Ethical behavior in workplace Essay Example | Topics and Well Written Essays - 500 words

Moral conduct in work environment - Essay Example Till as of late I was working for a cheap food joint. At some point, I was truly stunned at the manner in which my supervisor carried on towards a newcomer, an Afro American youth, who was anxious to serve the client. He had not just reproached the little fellow for indicating superfluous energy but at the same time was very vocal in demonstrating his racial partiality by denying him his entitlement to serve clients. I accept that if decent variety inside workforce is available, there is positively a bad situation for racial segregations. Working environment condition should continually support moral practices. It is basic that administrative initiative must show exclusive requirement of set of principles since they are individuals who are equipped for spurring other for ideal work execution. In reality, the pioneers, through self model and having commendable characteristics like resistance, multifaceted understanding and compassionate disposition enormously make an empowering workpl ace. They additionally advance positive relationship that reflects in improved profitability and cooperative attitude of the association. I was outraged by the entire scene and responded by bringing up that the administrator was damaging hard working attitudes as well as that his demonstration can be legitimately understood as racial segregation. As a lesser administrator, my remarks were not generally welcomed yet atleast the youngster was permitted to serve new clients. I was given a negative passage in my worker logbook.

The Middle Passage free essay sample

The Middle Passage, was it simply the course taken by the slave dispatches over the Atlantic, or rather, the time in our history when people were torn from their local land,chained shackled on board a slave transport, being moved to a New World. Which will you recall,the course or the boat? The consolidated abilities of writers, David Manic Malcolm Cooley offers a top to bottom view into our history as it identifies with The Middle Passage in their February 1 962 issue of American Heritage our supplemental perusing section 4.The writers makes it understood immediately, that Europeans didn't start the dead of sending out slaves along the African coast. This had been an act of the traders Of Timeout the Moorish realms north Of the Sahara. There had additionally been a long history of transoceanic slave exchange. Negroes (as called during this time period,refers to the African Americans of today) were in Santos Domingo by 1 503, the initial 20 slaves were sold in Jamestown,Virginia in 1619. The terrible and barbaric conditions which the Africans were confronted with on their journey obviously show the incredible insidiousness of the slave trade.The Middle Passage was the most notorious course of this triangular exchange. Despite the fact that peril hid continually all through the journey over the Atlantic, the most serious risk to the slave transports consistently came when they were stacking on the African coast. Once on board the boats, the Negroes understood that they were being sent far away from home, and frequently there was brutality even before the boat set sail. In any case, the greater part of these uprisings were effectively put down. Others bounced over the edge and dove from the boat into the ocean, deciding to either suffocate or be eaten up by murderous sharks as opposed to be taken from their country. The Middle Passage took somewhere in the range of one to five months relying upon climate conditions with wind conditions differing by season. The boats utilized were intended for the vehicle of merchandise as opposed to individuals since two of the legs of the triangular exchange included load, for example, containers of rum or molasses or boxes of materials and different products, for example, parcels of cotton and tobacco. Because of this structure, the conditions on board delivers running the Middle Passage with human payload were poor with essentially nonexistent sanitation offices as the boats were not intended for the vehicle of a few hundred people.African lords, warlords and private ruffians offered their prisoners to Europeans who held a few waterfront fortifications. Whenever uncommon open doors emerged, the Europeans themselves hijacked African individuals. The hostages were typically power walked to these ports along the western shore of Africa, where they were held for buy to the European or American slave brokers. Individuals were typically stuffed into the boats shipping at any rate 400 slaves that were affixed in the load hold, monitored by roughly 35 team. Numerous boats contained up to 700 slaves on board one slave ship.The male hostages were regularly affixed together two by two to spare space; right leg to the following keeps an eye on left leg CLC while the ladies and kids may have had fairly more space. The prisoners were taken care of extremely little segments of beans, corn, sweet potatoes, rice, and palm oil, regularly only enough to continue them. Slaves were taken care of two dinners every day with water, yet on the off chance that food was rare, slaveholders would get need over suppers. In some cases hostages were permitted to move around during the day, yet numerous boats kept the shackles on all through the strenuous excursion. Around 1 millionAfricans were compellingly taken from Africa and took the journey abroad. Illness and starvation because of the length of the entry were the principle supporters of the loss of life with amoebic loose bowels and scurvy causing most of passings. Moreover, flare-ups of smallpox, syphilis, jungle fever, measles, and different maladies spread quickly in the nearby quarter compartments. The quantity of dead expanded with the length of journey, since the frequency of looseness of the bowels and of scurvy expanded with longer stretches adrift as the quality and measure of food and water decreased with each spending day.In expansion to physical ailment, numerous slaves turned out to be too discouraged to even consider eating or capacity effectively as a result of the loss of opportunity, family, security, and their own mankind. This regularly prompted more awful treatment like coercively feeding or lashings. Some even ended it all before they showed up in the New World. The Haitian upset of 1 804 prompted the prohibiting of the Atlantic Slave Trade by the essential slave exchanging countries, Great Britain and the United States, in 1807. Be that as it may, the vehicle of hostages from Africa to the Americas proceeded on a decreased scale until the center of the century. Inside the United States, a few Southern slave states (basically Virginia) gave captives to other slave states particularly the new states appearing as the United States extended westbound (see Northwest Ordinance). This slave exchange interior to the Lignite States finished with the Emancipation Proclamation, the American Civil War, and the Thirteenth Amendment to the United States Constitution What has not been a subject of discussion is that the experience of the African slaves along the Middle Passage remains today as the central case of unman abuse and suffering.The conditions which the slaves were confronted with on this excursion graphically show the outright fear which was African-American bondage. For a considerable length of time the blacks were deceived by the unfeeling ravenousness of an European class which was further developed, and in this manner in a situation to misuse them. The Africans, who were caught, marked, and secured chains, had their mankind totally stripped away by bondage. Exemplified by the frightfulness of the Middle Passage, bondage and the slave exchange have forever imbrue the character Of all mankind.

Essay Topics - How to Write Your Own Disney Essay Topics

<h1>Essay Topics - How to Write Your Own Disney Essay Topics</h1><p>Writing a Disney paper points is simple. It takes a straightforward thought and transforms it into a balanced piece that will intrigue both your peruser and yourself. Realizing how to make an interesting contention for a subject can take a piece from normal to great, leaving you with a genuine inventive effort.</p><p></p><p>The initial phase recorded as a hard copy Disney exposition themes is to pick the point that you feel generally good with. This may appear to be essential, yet it is significant. You ought to have the option to pick a point that you can expound on without a lot of stress. Many paper subjects are naturally conventional, as they spin around a dearest film or toy line.</p><p></p><p>There are a few diverse article databases to look over. A few models are Stanford Encyclopedia of Philosophy, Merriam-Webster's Collegiate Dictionary, and W ebster's International Dictionary. Likewise, there are a lot of assets online that contain advisers for article themes, remembering those found for GoodStuffBlog.com.</p><p></p><p>Once you have picked the subject, you can begin to draft out your paper points. It is useful to utilize a blueprint or work diary to assist you with thoroughly considering your themes, as it can assist you with abstaining from copying composing. The layout you use ought to incorporate the various advances you should take to finish the assignment.</p><p></p><p>Once you have made your diagram, you will need to conceptualize your thoughts. This procedure is regularly alluded to as conceptualizing. By conceptualizing, you improve thought of what thoughts you have that can be transformed into an exposition theme. After this conceptualizing procedure, you will need to know whether there are any themes that would be reasonable to compose on.</p><p></p ><p>When you are chipping away at your article points, you will need to recall that perhaps the most ideal approaches to ensure that the whole paper ismemorable is to be unique. It is frequently said that you ought not duplicate something from another source, yet you can regularly discover thoughts through different sources than others may anticipate. Subjects, characters, and circumstances are everything that can be utilized to think of a unique article topic.</p><p></p><p>For your exposition points, you will probably need to make a nitty gritty layout. This will incorporate the entirety of the means you should take so as to finish the article. It tends to be a smart thought to work out an unfinished copy of your article before really expounding. This will guarantee that the style of your article is like others that you have seen, which causes you accomplish an exceptional style.</p><p></p><p>For Disney exposition themes, you might need to consider others' works. The thought is to pick a paper subject that is in accordance with different pieces that have been composed as of now. One case of an article theme that is like Disney is an exposition about how the arrangement has affected kids' writing. This is an extraordinary method to make a genuinely unique article topic.</p>

Writing Essays on Legal Issues - Is It Difficult to Write?

<h1>Writing Essays on Legal Issues - Is It Difficult to Write?</h1><p>Why would it be a good idea for you to be so specific with composing a unique paper on a legitimate issue? You have chosen to turn into an expert author and this will likely be your profession for quite a while. Toward the start of your profession, composing the expositions isn't unreasonably hard, yet later it is as troublesome as composing different kinds of articles.</p><p></p><p>For an individual, it has not been an issue to compose the papers in their underlying time of composing. In any case, later it turns out to be increasingly troublesome when they would prefer not to frustrate anyone by making something, which is really not the same as what an ordinary individual will be expecting.</p><p></p><p>The primary explanation is presumably that a large portion of the individuals are now doing it. They as of now have the information on the best way to compose and they can do it just without any problem. Furthermore, composing articles on legitimate issues will likewise be simpler in the event that you will have some information on the lawful field and you will have the option to discover how to expound on it.</p><p></p><p>Now, this is a reality that you have to know in light of the fact that the theme you will compose on is constantly identified with a specific piece of the law. It implies that in the event that you will attempt to compose something without having the information on the subject, it won't be acceptable by any means. This will cause you to compose something totally off-base and your entire possibility of being acknowledged by the college will be lost.</p><p></p><p>In request to defeat this situation, you should be exceptionally cautious when you are composing the exposition. As a matter of first importance, it will be fundamental for you to discover the perspective of the peruser. At the end of the day, you should discover what their brain needs to hear and you should realize the most appropriate approach to make them heard.</p><p></p><p>Second, you ought to be prepared to invest some energy in the exploration about the particular subject that you will compose. Along these lines, you will have the option to discover progressively about the subject and you will have the option to find the escape clauses that were left.</p><p></p><p>Third, during the underlying time of composing, you can think about the various approaches to do this. You can pick the free assets accessible in the web and the books that you read, or you can make your own exploration. Yet, for the individuals who have an enthusiasm for doing research and have the ability to do the exploration, they ought to be prepared to put some cash into the project.</p><p></p><p>Now, it is likewise fundamental for you to be cautious with the structure of the first article. In the event that you won't have the correct structure for the composition, you will think that its extremely hard to compose it. It is significant that you will realize how to compose the exposition appropriately before you start.</p>

Essay Hook for Social Topics - a Quick Overview

<h1> Essay Hook for Social Topics - a Quick Overview</h1> <p>Creating writings is a mind boggling task for all intents and purposes any individual, yet it isn't generally an ability it is a greater amount of aptitude. Clearly, you shouldn't make a paper for experts in science using young dialect. English language classes as a rule anticipate a ton of composing. Thusly, it's basic for the understudies to adhere to the very same techniques in passage two in the ensuing sections of the human body. </p> <p>There are examples when understudies are absolutely allowed to select a point. Recollect your last grade essentially is dependent upon the point. Indeed, in light of the fact that in the occasion you select a mistaken subject or one that is uncomfortable that you manage, you may stall out with it and end getting a less than stellar score. For example, you can pick a subject for rudimentary, center, or higher school. </p> <p>By posting demonstra ted realities at the very beginning of your paper, you will make intrigue that might be conveyed all through the rest of the article. The sole thing you have to focus on is whether your paper does or doesn't have to contain the absolute first individual portrayal. There are numerous conceivable thoroughly analyze exposition subjects, and various them are hard to perform. In any case, making sense of the absolute best theme for your paper isn't your lone worry for an understudy. </p> <p>If you wish to make your exposition fascinating, you can talk about bigotry with regards to contemporary culture. As you most likely know, such a paper begins with the presentation of introducing a theme and representing an announcement. An exposition might be utilized to give a contention the objective of persuading the crowd to have a remain on a particular issue. All in all, you can see that composing a powerful exposition isn't a mind medical procedure. </p> <p>Bear as a top priority, in any event, when you start with a diverting tale, it doesn't imply your entire exposition should be entertaining. Actually, be that as it may, you can hold up until your entire exposition is almost completed and afterward return and revamp the specific first passage. You may keep on saving your factious articles for your forthcoming activity portfolio on the off chance that they're profoundly reviewed. With a little energy and difficult work, you are sure to think about a great unlawful equity paper. </p> <p>As a paper generally means to give powerful answers for certain issues, the extraordinary thought is to begin with exhortation. Regardless, immediate and backhanded statements are fundamental to help your comprehension of scholastic composing style. Picking the right theme for an enticing discourse can be not such a simple issue to do as it would appear. Making up an excellent exposition snare incorporates practice, yet there can be times which you can't seem to pull it off. </p> <h2>The Little-Known Secrets to Essay Hook for Social Topics </h2> <p>It's currently easier and modest to convey and interface with individuals around the globe. The essentialness of internet based life can't be overlooked since it has an incredibly pivotal impact in our lives today. The capacity of online networking is fairly high and has its impacts on every single person. Innovation has caused a far reaching shift in how individuals experience the world and the manner by which they live their lives. </p> <p>You might need to type in an inquisitive truth on the subject that is obscure to most of the people. Forceful youngsters and ladies use web based life to support their status in school and different establishments. In rundown, perusers don't have a great time following the surge of your considerations. In the event that your perusers are generally children and youthful people, the simple tale will be a perfect match. </p> <h2>Essay Hook for Social Topics Options </h2> <p>Don't disregard to take the preliminary measures and figure out which kind of snare is the most valuable. A snare isn't simply an allegory. It ought to be solid and proper. An awesome snare is the one which has numerous unmistakable applications in 1 text.</p> <p>Taking the chance to indicate a careful scene will help your peruser have a perfectly clear picture in their brains and make a beneficial snare. It is critical to characterize what an astounding acquaintance is before figuring out how with form an awesome snare. Expounding on affection can be somewhat dubious. In the occasion the style of composing permits you to be inventive, scan for a strange, unique intends to communicate the significant subject of your paper with the help of such incredible snares for papers. </p> <h2> The Downside Risk of Essay Hook for Social Topics </h2> <p>The constructive outcome on correspondence unquestionably defeats the negative and makes it very valuable. You just need to arrange a generally excellent paper from specialists with the best scholastic degrees in a variety of fields. Regardless of whether you're a master in a specific field, don't be hesitant to utilize and refer to outside sources. Choosing the correct sub jects may take some time on the off chance that you don't have a rundown of test points confronting you. </p>

How Do I Get My Old College Essay Secrets That No One Else Knows About

<h1> How Do I Get My Old College Essay Secrets That No One Else Knows About </h1> <h2> The Ideal Approach for How Do I Get My Old College Essay </h2> <p>In ordinary conditions once the cost of assembling an item expands, the expense of that thing increments. At the point when it respects the extremely low sticker price of food in the usa, belts need to get fixed and corners must be cut. At the point when you place your buy, you will be provided a cost estimate. At the point when it has to do with protracted requests, they'll be consequently partitioned into a few sections for you just as your essayist's wellbeing and comfort. </p> <h2>The New Fuss About How Do I Get My Old College Essay </h2> <p>It's critical to show your ability to be an inside and out eyewitness of the Earth, since that will be one of your key occupations as an undergrad. Possibly you're troubled or satisfied with the work done, don't stress. Clarify your respon sibilities, and you'll be the kind of understudy universities find tremendously appealing. Most understudies react that way. </p> <p>College life is a troublesome test for some. Your incapacity or emotional well-being could be a basic part of your character. Be reasonable as you are defining up objectives. In the two circumstances, you hit your objective of more prominent peruser engagement.</p> <h2>The Basic Facts of How Do I Get My Old College Essay </h2> <p>Instead, the job of a school article is to be a piece of an all out promoting and publicizing bundle. Scholarly composing can be a difficult and debilitating undertaking to complete, yet in the event that you realize the best spot to discover master help, you won't battle any longer. The paper is the place to empower the affirmations office of your expected school get the chance to comprehend your character, character, and the gifts and capacities that aren't on your transcript. The school affirmations exposition is the ideal opportunity to grandstand the uncommon parts of your temperament and developmental encounters that ma de you the individual you're today. </p> <p>When you have set your buy, the journalists that are intrigued and capable in the worthy field begin offering for it. As such, you might want to ensure that you're introducing your actual self in the absolute best light. Applying to school can be a baffling and threatening procedure for everyone. In the occasion you need more time to deal with all your composing assignments, leave it to us. </p> <p>A explicit entertainer could be successful paying little heed to her evil presences. Plunk down, consider the story that you need to compose. </p> <p>If you can make your voice pervade all through your paper, it will surely be yours. Afterward, when you're listening that what you recorded story to discover a sentiment of the best approach to compose it, you may likewise get a sentiment of the tone with which you have to recount to that story. To make you progressively alright with the general understanding, we've planned a live talk, so you may stay on top of your author during the activity practice. Said that way, there was no inclination of novelty to it. </p> <h2>What Does How Do I Get My Old College Essay Mean? </h2> <p>There's a ton of work which goes into making an eminent article. Right now, how about we look at a few instances of genuine school article beginnings to show how and why they work. Along these lines, in case you're figuring, who can do my school paper as fast as could reasonably be expected, the answer will be EssayShark.com. </p> <p>Deciding upon the most reasonable association to adapt to your school affirmation article isn't exactly as simple as you would might suspect. So far as exposition structure goes, a 4 or 5 section article dependent on the quantity of focuses you are going to need to contend is a fantastic beginning. Next time your educator utilizes the words compose an article you don't have to flinch or kick the bucket only somewhat inside. </p> <p>Unfortunately, bumbling in the TMI zone of article points is more common than you accept. Our journalists have finished a few papers of premium quality. The greater part of the article utilizes standard English and English sentence structure. In case you're in the focal point of your exposition composing strategy, you are going to need to see our recommendations on what article entanglements to prevent.</p> <p>Writing your article will be much less complex on the off chance that you work out the total of it first and simply, at that point return and work out definitely the way that it should begin. You're not composing for yourself here, yet rather for a significant explicit kind of peruser. Presently you comprehend that a genuine and subjective on-line article composing administration may give extraordinary help to your learning, it's an ideal opportunity to put your request. In the event that you comprehend that you've misread the brief in the focal point of your composing technique, you have to begin composing again from the very beginning. </p>

College Expository Essay Topics - Choosing the Right Ones

<h1>College Expository Essay Topics - Choosing the Right Ones</h1><p>Many understudies will battle with the issue of looking over a wide range of school explanatory paper themes. Actually, the most ideal approach to conclude which is directly for you is to examine a couple of various models and pick a theme that sounds intriguing to you. Here are a couple of thoughts to get you started.</p><p></p><p>-Students who appreciate these kinds of subjects ordinarily utilize the word 'investigate'get to the base of.' Examples may include: government, human expressions, food, design, history, or math. For instance, you could compose an article on why some engineering is wonderful and others aren't; talk about how food is an image of development; and get to the base of the morals of corporate business.</p><p></p><p>-College informative paper themes that you may likewise like are 'people'truths and fantasies.' You could discuss wh y your preferred nourishments and beverages are still around in eateries today; examine the significance of words, for example, 'popular'retro;' or read about the historical backdrop of different societies. In the event that you need to get into legislative issues, ask yourself 'What is reality behind the bits of gossip in the news?'</p><p></p><p>-The theme you may discover fascinating is called 'fiction.' You could discuss how expressions of the human experience have been coordinated into regular day to day existence; or talk about why the word 'fun' is utilized so frequently. You could likewise discuss the legislative issues of individuals who behave recklessly; or notice how American goals are as yet alive in Japan.</p><p></p><p>-Some of the best school interpretive exposition subjects originate from where they happen to be composed, explicitly 'commentaries.' The model frequently offered is to discuss how a specific foot needs medi cal procedure or why perusing a specific page or bit of paper is significant. Another thought may be to investigate what a foot resembles in specific situations and to take note of how individuals get injured by botches they make, for example, being careless.</p><p></p><p>Whatever you do, don't stress on the off chance that you concoct something unordinary in the subject of your school interpretive article points. One thing you can do is to look into a few words and check whether they sound like you. Maybe you will think that its simpler to concoct the right words, or maybe you will locate that another word is more appropriate.</p><p></p><p>College explanatory paper subjects like these are unquestionably not equivalent to an ideal theme for you. They are only a start for you, and it is essential to think about the entirety of your alternatives, before you choose.</p>

Tips for Writing an Ethiopian College Essay

Tips for Writing an Ethiopian College EssayAn Ethiopian college essay is an important aspect of college admissions. It shows that you understand and appreciate the culture and history of Ethiopia. The essay should be written in clear, easy to understand English.The goal of an Ethiopian college essay is to explain your reasoning behind a particular decision. You will want to demonstrate to your college what type of person you are. You also need to find out what kind of college you would like to attend. This essay does not need to be long and boring.When writing your essay, think about what you want to accomplish and why. You need to discuss what kind of person you are, your situation, and how the issues you face are related to this. Also take time to articulate why you are writing this essay. This needs to be a concise statement. The facts should flow with ease.One of the most important things you can do when writing your essay is to write with your voice. This does not mean that you have to rewrite the essay and include a different voice. This just means that you need to write from your own perspective.What I mean by this is to be honest with yourself about what it is that makes you a strong point of view. Make sure that you are getting across the things that you feel strongly about. When you are done outlining these points, take the time to translate them into your essay.When you first meet someone, you may have a feeling that you are this person. However, until then, we may not fully understand each other. Writing your essay allows you to open up and share your thoughts, feelings, and emotions.Another important aspect of writing your essay is to focus on your objective. This allows you to be clear with what you want and what you need. This will help make your topic easier to read.The best part about writing this essay is that it is not as hard as it seems. You can even get some help from your friend or family. With so many resources, you will find it easier t han you ever imagined.

Vedic Mathematics Multiplication

Abstract Vedic Mathematics has been the rage in American schools. The clear difference between Asian Indians and average American students approach to solving math problems had been evident for many years, finally prompting concerted research efforts into the subject. Many students have conventionally found the processes of algebraic manipulation, especially factorisation, difficult to learn. Research studies have investigated the value of introducing students to a Vedic method of multiplication of numbers that is very visual in its application. The question was whether applying the method to quadratic expressions would improve student understanding, not only of the processes but also the concepts of expansion and factorisation. It was established that there was some evidence that this was the case, and that some students also preferred to use the new method. Introduction Is Vedic mathematics a kind of magic? American students certainly thought so, in seeing the clear edge it gave to their Asian counterparts in public and private schools. Vedic schools and even tuition centers are advertised on the Web. Clearly it has taken the world by storm, and for valid reasons. The results are evident in math scores for every test administered. Vedic mathematics is based on some ancient, but superb logic. And the truth is that it works. Small wonder that it hails from India, purported to be the land that gave us the Zero or cipher. This one digit is the basis for counting or carrying over beyond nine- and is in fact the basis of our whole number system. It is the Arabs and the Indians that we should be indebted to for this favour to the West. The other thing about Vedic mathematics is that it also allows one to counter check whether his or her answer is correct. Thus one is doubly assured of the results. Sometimes this can be done by the Indian student in a shorter time span than it can using the traditional counting and formulas we have developed through Western and European mathematicians. That makes it seem all the more marvellous. If that doesnt sound magical enough, its interesting to note that the word Vedic means coming from Vedas a Sanskrit word meaning divinely revealed. The Hindus believe that these basic truths were revealed to holy men directly once they had achieved a certain position on the path to spirituality. Also certain incantations such as Om are said to have been revealed by the Heavens themselves. According to popular beliefs, Vedic Mathematics is the ancient system of Mathematics which was rediscovered from the Vedas between 1911 and 1918 by Sri Bharati Krsna Tirthaji (1884-1960). According to him, all Mathematics is based on sixteen Sutras or word-formulas. Based on Vedic logic, these formulas solve the problem in the way the mind naturally works and are therefore a great help to the student of logic. Perhaps the most outstanding feature of the Vedic system is its coherence. The whole system is beautifully consistent and unified- the general multiplication method, for example, is easily reversed to allow one-line divisions and the simple squaring method can be reversed to give one-line square roots. Added to that, these are all simply understood. This unifying quality is very satisfying, as it makes learning mathematics easy and enjoyable. The Vedic system also provides for the solution of difficult problems in parts; they can then be combined to solve the whole problem by the Vedic method. These magical yet logical methods are but a part of the whole system of Vedic mathematics which is far more systematic than the modern Western system. In fact it is safe to say that Vedic Mathematics manifests the coherent and unified structure of mathematics and the methods are complementary, straight and easy. The ease of Vedic Mathematics means that calculations can be carried out mentally-though the methods can also be written down. There are many advantages in using a flexible, mental system. Pupils can invent their own methods, they are not limited to the one accurate method. This leads to more creative, fascinated and intelligent pupils. Interest in the Vedic system is increasing in education where mathematics teachers are looking for something better. Finding the Vedic system is the answer. Research is being carried out in many areas as well as the effects of learning Vedic Maths on children; developing new, powerful but easy applications of the Vedic Sutras in geometry, calculus, computing etc. But the real beauty and success of Vedic Mathematics cannot be fully appreciated without actually practising the system. One can then see that it is perhaps the most sophisticated and efficient mathematical system possible. Now having known that even the 16 sutras are the Jagadguru Sankaracharyas invention we mention the name of the sutras and the sub sutras or corollaries in this paper. The First Sutra: Ekdhikena Prvena The relevant Sutra reads Ekdhikena Prvena which rendered into English simply says By one more than the previous one. Its application and modus operandi are as follows. (1) The last digit of the denominator in this case being 1 and the previous one being 1 one more than the previous one evidently means 2. Further the proposition by (in the sutra) indicates that the arithmetical operation prescribed is either multiplication or division. Let us first deal with the case of a fraction say 1/19. 1/19 where denominator ends in 9. By the Vedic one line mental method. A. First method B. Second Method This is the whole working. And the modus operandi is explained below. Modus operandi chart is as follows: (i) We put down 1 as the right-hand most digit 1 (ii) We multiply that last digit 1 by 2 and put the 2 down as the immediately preceding digit. (iii) We multiply that 2 by 2 and put 4 down as the next previous digit. (iv) We multiply that 4 by 2 and put it down thus 8 4 2 1 (v) We multiply that 8 by 2 and get 16 as the product. But this has two digits. We therefore put the product. But this has two digits we therefore put the 6 down immediately to the left of the 8 and keep the 1 on hand to be carried over to the left at the next step (as we always do in all multiplication e.g. of 69 2 = 138 and so on). (vi) We now multiply 6 by 2 get 12 as product, add thereto the 1 (kept to be carried over from the right at the last step), get 13 as the consolidated product, put the 3 down and keep the 1 on hand for carrying over to the left at the next step. (vii) We then multiply 3 by 2 add the one carried over from the right one, get 7 as the consolidated product. But as this is a single digit number with nothing to carry over to the left, we put it down as our next multiplicand. (viii) and xviii) we follow this procedure continually until we reach the 18th digit counting leftwards from the right, when we find that the whole decimal has begun to repeat itself. We therefore put up the usual recurring marks (dots) on the first and the last digit of the answer (from betokening that the whole of it is a Recurring Decimal) and stop the multiplication there. Our chart now reads as follows: The Second Sutra: Nikhilam Navatacaramam Daatah Now we proceed on to the next sutra Nikhilam sutra The sutra reads Nikhilam Navatacaramam Daatah, which literally translated means: all from 9 and the last from 10. We shall and applications of this cryptical-sounding formula and then give details about the three corollaries. He has given a very simple multiplication. Suppose we have to multiply 9 by 7. 1. We should take, as base for our calculations that power of 10 which is nearest to the numbers to be multiplied. In this case 10 itself is that power. Put the numbers 9 and 7 above and below on the left hand side (as shown in the working alongside here on the right hand side margin); 3. Subtract each of them from the base (10) and write down the remainders (1 and 3) on the right hand side with a connecting minus sign () between them, to show that the numbers to be multiplied are both of them less than 10. 4. The product will have two parts, one on the left side and one on the right. A vertical dividing line may be drawn for the purpose of demarcation of the two parts. 5. Now, Subtract the base 10 from the sum of the given numbers (9 and 7 i.e. 16). And put (16 10) i.e. 6 as the left hand part of the answer 9 + 7 10 = 6 The First Corollary The first corollary naturally arising out of the Nikhilam Sutra reads in English whatever the extent of its deficiency lessen it still further to that very extent, and also set up the square of that deficiency. This evidently deals with the squaring of the numbers. A few elementary examples will suffice to make its meaning and application clear: Suppose one wants to square 9, the following are the successive stages in our mental working. (i) We would take up the nearest power of 10, i.e. 10 itself as our base. (ii) As 9 is 1 less than 10 we should decrease it still further by 1 and set 8 down as our left side portion of the answer 8/ (iii) And on the right hand we put down the square of that deficiency 12 (iv) Thus 92 = 81 The Second Corollary The second corollary in applicable only to a special case under the first corollary i.e. the squaring of numbers ending in 5 and other cognate numbers. Its wording is exactly the same as that of the sutra which we used at the outset for the conversion of vulgar fractions into their recurring decimal equivalents. The sutra now takes a totally different meaning and in fact relates to a wholly different setup and context. Its literal meaning is the same as before (i.e. by one more than the previous one) but it now relates to the squaring of numbers ending in 5. For example we want to multiply 15. Here the last digit is 5 and the previous one is 1. So one more than that is 2. Now sutra in this context tells us to multiply the previous digit by one more than itself i.e. by 2. So the left hand side digit is 1 2 and the right hand side is the vertical multiplication product i.e. 25 as usual. Thus 152 = 1 2 / 25 = 2 / 25. Now we proceed on to give the third corollary. The Third Corollary Then comes the third corollary to the Nikhilam sutra which relates to a very special type of multiplication and which is not frequently in requisition elsewhere but is often required in mathematical astronomy etc. It relates to and provides for multiplications where the multiplier digits consists entirely of nines. The procedure applicable in this case is therefore evidently as follows: i) Divide the multiplicand off by a vertical line into a right hand portion consisting of as many digits as the multiplier; and subtract from the multiplicand one more than the whole excess portion on the left. This gives us the left hand side portion of the product; or take the Ekanyuna and subtract therefrom the previous i.e. the excess portion on the left; and ii) Subtract the right hand side part of the multiplicand by the Nikhilam rule. This will give you the right hand side of the product. The following example will make it clear: The Third Sutra: rdhva Tiryagbhym rdhva Tiryagbhym sutra which is the General Formula applicable to all cases of multiplication and will also be found very useful later on in the division of a large number by another large number. The formula itself is very short and terse, consisting of only one compound word and means vertically and cross-wise. The applications of this brief and terse sutra are manifold. A simple example will suffice to clarify the modus operandi thereof. Suppose we have to multiply 12 by 13. (i) We multiply the left hand most digit 1 of the multiplicand vertically by the left hand most digit 1 of the multiplier get their product 1 and set down as the left hand most part of the answer; (ii) We then multiply 1 and 3 and 1 and 2 crosswise add the two get 5 as the sum and set it down as the middle part of the answer; and (iii) We multiply 2 and 3 vertically get 6 as their product and put it down as the last the right hand most part of the answer. Thus 12 13 = 156. The Fourth Sutra: Parvartya Yojayet The term Parvartya Yojayet which means Transpose and Apply. Here he claims that the Vedic system gave a number is applications one of which is discussed here. The very acceptance of the existence of polynomials and the consequent remainder theorem during the Vedic times is a big question so we dont wish to give this application to those polynomials. However the four steps given by them in the polynomial division are given below: Divide x3 + 72 + 6x + 5 by x 2. i. x3 divided by x gives us x2 which is therefore the first term of the quotient x2 2 = 22 but we have 72 in the divident. This means that we have to get 92 more. This must result from the multiplication of x by 9x. Hence the 2nd term of the divisor must be 9x As for the third term we already have 2 9x = 18x. But we have 6x in the dividend. We must therefore get an additional 24x. Thus can only come in by the multiplication of x by 24. This is the third term of the quotient. Q = x2 + 9x + 24 Now the last term of the quotient multiplied by 2 gives us 48. But the absolute term in the dividend is 5. We have therefore to get an additional 53 from some where. But there is no further term left in the dividend. This means that the 53 will remain as the remainder Q = x2 + 9x + 24 and R = 53. The Fifth Sutra: Snyam Samyasamuccaye Samuccaya is a technical term which has several meanings in different contexts which we shall explain one at a time. Samuccaya firstly means a term which occurs as a common factor in all the terms concerned. Samuccaya secondly means the product of independent terms. Samuccaya thirdly means the sum of the denominators of two fractions having same numerical numerator. Fourthly Samuccaya means combination or total. Fifth meaning: With the same meaning i.e. total of the word (Samuccaya) there is a fifth kind of application possible with quadratic equations. Sixth meaning With the same sense (total of the word Samuccaya) but in a different application it comes in handy to solve harder equations equated to zero. Thus one has to imagine how the six shades of meanings have been perceived by the Jagadguru Sankaracharya that too from the Vedas when such types of equations had not even been invented in the world at that point of time. The Sixth Sutra: nurpye nyamanyat As said by Dani [32] we see the 6th sutra happens to be the subsutra of the first sutra. Its mention is made in {pp. 51, 74, 249 and 286 of [51]}. The two small subsutras (i) Anurpyena and (ii) Adayamadyenantyamantyena of the sutras 1 and 3 which mean proportionately and the first by the first and the last by the last. Here the later subsutra acquires a new and beautiful double application and significance. It works out as follows: i. Split the middle coefficient into two such parts so that the ratio of the first coefficient to the first part is the same as the ratio of that second part to the last coefficient. Thus in the quadratic 22 + 5x + 2 the middle term 5 is split into two such parts 4 and 1 so that the ratio of the first coefficient to the first part of the middle coefficient i.e. 2 : 4 and the ratio of the second part to the last coefficient i.e. 1 : 2 are the same. Now this ratio i.e. x + 2 is one factor. ii. And the second factor is obtained by dividing the first coefficient of the quadratic by the first coefficient of the factor already found and the last coefficient of the quadratic by the last coefficient of that factor. In other words the second binomial factor is obtained thus Thus 22 + 5x + 2 = (x + 2) (2x + 1). This sutra has Yavadunam Tavadunam to be its subsutra which the book claims to have been used. The Seventh Sutra: Sankalana Vyavakalanbhym Sankalana Vyavakalan process and the Adyamadya rule together from the seventh sutra. The procedure adopted is one of alternate destruction of the highest and the lowest powers by a suitable multiplication of the coefficients and the addition or subtraction of the multiples. A concrete example will elucidate the process. Suppose we have to find the HCF (Highest Common factor) of (x2 + 7x + 6) and x2 5x 6 x2 + 7x + 6 = (x + 1) (x + 6) and x2 5x 6 = (x + 1) ( x 6) the HCF is x + 1 but where the sutra is deployed is not clear. The Eight Sutra: Puranpuranbhym Puranpuranbhym means by the completion or not completion of the square or the cube or forth power etc. But when the very existence of polynomials, quadratic equations etc. was not defined it is a miracle the Jagadguru could contemplate of the completion of squares (quadratic) cubic and forth degree equation. This has a subsutra Antyayor dasakepi use of which is not mentioned in that section. The Ninth Sutra: Calan kalanbhym The term (Calan kalanbhym) means differential calculus according to Jagadguru Sankaracharya. The Tenth Sutra: Yvadnam Yvadnam Sutra (for cubing) is the tenth sutra. It has a subsutra called Samuccayagunitah. The Eleventh Sutra: Vyastisamastih Sutra Vyastisamastih sutra teaches one how to use the average or exact middle binomial for breaking the biquadratic down into a simple quadratic by the easy device of mutual cancellations of the odd powers. However the modus operandi is missing. The Twelfth Sutra: esnyankena Caramena The sutra esnyankena Caramena means The remainders by the last digit. For instance if one wants to find decimal value of 1/7. The remainders are 3, 2, 6, 4, 5 and 1. Multiplied by 7 these remainders give successively 21, 14, 42, 28, 35 and 7. Ignoring the left hand side digits we simply put down the last digit of each product and we get 1/7 = .14 28 57! Now this 12th sutra has a subsutra Vilokanam. Vilokanam means mere observation He has given a few trivial examples for the same. The Thirteen Sutra: Sopantyadvayamantyam The sutra Sopantyadvayamantyam means the ultimate and twice the penultimate which gives the answer immediately. No mention is made about the immediate subsutra. The illustration given by them. The proof of this is as follows. The General Algebraic Proof is as follows. Let d be the common difference Canceling the factors A (A + d) of the denominators and d of the numerators: It is a pity that all samples given by the book form a special pattern. The Fourteenth Sutra: Ekanynena Prvena The Ekanynena Prvena Sutra sounds as if it were the converse of the Ekadhika Sutra. It actually relates and provides for multiplications where the multiplier the digits consists entirely of nines. The procedure applicable in this case is therefore evidently as follows. For instance 43 9. i. Divide the multiplicand off by a vertical line into a right hand portion consisting of as many digits as the multiplier; and subtract from the multiplicand one more than the whole excess portion on the left. This gives us the left hand side portion of the product or take the Ekanyuna and subtract it from the previous i.e. the excess portion on the left and ii. Subtract the right hand side part of the multiplicand by the Nikhilam rule. This will give you the right hand side of the product The Fifthteen Sutra: Gunitasamuccayah Gunitasamuccayah rule i.e. the principle already explained with regard to the Sc of the product being the same as the product of the Sc of the factors. Let us take a concrete example and see how this method (p. 81) can be made use of. Suppose we have to factorize x3 + 62 + 11x + 6 and by some method, we know (x + 1) to be a factor. We first use the corollary of the 3rd sutra viz. Adayamadyena formula and thus mechanically put down x2 and 6 as the first and the last coefficients in the quotient; i.e. the product of the remaining two binomial factors. But we know already that the Sc of the given expression is 24 and as the Sc of (x + 1) = 2 we therefore know that the Sc of the quotient must be 12. And as the first and the last digits thereof are already known to be 1 and 6, their total is 7. And therefore the middle term must be 12 7 = 5. So, the quotient x2 + 5x + 6. This is a very simple and easy but absolutely certain and effective process. The Sixteen Sutra :Gunakasamuccayah. It means the product of the sum of the coefficients in the factors is equal to the sum of the coefficients in the product. In symbols we may put this principle as follows: Sc of the product = Product of the Sc (in factors). For example (x + 7) (x + 9) = x2 + 16 x + 63 and we observe (1 + 7) (1 + 9) = 1 + 16 + 63 = 80. Similarly in the case of cubics, biquadratics etc. the same rule holds good. For example (x + 1) (x + 2) (x + 3) = x3 + 62 + 11 x + 6 2 3 4 = 1 + 6 + 11 + 6 = 24. Thus if and when some factors are known this rule helps us to fill in the gaps. Literature Research has documented the difficulties students face in algebra and how these can often be traced to their limited understanding of numbers and their operations (Stacey MacGregor, 1997; Warren, 2001). Of growing concern is the artificial separation of algebra and arithmetic, since knowledge of mathematical structure seems essential for a successful transition. In particular, this mathematical structure is concerned with (i) relationships between quantities, (ii) group properties of operations, (iii) relationships between the operations and (iv) Relationships across the quantities (Warren, 2003). Thus it has been suggested by Stacey and MacGregor (1997) that the best preparation for learning algebra is a good understanding of how the arithmetic system works. An understanding of the general properties of numbers and the relationships between them may be crucial, and students need to have thought about the general effects of operations on numbers (MacGregor Stacey, 1999). This study sought to test the hypothesis that arithmetic knowledge can improve algebraic ability by applying a Vedic method of multiplying arithmetic numbers to algebra, based on the similarity of structural presentation. Vedic mathematics has its origins in the ancient Indian texts, the Vedas, an integrated and holistic system of knowledge composed in Sanskrit and transmitted orally from one generation to the next. The first versions of these texts were possibly recorded around 2000 BC, and the works contain the genesis of the modern science of mathematics (number, geometry and algebra) and astronomy in India (Datta Singh, 2001; Joseph, 2000). Sri Tirthaji (1965) has expounded 16 sutras or word formulas and 13 sub-sutras that he claims have been reconstructed from the Vedas. The sutras, or rules as aphorisms, are condensed statements of a very precise nature, written in a poetic style and dealing with different concepts (Joseph, 2000; Shan Bailey, 1991). A sutra, which literally means thread, expresses fundamental principles and may contain a rule, an idea, a mnemonic or a method of working based on fundamental principles that run like threads through diverse mathematical topics, unifying them. As Williams (2002) describes them: We use our mind in certain specific ways: we might extend an idea or reverse it or compare or combine it with another. Each of these types of mental activity is described by one of the Vedic sutras. They describe the ways in which the mind can work and so they tell the student how to go about solving a problem. (Williams, 2002, p. 2). Examples of the sutras are the Vertically and Crosswise sutra, which embodies a method of multiplication with applications to determinants, simultaneous equations, and trigonometric functions, etc. (this is the sutra used in the research reported here see Figure 3), and the All from nine and the last from ten sutra that may be used in subtraction, vincula, multiplication and division. Barnard and Tall (1997, p. 41) have introduced the idea of a cognitive unit, A piece of cognitive structure that can be held in the focus of attention all at one time, and may include other ideas that can be immediately linked to it. This enables compression of ideas, so that a collection of ideas or symbols that is too big for the focus of attention can be compressed into a single unit. It seems as if the sutras nicely fit this description, with the mnemonic or other memory device being used as a peg to hang the collection of ideas on. Thus the theoretical advantage of using the sutras is that they allow encapsulation of a process into a manageable chunk, or cognitive unit, that can then be processed more easily, sometimes using a visual reminder, such as in the Vertically and Crosswise sutra. Here the essential procedure is signified holistically by the symbol 5, unlike the symbol FOIL that signifies in turn four separate procedures. It might be possible for a symbol such as to be used in much the same way for FOIL, but this may appear more visually complex, and it is not usually separated from the accompanying binomials like this. In this way sutras often make use of the power of visualisation, which has been shown to be effective in learning in various areas of mathematics (Booth Thomas, 2000; Presmeg, 1986; van Hiele, 2002). Such visualisation accesses the brains holistic activity (Tall Thomas, 1991) and intuition, and this assists in providing an overview of the mathematical structure. The sutras also aid intuitive thinking (Williams, 2002) and being based on patterns and mnemonics they make recall much easier, reducing the cognitive load on the individual (Morrow, 1998; Sweller, 1994). The sutras were originally envisaged as applying both to arithmetic and algebra, and Joseph (2000) and Bhatanagar (1976) have explained that since polynomials may be perceived as simply arithmetic sequences, the principles apply equally well to them. This research considered a possible role of the vertically and Crosswise sutra for improving facility with, and understanding of, the expansion of algebraic binomials and the factorisation of quadratic expressions. Methodology The research employed a case study methodology, using a single class of Year 10 (age 15 years) students. The school used is a co-educational state secondary school in Auckland, New Zealand and the class contained 19 students, 11 boys and 8 girls. The students, who included 9 recent immigrants, were drawn from several cultural backgrounds, and accordingly have been exposed to different approaches and teaching environments with respect to learning mathematics. This also meant that nine of the students have a first language other than English and these language difficulties tend to hinder their learning (for example, three of the students are on a literacy program at the school). Two anonymous questionnaires (see Figure 1 for some questions from the second) were constructed using concepts we identified as important in developing a structural understanding of binomial expansion and factorisation, such as testing the concept of a factor and the ability to apply a procedure in reverse. Questions included: multiplication of numbers; multiplication of binomial expressions; factorisation of quadratic expressions; word problems on addition and subtraction of like terms; and expansion of expressions in a practical context. Some questions also involved description of procedures and meanings attached to words. In particular, the second questionnaire contained items on the use of the Vedic method applied to binomial expansion and factorisation. The lessons were taught by the first-named author in 2003 in a supportive classroom environment that encouraged student-to-student and teacherstudent interactions. Students were assured that the teacher was genuinely interested in their mathematical thinking and respected their attempts, that it was fine to make mistakes and that understanding how the mistake occurred was a learning opportunity for everyone concerned. Students were encouraged to explain and check the validity of their answers, and positive contributions were praised. The first teaching session comprised work on multiplication of numbers and revision of work on algebra that the students had learned in Year 9 (age 14 years). Substitution, collection of like terms and multiplication of a binomial expression by a single value were revised, using, for example, expressions such as 5(x 4), (p + 2)4, and k(4 + k). Students were also reminded of the meanings of words such as term, expression, factor, expansion, coefficient and simplify. Diagrammatic representations of 3(5 + 6) and k(4 + k) using rectangles were drawn and discussed, and then students drew similar rectangle diagrams representing multiplications such as (3 + 5)(2 + 5) and (k + 2)(k + 4) (see Figure 2). Following a review of factorisation of expressions such as 15p + 10, the FOIL (First, Outside, Inside, Last) method of expanding binomials was taught, where the First terms in each bracket are multiplied together, then the Outside terms, the Inside terms and then the Last term in each bracket, to give four products. Finally factorisation of quadratic expressions, followed by a guess and check method for factorising quadratic expressions was covered. The students did not find these topics easy, especially factorising of quadratic expressions. This took a total of four hours, after which, questionnaire one was administered. Students were then exposed for one hour to the Vedic vertically and crosswise method, where initially they practised multiplying two- and three-digit numbers with this approach. Subsequently, the next three hours were spent expanding binomials and factorising quadratic expressions with the vertically and crosswise method. This method (see Figure 3) involves a sequence of four multiplications, the answers to each of which are placed into a single answer line. The middle two terms are added together mentally to supply the final answer. Results The first question (1a) in each questionnaire was a two-digit multiplication. In the first, it was 37 58, and the second 23 47, and in this second case the question asked that this be done by the vertically and crosswise method. The aim was to check students facility with arithmetic multiplication and to see if the vertically and crosswise sutra was of assistance in this area. In the event 11 of the 18 (61%) students who completed both questionnaires, correctly answered the question in the first test, and 13 (72%) in the second, with only one student not using the sutra in that test. There was no statistical difference between these proportions (c2 = 0.125). When asked to explain what they had done using the Vedic approach, students who were able to write down the final answer were often able to write something like student 4s explanation for 1c), 32 69: 2 times 9 is 18 3 times 9 + 2 times 6 is 39 + carried 1 = 40 3 times 6 + carried 4 = 22 Expansion of binomials A summary of the results in the first of the algebra questions (Q2 see Figure 1 for format), requiring students to multiply together two basic binomials, is given in Table 1. Question 2 was presented in each case with the binomials in the same line. Since the first questionnaire was administered immediately after the FOIL method was taught, most students employed this method, and only 8 (44.4%) correctly performed the expansion in the simplest example, question 2a). In the second questionnaire, where students were asked to use the vertically and Crosswise method, 10 (55.6%) were correct, but there was no statistically significant difference (c2 = 0.11, df = 1, ns). However, when the presentation format was changed from a single line to the grid format of question 3 (see Figure 1), the facility on 3a) (Multiply x + 3 and x + 4) improved to 14 correct answers (77.8%). Thus there was weak evidence (c2 = 2.92, df = 1, p = 0.1) of an improvement in students performance on this basic expansion of binomials in the second questionnaire, using the Vedic method with a grid presentation. However, the improvement was not sustained for question 3b) which had negative signs (see Table 2: c2 = 0.45), or for 2b), which involved 2x and negative signs. It seems that the arithmetic complexity caused problems, with only 3 students answering 2b) correctly on each test. The other results of question 3 on the second questionnaire also support the idea of improved understanding; Table 2 gives the results of the multiplications in this question. In this case question 3c) was the question of a standard corresponding to 2b) in the first test (2x 3 times x + 4), and yet the students did significantly better (50% correct) than they did on that question (c2 = 3.13, df = 1, p 0.05). It is also of interest that on question 2 in the first test all eight students who successfully applied the FOIL method wrote out all four terms and then added the two middle terms. No student wrote the final answer without the intermediate step of giving both middle terms. In contrast, when using the vertically and crosswise approach, all 14 students who were successful were able to write the answers straight down, as seen in the example in Figure 4. Furthermore, 5 students (12, 15, 16, 17, and 18) who were unable to multiply binomials using the standard method achieved success using the Vedic method. Figure 5 shows the corresponding working of student 18 on these questions. In test 1, following the FOIL method she was unable to multiply any terms together and even seemed to confuse the question with factorisation. However, with the Vedic method she makes a good attempt, correctly answering two parts. It might be argued that the improvement above was due to students spending more time learning how to perform such expansions, or that the previous FOIL learning took time to assimilate. However, it should be noted that the questions where the improvement occurred specifically involved use of the Vedic method, which, while it can be related to FOIL by an experienced mathematician, would no doubt look quite different to these students, since it is set out in a grid format rather than being performed in a single line. Furthermore, it was noted during the teaching episode that there was some resistance from the students to learning a second method when they already knew the FOIL method, and this could be expected to have a detrimental effect on performance. Factorisation of quadratic expressions Table 3 contains a summary of the results of question 3 from the first questionnaire and question 5 in the second, these being corresponding single line, traditional format factorisation questions (see Figure 1). Individually the results of these questions did not show any statistical difference between the performance before and after the Vedic method was introduced. For example, between questions 3a) and 5a), c2 = 0.9, which is not significant. However, if the question parts are grouped together and the number of students correct on question 3 compared with those correct on question 5 then we find that there is a significant improvement (Q3 v Q5 c2 = 6.65, p 0.01) on the second questionnaire. For question 4 in each questionnaire the students were asked to supply the missing terms in two binomials that were multiplied together. Boxes were provided for the missing terms, which were in the binomials, the quadratic, or both (see Figure 1). While these are not standard straight factorisation questions they do require students to work backwards from the answer and thus display some conceptual knowledge of how to undo multiplication of binomials. There was no difference in facility on any of these matching questions (see Table 4), or on a comparison of the total number of correct scores between the two questionnaires (c2 = 0.39, ns). The students appeared to be able to do them equally well using either guess or check and decomposition or the Vedic approach. While the discussion above shows that the evidence for a better performance on individual questions following the teaching of the Vedic method was rarely present, a consideration of the students overall scores on the expansion and factorisation algebra questions did show a significantly better performance on the second test, (_x1 = 41.4%,_x2 = 51.5%, t = 2.66, p 0.05). Thus it appears that, overall, the Vedic approach may have contributed to student understanding of the methods, either by cementing in place the previous methods, or by complementing them. It is worth noting too that some students preferred to use the vertically and Crosswise method even when not directed to do so. For example, in question 2 of the second questionnaire students were simply asked to multiply two binomials together, with no method specified. In the event 4 students (4, 5, 16, and 18) chose to use the vertically and Crosswise approach, setting out their work in a grid. In addition, 3 of these students (15, 16 and 18) used it for the factorisation in question 5. An example of their work is shown in Figure 6. While they used the method with varying levels of success, it seems to have benefited both student 5, who answered no algebra questions correctly in test 1 (and 2 in test 2), and student 16 who used it for factorisation and went from 3 correct to 8 correct (see Figure 6). While student 18 preferred the Vedic method to expand and to factorise expressions, she used the traditional method to multiply numbers even when asked to multiply by the vertically and Crosswise method. This seems to suggest that she was comfortable using different methods in algebra from those employed in arithmetic. Discussion India has good reasons to be proud of a rich heritage in science, philosophy and culture in general, coming to us down the ages. In mathematics, which is my own area of specialization, the ancient Indians not only took great strides long before the Greek advent, which is a standard reference point in the Western historical perspective, but also enriched it for a long period making in particular some very fundamental contributions such as the place-value system for writing numbers as we have today, introduction of zero and so on. Further, the sustained development of mathematics in India in the post-Greek period was indirectly instrumental in the revival in Europe after its dark ages. Notwithstanding the enviable background, lack of adequate attention to academic pursuits over a prolonged period, occasioned by several factors, together with about two centuries of Macaulayan educational system, has unfortunately resulted, on the one hand, in a lack of awareness of our historical role in actual terms and, on the other, an empty sense of pride which is more of an emotional reaction to the colonial domination rather than an intellectual challenge. Together they provide a convenient ground for extremist and misguided elements in society to reconstruct history from nonexistent or concocted source material to whip up popular euphoria. That this anti-intellectual endeavour is counter-productive in the long run and, more important, harmful to our image as a mature society, is either not recognized or ignored in favour of short-term considerations. Along with the obvious need to accelerate the process of creating an awareness of our past achievements, on the strength of authentic information, a more urgent need has also arisen to confront and expose such baseless constructs before it is too late. This is not merely a question of setting the record straight. The motivated versions have a way of corrupting the intellectual processes in society and weakening their very foundations in the long run, which needs to be prevented at all costs. The so-called Vedic Mathematics is a case in point. A book by that name written by Jagadguru Swami Shri Bharati Krishna Tirthaji Maharaja (Tirthaji, 1965) is at the centre of this pursuit, which has now acquired wide following; Tirthaji was the Shankaracharya of Govardhan Math, Puri, from 1925 until he passed away in 1960. The book was published posthumously, but he had been carrying out a campaign on the theme for a long time, apparently for several decades, by means of lectures, blackboard demonstrations, classes and so on. It has been known from the beginning that there is no evidence of the contents of the book being of Vedic origin; the Foreword to the book by the General Editor, Dr. A.S.Agrawala, and an account of the genesis of the work written by Manjula Trivedi, a disciple of the swamiji, makes this clear even before one gets to the text of the book. No one has come up with any positive evidence subsequently either. There has, however, been a persistent propaganda that the material is from the Vedas. In the face of a false sense of national pride associated with it and the neglect, on the part of the knowledgeable, in countering the propaganda, even educated and well meaning people have tended to accept it uncritically. The vested interests have also involved politicians in the propaganda process to gain state support. Several leaders have lent support to the Vedic Mathematics over the years, evidently in the belief of its being from ancient scriptures. In the current environment, when a label as ancient seems to carry considerable premium irrespective of its authenticity or merit, the purveyors would have it going easy. Large sums have been spent both by the Government and several private agencies to support this Vedic Mathematics, while authentic Vedic studies continue to be neglected. People, especially children, are encouraged to learn and spread the contents of the book, largely on the baseless premise of their being from the Vedas. With missionary zeal several devotees of this cause have striven to take the message around the world; not surprisingly, they have even met with some success in the West, not unlike some of the gurus and yogis peddling their own versions of Indian philosophy. Several people are also engaged in research in the new Vedic Mathematics. To top it all, when in the early nineties the Uttar Pradesh Government introduced Vedic Mathematics in school text books, the contents of the swamijis book were treated as if they were genuinely from the Vedas; this also naturally seems to have led them to include a list of the swamijis sutras on one of the opening pages (presumably for the students to learn them by heart and recite!) and to accord the swamiji a place of honour in the brief history of Indian mathematics described in the beginning of the textbook, together with a chart, which curiously has Srinivasa Ramanujans as the only other name from the twentieth century! For all their concern to inculcate a sense of national pride in children, those responsible for this have not cared for the simple fact that modern India has also produced several notable mathematicians and built a worthwhile edifice in mathematics (as also in many other areas). Harish Chandras work is held in great esteem all over the world and several leading seats of learning of our times pride themselves in having members pursuing his ideas; (see, for instance, Langlands, 1993). Even among those based in India, several like Syamdas Mukhopadhyay, Ganesh Prasad, B.N.Prasad, K.Anand Rau, T.Vijayaraghavan, S.S.Pillai, S.Minakshisundaram, Hansraj Gupta, K.G.Ramanathan, B.S.Madhava Rao, V.V.Narlikar, P.L.Bhatnagar and so on and also many living Indian mathematicians have carved a niche for themselves on the international mathematical scene (see Narasimhan, 1991). Ignoring all this while introducing the swamijis name in the brief history would inevitably create a warped perspective in childrens minds, favouring gimmickry rather than professional work. What does the swamijis Vedic Mathematics seek to do and what does it achieve? In his preface of the book, grandly titled A Descriptive Prefatory Note on the astounding Wonders of Ancient Indian Vedic Mathematics, the swamiji tells us that he strove from his childhood to study the Vedas critically to prove to ourselves (and to others) the correctness (or otherwise)of the derivational meaning of Veda that the Vedas should contain within themselves all the knowledge needed by the mankind relating not only to spiritual matters but also those usually described as purely secular, temporal or worldly; in other words, simply because of the meaning of the word Veda, everything that is worth knowing is expected to be contained in the vedas and the swamiji seeks to prove it to be the case! It may be worthwh ile to point out here that there would be room for starting such an enterprise with the word science! He also describes how the contemptuous or at best patronising attitude of Orientalists, Indologists and so on strengthened his determination to unravel the too-long-hidden mysteries of philosophy and science contained in ancient Indias Vedic lore, with the consequence that, after eight years of concentrated contemplation in forest solitude, we were at long last able to recover the long lost keys which alone could unlock the portals thereof. The mindset revealed in this can hardly be said to be suitable in scientific and objective inquiry or pursuit of knowledge, but perhaps one should not grudge it in someone from a totally different milieu, if the outcome is positive. One would have thought that with all the commitment and grit the author would have come up with at least a few new things which can be attributed to the Vedas, with solid evidence. This would have made a worthwhile contribution to our understanding of our heritage. Instead, all said and done there is only the authors certificate that we were agreeably astonished and intensely gratified to find that exceedingly though mathematical problems can be easily and readily solved with the help of these ultra-easy Vedic sutras (or mathematical aphorisms) contained in the Parishishta (the appendix portion) of the Atharva Veda in a few simple steps and by methods which can be conscientiously described as mere mental arithmetic (paragraph 9 in the preface). That passing reference to the Atharva Veda is all that is ever said by way of source material for the contents. The sutras, incidentally, which appeared later, scattered in the book, are short phrases of just about two to four words in Sanskrit, such as Ekadhikena Purvena or Anurupye Shunyam Anyat. (There are 16 of them and in addition there are 13 of what are called sub-sutras, similar in nature to the sutras). The mathematics of today concerns a great variety of objects beyond the high school level, involving various kinds of abstract objects generalising numbers, shapes, geometries, measures and so on and several combinations of such structures, various kinds of operations, often involving infinitely many entities; this is not the case only about the frontiers of mathematics but a whole lot of it, including many topics applied in physics, engineering, medicine, finance and various other subjects. Despite its entire pretentious verbiage page after page, the swamijis book offers nothing worthwhile in advanced mathematics whether concretely or by way of insight. Modern mathematics with its multitude of disciplines (group theory, topology, algebraic geometry, harmonic analysis, ergodic theory, combinatorial mathematics-to name just a few) would be a long way from the level of the swamijis book. There are occasionally reports of some researchers applying the swamijis Vedic Mathematics to advanced problems such as Keplers problem, but such work involves nothing more than tinkering superficially with the topic, in the manner of the swamijis treatment of calculus, and offers nothing of interest to professionals in the area. Even at the western teaching Vedic Mathematics deals only with a small part and, more importantly, there too it concerns itself with only one particular aspect, that of faster computation. One of the main aims of mathematics education even at the western teaching consists of developing familiarity with a variety of concepts and their significance. Not only does the approach of Vedic Mathematics not contributes anything towards this crucial objective, but in fact might work to its detriment, because of the undue emphasis laid on faster computation. The swamijis assertion 8 months (or 12 months) at an average rate of 2 or 3 hours per day should be enough for finishing the whole course of mathematical studies on these Vedic lines instead of 15 or 20 years required according to the existing systems of the Indian and also foreign universities, is patently absurd and hopefully nobody takes it seriously, even among the activists in the area. It would work as a cruel joke if some people choose to make such a substitution in respect of their children. It is often claimed that Vedic Mathematics is well appreciated in other countries, and even taught in some schools in UK etc. In the normal course one would not have the means to examine such claims, especially since few details are generally supplied while making the claims. Recent years have brought about the development of powerful tools for verifying specifications of hardware and software systems. By now, major companies, such as Intel, IBM, and [emailprotected]/* */ Molecules have realized the impact and importance of such tools in their own design and implementation processes as a means of coping with the ever-increasing complexity of chip and computing tools. Protocols, networks, and distributed systems can generally not be described by code of some deterministic programming language. Such systems exhibit concurrent behavior and they are typically reactive in the sense that their behavior depends on what the environment can offer (e.g. Is the printer busy?). Computation tree logic (CTL) is currently one of the popular frameworks used in verifying properties of concurrent systems. We study its syntax and semantics, and use those insights to design an automated verification algorithm which takes a description of a system and specifications of expected behavior as input and checks whether that system meets those expectations. That algorithm is the foundation for a tool, the symbolic model verifier (SMV), which they use to evaluate some basic designs, e.g. simple elevator systems and a mutual exclusion protocol (3-4 weeks). Exposure to a labeling algorithm for finite-state verification illustrates depth-first backwards search in a directed graph; this search is recursive and the recursion is driven by the logical structure of the specified behavior, written as a CTL formula. The description and evaluation of small designs with the tool SMV makes students appreciate how such graphs can be modeled with a modular guarded-command language with non-deterministic assignment. The discussion of program logic contains the linear algorithm for computing minimal-sum sections of integer arrays as a case study. Finally, binary decision diagrams require algorithms that implement the familiar logical operations on such diagrams. Some of these algorithms illustrate dynamic programming at an accessible level. Conclusion In this study students were taught an appropriate Vedic sutra following teaching of the traditional FOIL method of multiplication of binomials, and the decomposition method for factorisation. We found that afterwards the students performed significantly better overall on these types of algebra questions, and specifically on the factorisations, and there was weak evidence of better results on expansion using a grid format. The reasons for the improvement are not easy to pinpoint since they appear in some areas and not in others. This seems to indicate that the value of the method may lie in what it adds to the students overall algebraic conceptions and knowledge of mathematical structure. Thus we have found no evidence that it should be seen as a replacement for the former approaches, but our results suggest it could rather be recommended as a useful adjunct, a complementary method. While this may take longer in terms of teaching time, the results indicate that possession of a range of strategies may have value above and beyond their individual benefit. References Barnard, T. Tall, D. O. (1997). Cognitive units, connections and mathematical proof. In E. Pekhonen (Ed.), Proceedings of the 21st Conference of the International Group for the Psychology of Mathematics Education, Vol. 2 (pp. 4148). Lahti, Finland. Bhatnagar, P. L. (1976). Some Vedic Sutras for arithmetical operations or a fresh look at arithmetic after learning some algebra. Mathematics Teacher (India) 11A, 85120. Booth, R. D. L. Thomas, M. O. J. (2000). Visualisation in mathematics learning: Arithmetic problem-solving and student difficulties. Journal of Mathematical Behavior, 18(2), 169190. Datta, B. B. Singh, A. N. (2001). History of Hindu Mathematics: A Source Book Parts I and II. New Delhi: Bharatiya Kala Prakashan. Joseph, G. G. (2000). The Crest of the Peacock: Non-European Roots of Mathematics. Harmondsworth: Penguin. MacGregor, M. Stacey, K. (1999). A flying start to algebra. Teaching Children Mathematics, 6(2), 7885. Morrow, L. J. (1998). Wither algorithms? Mathematics educators express their views. In L. J. Morrow M. J. Kenney (Eds), The Teaching and Learning of Algorithms in School Mathematics (pp. 119), National Council of Teachers of Mathematics. Presmeg, N. C. (1986). Visualisation in high school mathematics. For the Learning of Mathematics, 6(3), 4246. Shan, S. J. Bailey, P. (1991). Multiple Factors: Classroom Mathematics for Equality and Justice. Trentham Books. Stacey, K. MacGregor, M. (1997). Building foundations for algebra. Mathematics in the Middle School, 2, 253260. Sweller, J. (1994). Cognitive load theory, learning difficulty, and instructional design. Learning and Instruction, 4, 295312. Tall, D. Thomas, M. (1991). Encouraging versatile thinking in algebra using the computer. Educational Studies in Mathematics, 22, 125147. Tirthaji, B. K. (2001). Vedic Mathematics. New Delhi: Motilal Banarasidass. Van Hiele, P. (2002). Similarities and differences between the theory of learning and teaching of Skemp and the van Hiele levels. In D. O. Tall M. O. J. Thomas (Eds), Intelligence, Learning and Understanding in Mathematics: A Tribute to Richard Skemp (pp. 2748). Flaxton, Queensland: Post Pressed. Warren, E. (2001). Algebraic understanding: The importance of learning in the early years. In H. Chick, K. Stacey, J. Vincent J. Vincent (Eds), The Future of the Teaching and Learning of Algebra, Proceedings of the 12th ICMI Study Conference, Vol. 2 (pp. 633646). Melbourne, Australia. Warren, E. (2003). The role of arithmetic structure in the transition from arithmetic to algebra. Mathematics Education Research Journal, 15(2), 122137. Williams, K. (2002). The cosmic computer course. Obtained from www.vedicmaths.com. Abhyankar, K.D. A rational approach to study ancient literature, Current science, 87 (Aug.2004) 415-416. Adams, E.S., and D.A. Farber. Beyond the Formalism Debate: Expert Reasoning, Fuzzy Logic and Complex Statutes, Vanderbilt Law Review, 52 (1999), 1243-1340. https://law.vanderbilt.edu/lawreview/vol525/adams.pdf Allen, J., S. Bhattacharya and F. Smarandache. Fuzziness and Funds allocation in Portfolio Optimization. https://lanl.arxiv.org/ftp/math/papers/0203/0203073. Anitha, V. Application of Bidirectional Associative Memory Model to Study Female Infanticide, Masters Dissertation, Guide: Dr. W. B. Vasantha Kandasamy, Department of Mathematics, Indian Institute of Technology, Chennai, March 2000. Ashbacher, C. Introduction to Neutrosophic Logic, American Research Press, Rehoboth, 2002. https://www.gallup.unm.edu/~smarandache/IntrodNeutLogic. Axelord, R. (ed.) Structure of Decision: The Cognitive Maps of Political Elites, Princeton Univ. Press, New Jersey, 1976. Bibliography Discover Mathematics, Kenneth Williams Vertically and Crosswise, Kenneth Williams Vedic Mathematics, Bharati Krsna Tirthaji www.hinduism.co.za/vedic.htm https://vedicmathsindia.blogspot.com/search/label/vedic%20math%20research https://vedicmathsindia.blogspot.com/ https://vedicmathsindia.blogspot.com/2007/06/10-questions-to-kenneth-r-williams-on.html

Learning the Science of Essay Writing - Using Colors

<h1>Learning the Science of Essay Writing - Using Colors</h1><p>If you are prepared to get into the study of paper composing, you might need to make the following stride up to composing shading coded useful article tips. By investigating the different segments of the study of article composing, you will have the option to comprehend what steps to take and what alternatives to investigate in your readiness. You will find that with the correct advances and alternatives, you can see yourself composing a wide scope of article points inside a short measure of time.</p><p></p><p>There are two sections to the study of paper composing, and they are more about hues than they are about advances, however you should ensure that you follow the means accurately, in such a case that you don't, you might be losing your opportunity to build up your specialty. The initial segment of the study of paper composing is shading coding. That implies comprehending wha t hues to use so as to create the best outcomes with the data that you are attempting to convey.</p><p></p><p>By investigating the areas of the study of paper composing, you will find that there are various hues that you can use so as to assist you with delivering great outcomes with your educational exposition tips. For instance, in the event that you are searching for data on the medical advantages of doing certain activities, at that point you will need to locate a decent shading guide with the goal that you can ensure that you have the fitting data to present to the perusers. On the off chance that you are utilizing shading to assist you with passing on how you need your data to sound, at that point you will find that you will be in a greatly improved situation to compose progressively powerful paper topics.</p><p></p><p>One approach to utilize hues to assist you with utilizing to recount to the perusers the story that you need to advise is to utilize a mix of hues that stress your data. By utilizing corresponding hues, you will have the option to have an increasingly normal sounding method for introducing the realities to the perusers. This permits you to introduce both side of the data without it sounding constrained or befuddling, which is significant when you are attempting to impart data in a reasonable manner.</p><p></p><p>You can likewise utilize different hues that will show your data in an increasingly explicit manner. Utilizing shades of blue for instance, you can make a style that will show the data without appearing to be unreasonably convoluted for the peruser. With this style, you can make the data stand apart effectively and give the data more attention.</p><p></p><p>You can likewise utilize various shades of reds to stress the data that you are attempting to hand-off. You can do this by utilizing hues that seem, by all accounts, to be red yet are not red. At the point when you utilize this kind of shading guide, you will have the option to utilize hues that are not red and still cause to notice your information.</p><p></p><p>You can likewise utilize blues to stress the data that you are attempting to pass on. In this occurrence, you will need to utilize various shades of blues that show the data that you are attempting to pass on in a quite certain manner. This can be hard to do on the off chance that you utilize just one shading in a solitary sentence, however by utilizing various shades of blues that are utilized in various gatherings, you can make the data hang out in various manners without causing it to appear confusing.</p><p></p><p>As you keep on utilizing hues to plot your data, you will have the option to find that you can change the shading plan that you are utilizing to make the data stick out and give it more consideration. It is essential to remember that utilizin g the correct hues will make the data increasingly compelling and simple to peruse. You will find that the study of exposition composing is progressively compelling on the off chance that you keep on working with the best possible aides so as to ensure that you can utilize the correct hues to pass on the data to the perusers effectively.</p>

Choosing the Best Examples For Your American History Essay

<h1>Choosing the Best Examples For Your American History Essay</h1><p>When you're searching for American history exposition tests, there are numerous to such an extent that you will be unable to locate a decent match. This can leave you feeling disappointed and confounded, however when you begin perusing a portion of the models, it will be extremely certain that not all models are the equivalent. There are a lot of them that are actually the ones you need, and you should simply set aside the effort to discover them.</p><p></p><p>Your nearby library is an extraordinary spot to begin. You may discover a model you like, and on the off chance that you have a companion or relative who has taken a class at the school you are learning at, you can approach them for a recommendation.</p><p></p><p>The web can likewise help you a great deal, as most libraries and book shops have great example reports accessible on the web. Numero us individuals have additionally made accessible these models for download. Notwithstanding, you ought to be cautious about downloading them, as some of them can be pernicious and you could wind up downloading destructive programming to your computer.</p><p></p><p>A genuine model for you to take a gander at is an article that was composed by an undergrad who took that class. It would most likely be very explicit and would presumably incorporate a modest quantity of composing counsel. This sort of paper is perfect for you to peruse and study.</p><p></p><p>If you pick this sort of exposition for a class, ensure that it is a difficult article that has bunches of significance to it. Additionally ensure that it gives you a decent establishment of information on a specific subject. While it can even now be viewed for instance of a paper, it is additionally a generally excellent hotspot for your own learning experience.</p><p>< /p><p>One of the best hotspots for article tests that are pertinent to your subject is a book that is explicitly outfitted towards your point. Books have the benefit of having the option to maintain your center, as they give you models dependent on the real theme you are managing. Likewise, more often than not, books are loaded with genuine models that you can put to use.</p><p></p><p>You can locate some genuine instances of papers from individual experience. This can assist you with getting to holds with building up a draft that incorporates both the composed and the oral components. It can likewise assist you with understanding the distinction among composing and talking, and how you can best approach passing on your thoughts in both formats.</p><p></p><p>Once you have a draft that you believe you have to return to your educator for criticism, you should likewise peruse it altogether to see whether it is up to your norm. A f ew understudies feel that this implies looking again at the entire task. Notwithstanding, this isn't the case.</p>

Essay Writing Tips For the Four Square Format

Essay Writing Tips For the Four Square FormatAre you thinking about writing a four square essay? There are a lot of tips out there that can help you make the most of your essay. Most of these tips are focused on making the essay more compelling and interesting to read, so you should keep these tips in mind before you begin to write your four square essay.You should first decide what topic you want to write about. This will be a good idea when choosing the template for your four square essay. You should also know what types of examples you will need to use in order to help you make the best choice. If you do not have enough examples to use, you may want to consider hiring a professional essay writer.Second, you should decide what format you want your essay to follow. You should know that there are several formats that are available. Some are very detailed, while others may be very simple. You may want to do some research in order to find out which style of writing you prefer.Third, yo u should decide how you will turn your essay into a resource. You can either use the forms or letters on the back of the essay to add extra information. You may also use the Q&A format to find additional examples and information. Whatever format you choose, you should make sure to include all of the information you need for the essay.The last but very important aspect of writing an essay is your conclusion. In addition to the contents of the essay, you must include your conclusion. This should provide your reader with all of the information they need to properly understand the essay.The conclusion is probably the most important aspect of your essay, as it is where you can go to write an engaging conclusion. It is also a place where you can provide extra details about the information you have included in the essay. This will ensure that the reader will understand the entire purpose of the essay.An effective way to compose a conclusion is to use bullet points, which are a perfect plac e to give a brief summary of the overall content of the essay. However, it is best to avoid using just one or two bullet points. You may want to use as many as necessary to get your point across.Finally, make sure that you allow enough time for editing. Although there are a lot of resources out there that can help you edit your essay, it is always important to allow yourself the chance to edit before you send it off to be published. Making the most of your four square essay writing skills will allow you to produce a high-quality essay.

Apush DBQ - A Review of the Essay

<h1>Apush DBQ - A Review of the Essay</h1><p>The Apush DBQ Sample Essay has taken a considerable amount of individuals off guard. Indeed, the presentation of this exposition causes an individual to pay attention. All things considered, this article isn't one that is utilized in typical study halls. An individual who composes such an article would be up for some national attention.</p><p></p><p>This appears to infer that the instructor is accomplishing something else when encouraging this example exposition. Most educators don't have this sort of room accessible. In the event that the understudy is composing something uncommon, they need to utilize a paper from an outside source. On the off chance that they are going to utilize it from another understudy, there might be a great deal of inquiries posed by other students.</p><p></p><p>The instructor who is utilizing this composition as their foundation for educating has d iscovered it is ideal to get individual consideration. With regards to showing a seminar on web advancement, having an alternate sort of paper to present to the class will give them more odds of turning in the essential data required for the class. It might appear as though a great deal of cash to pay for progressively scholastic materials however in all actuality it pays off.</p><p></p><p>Most of the time the understudy who gets the most acknowledgment is the person who has a ton of year abilities. For whatever length of time that the educator realizes how to compose a decent paper that has great language, the understudy can draw out the cream of the crop. This outcomes in having more consideration from the teacher.</p><p></p><p>It is normal for an understudy to know what number of specific quantities of words that ought to be utilized in their exposition. Be that as it may, on the off chance that you have inquiries concerning to what extent to compose a specific area, the instructor is the one to address those inquiries. An individual can find that in any event the teacher has their turn recorded as a hard copy the exam.</p><p></p><p>The style that an understudy inclines toward is likewise going to figure out what kind of article they will compose. Individuals who like to have a proper tone to their expositions will utilize an unexpected technique in comparison to the individuals who incline toward a casual tone. The most ideal approach to conclude this is to attempt an example paper and choose whether you like it or not.</p><p></p><p>The understudy who utilizes this example article to support that person become increasingly acquainted with the strategies will have a superior possibility of getting An evaluation than one who doesn't utilize this activity. The significance of the paper is that the understudy ought to consistently know about the way that it is the u nderstudy's exertion that matters. They are the ones who need to willingly volunteer to figure out how to compose a decent paper that is unique.</p><p></p><p>The Apush DBQ Sample Essay will be a wondrous thing when it is utilized appropriately. Utilizing it to help compose a superior exposition will have a superior final product than simply sending the paper out for a reviewing. Numerous individuals will look to the web to perceive what is being composed by others and how others have utilized this essay.</p>

The Land Of Land For Urban Land - 1643 Words

4.1 Introduction Following a six-week fieldwork into the operations of private companies involved in the purchase, registration and sale of land to urban dwellers particularly peri-urban lands in Accra, this chapter now presents a summary of the results from the research and then details a discussion of what the findings mean for policy and practice. 4.2 Research Findings 4.2.1 Individual Urban Land Brokers The land market in Ghana as discussed earlier is growing fast but still largely informal. The process of urban land acquisition was facilitated by individuals who had created networks with key players in the land acquisition and registration system. Until recently, urban land seekers acquired their lands with the help of a land agent.†¦show more content†¦Proof of transactions were difficult to provide. Majority of the time, the agents were recommended by friends, colleagues, or fellow members from social clubs. Participants indicated that the agents were from different backgrounds noting that in some situations, they were employees of one the government agencies responsible for title registration. They worked on a ‘part-time’ basis. A few ‘full-time’ agents set up temporary structures usually along busy roads but were difficult to trace. In some extreme cases, these land agents are members of vigilante groups who ensured security of tenure by threatening the lives of any ‘unapproved’ persons found on their allocated plots. One of the participants pointed out a situation where different vigilante groups clashed over the same piece of land. This has been a common case in many peri-urban areas where there’s inadequate police protection. The groups usually consist of young men of the landowning stool or family who believe they are entitled to some proceeds from the sale of ‘their’ only held in custody by the chiefs or family heads. 4.2.2 Private Sector Involvement in Land Delivery As already seen from the previous chapter, the private sector is involved heavily in the urban land market in Ghana albeit in real estate development and management. However, in recent years their operations have now spread to the provision of land titles. All the nine (9) companies interviewed, in addition to some