. In 1635 a list of requirements were written for the servant and owner to follow. The form included orders for the owner to provide the servant with food, drink, clothing, shelter, free passage to the new world, and after their years of work are over to provide them with corn for a year and 0 acres of land, In my opinion, I think this contract is pretty fair. The contract makes the indentured servants seem like employees for a job. The indentured servants aren’t being forced to work; they are making the ecision to. Also, in return for their work they’re being repaid by their owners. The contract seems to give both parties a reasonable payment which makes the contract fair. Although I agree with the methods and payments of indentured servants, I don’t agree with the punishments some servants received. I do think some of the servants behaviors should be looked down upon, but I also think the punishment they faced was a bit harsh. Charles City County Court in Virginia has a record that shows how harsh the punishments got. Elizabeth Hatcher owned servant Anne Parke. When Anne Parke had a child her years of work were doubled. Every indentured servant and their owner had a contract for the amount of years they worked. Therefore, when Anne Parke’s contract was doubled, it was violating her rights. I personally think the system created for indentured servants was fair, but since the agreement was not always followed it wasn’t carried out equally. The system could have been successful if both the owners and servants had followed it properly. How to cite Primary Sourse, Essay examples

The Suicide Machines free essay sample

If youare into punk music, you will love The Suicide Machines, a band fromMichigan. The four members are Jason Navarro on vocals, Royce Nunley onbass, Dan Lukacinsky on guitar and Erin Pitman on drums replacing DerekGrant. The Suicide Machines have three albums; their first on amajor label was Destruction by Definition. This albumconsists of mainly new-school punk similar to Rancid, and a heavy doseof ska. My favorites off this album are No Face, aspectacular ska song, and Hey, a song that beautifullycombines punk and ska. The Suicide Machines second album isBattle Hymns, and focuses on the roots of punk music,similar to Operation Ivy. High Society is an excellent punksong, and Black and White World deals with the brutishrealities of society. The Suicide Machines self-titled third CD wasreleased this February. To hear the single Sometimes I DontMind, go to www. suicidemachines.com. The band also puts onan excellent live performance; Ive seen them twice. We will write a custom essay sample on The Suicide Machines or any similar topic specifically for you Do Not WasteYour Time HIRE WRITER Only 13.90 / page The crowds wereespecially rowdy, and the mosh pits were outrageous both times. Peoplewere getting stomped left and right. I left with minor bruises, but itwas well worth it. The downside of the night was I brought myvideo camera and the manager seized it. I asked if I could get my tapeand he said, Why dont you go ask the Suicide Machines, theyreout back. Astonished, I went to meet them. I first talked to Erin,who was signing autographs. I told him how big a fan I was and asked ifI could get Royces autograph. (I like Royce because I play bass too.)Instead of just getting Royces autograph he got Royce, which was quitepossibly the greatest thing that has ever happened to me. Royce was verycool and told me all about how the band made it big, and how he learnedto play bass. I really suggest purchasing their albums if youare looking for something new, or if you like punk.