“Mathematics and Learning”

What subject should be learned first? The question rightly troubles anyone who’s interest is in education. Of course, young children often must learn in a very basic and rote fashion, applying their apt memorization skills to simple tasks that will serve them very well in later years when they go one to apply such knowledge to more complex topics. However, when the time comes to designing curricula, an important question must be answered for older students, namely “What is most important first topic in these students’s education?”

An argument can be made for the use of mathematics as a tool for teaching students how to reason more clearly. This is not because mathematics is the basis of all knowledge. Indeed not. There are many important subjects including not only the humanities like poetry and history but sciences like biology and physiology too. These topics are not strictly speaking mathematical in nature, even though mathematics can be used in it in many ways.

Our minds are best geared for learning things that we can sense, things that are visible and tangible. Although mathematics is abstract, it can begin with this kind of sense derived experience. Beginning with simple everyday examples, children can be taught the more abstract and difficult skills that must be learned for the sake of the development of mathematical skills. In the process of learning these topics, the children will begin to learn important rules about reasoning. He or she will learn how several propositions can serve as the basis for conclusions. They will learn how certain properties are related to various geometric figures and arithmetical rules. Although much of this will be memorized at first, with time, they will have the opportunity to see that human reasoning in mathematical subjects is orderly and logical. On the basis of such “logical experience,” young learners can then begin to be taught the rules of logic that they have been using all along. As the medievals used to say, they could go from logica utens, logic used in other subjects, to logica docens logic taught, as a unique, and separate subject.

Choose the answer that best corrects the underlined portion of the sentence. If the underlined portion is correct as written, choose "NO CHANGE."

As the class entered the museum, Ms. Johnson noticed that two of her students had fallen behind the group. After all of the tickets had been secured, she approached the two girls, saying: “what on Earth is causing you to go so slow?” The taller girl, whose name was Ashley, was the first to respond:

“Veronica and I were just discussing something very private. Nobody can hear what her and I are discussing.”

“Well, Ashley, I think that our tour guide, Dr. Mitchell, will be offended by your behavior. You and Veronica should find separate places in the group and you should pay attention to him and me.”

The two girls reluctantly joined the rest of the class. Ms. Johnson looked to see if another student was out of their place, but everything seemed to be in order. The tour guide, Dr. Mitchell, introduced himself to the class:

“Hello everyone! My name is Dr. Mitchell. I’m so glad that you have all come to the Museum of Natural History today; I think you’ll really enjoy our exhibits, which have been curated with the utmost care. The museum has three distinct types of exhibitions. Permanent exhibitions, temporary exhibitions, and space shows. The permanent exhibition and the space show is always available for viewing, but the temporary exhibition changes seasonally.“

Having finished his introduction, the permanent exhibition was the first thing that Dr. Mitchell showed to the class.

Choose the answer that best corrects the bolded portion of the passage. If the bolded portion is correct as written, choose "NO CHANGE."

One of the most popular programs of all those featured on the Internet (1) is a video clip show. The format of the show is simple, each (2) week the host, a short but attractive New York native named John Jackson introduces (3) a set of three video clips from all over the Internet. These clips shows (4) people hurting themselves in accidents, getting into crazy situations, interacting stupidly with animals, and et cetera. (5) Jackson introduces each clip comically and often comments on the action with animations where (6) he makes fun of the people in the videos. While the videos are often funny, there is definitely an element of schadenfreude involved in watching these clips. Schadenfreude is a German word for "the pleasure one takes at seeing the suffering of others". (7) Jacksons (8) show are (9) not far removed from popular TV programs like (10) The U.S. Laughs at You there is also a version of which (11) on the Internet. It is an open question whether laughing at these videos is a harmless activity or it causes harm to us. (12)

Choose from the following four options the answer that best corrects the underlined mistake preceding the question number. If there is no mistake or the original text is the best option, choose "NO CHANGE."

As the class entered the museum, Ms. Johnson noticed that two of her students had fallen behind the group. After all of the tickets had been secured, she approached the two girls, saying: “what on Earth is causing you to go so slow?” The taller girl, whose name was Ashley, was the first to respond:

“Veronica and I were just discussing something very private. Nobody can hear what her and I are discussing.”

“Well, Ashley, I think that our tour guide, Dr. Mitchell, will be offended by your behavior. You and Veronica should find separate places in the group and you should pay attention to him and me.”

The two girls reluctantly joined the rest of the class. Ms. Johnson looked to see if another student was out of their place, but everything seemed to be in order. The tour guide, Dr. Mitchell, introduced himself to the class:

“Hello everyone! My name is Dr. Mitchell. I’m so glad that you have all come to the Museum of Natural History today; I think you’ll really enjoy our exhibits, which have been curated with the utmost care. The museum has three distinct types of exhibitions. Permanent exhibitions, temporary exhibitions, and space shows. The permanent exhibition and the space show is always available for viewing, but the temporary exhibition changes seasonally.“

Having finished his introduction, the permanent exhibition was the first thing that Dr. Mitchell showed to the class.

Choose the answer that best corrects the bolded portion of the passage. If the bolded portion is correct as written, choose "NO CHANGE."

When the patent on Alexander Graham Bell’s revolutionary invention, the telephone, expired in 1894 thousands of new firms entered the telecommunication industry. Among them were a collection of profitable companies that merged to form what would later become known as The Bell System. The Bell System had amassed such weight in the industry that in 1933, when Congress passed a law declaring phone service a public utility, the Bell System quickly transformed into a monopoly. Lawmakers enthusiastic supported a series of provisions intended to stimulate competition. Appointed as the nation’s sole provider of telecommunication services, widespread criticism about the Bell System began to surface.

The Federal Communications Act has so far been highly effective and the industry has grown tremendously as a result. In fact, for the past three years, the profitability of the largest three telecommunication companies has been greater than the largest three automotive companies. The number of calls provided by the top three companies range from five billion to six billion per day. Today, virtually everyone has made a phone call over the course of their lives. Most people do not know, however, that payment for swaths of electromagnetic wavelengths have become commonplace.

One explanation for such high call volume and large profits is that calls are becoming much less expensive for companies to provide, regardless for many large fixed expenses such as communication towers, base stations, and paying for utility poles. Over the last century, telephones had become an important part of modern society. In fact, the cost of delivering one telephone call today is about a thousandth of the cost in the 1950s. The increasing affordability and abundance of phone calls mark the progress made since the time of Alexander Graham Bell and the Bell System.

Choose the answer that best corrects the bolded portion of the passage. If the bolded portion is correct as written, choose "NO CHANGE."

Adapted from The Sorrows of Young Werther by Johann Wolfgang von Goethe (1774; trans. Boylan 1854)

That the life of man is but a dream, many a man has surmised heretofore. I, too, am everywhere pursued by this feeling. When I consider the narrow limits within which our active and inquiring faculties are confined, I am silent. Likewise, when I see how all our energies are wasted in providing for mere necessities, which again has no further end than to prolong a wretched existence, I find myself to be silenced. Indeed, discovering that all our satisfaction concerning certain subjects of investigation ends in nothing better than a passive resignation, while we amuse ourselves painting our prison-walls with bright figures and brilliant landscapes—when I consider all this Wilhelm—I am silent. I examine my own being, and find there a world, but a world rather of imagination and dim desires, than of distinctness and living power. Then, everything swims before my senses, and I smile and dream while pursuing my way through the world.

All learned professors and doctors are agreed that children do not comprehend the cause of their desires; however, nobody is willing to acknowledge that the grown-ups should wander about this earth like children, without knowing whence they come or whither they go, influenced as little by fixed motives but, instead, guided like them by biscuits, sugar-plums, and the rod.

I know what you will say in reply. Indeed, I am ready to admit that they are happiest, who, like children, amuse themselves with their playthings, dress and undress their dolls. They are happiest, who attentively watch the cupboard, where mamma has locked up her sweet things, and, when at last they get a delicious morsel, eat it greedily, and exclaim, "More!" These are certainly happy beings; but others also are objects of envy, who dignify their paltry employments (and sometimes even their passions) with pompous titles, representing them to mankind as gigantic achievements performed for their welfare and glory. However, the man who humbly acknowledges the vanity of all this, who observes with what pleasure the thriving citizen converts his little garden into a paradise, and how patiently even the poor man pursues his weary way under his burden, and how all wish equally to behold the light of the sun a little longer—yes, such a man is at peace, and creates his own world within himself. Indeed, he is also happy precisely because he is a man. And then, however limited his sphere, he still preserves in his bosom the sweet feeling of liberty and knows that he can quit his prison whenever he likes.

What is the antecedent of the bolded relative pronoun “who”?

Many people watch football however (1) some do not. With (2) those who do not watch this sport (3) football is an incomprehensible pastime. Non football (4) fans cannot understand what is so exciting about watching two packs of grown men running away or toward each other, while (5) clinging for dear life to a piece of pigskin. It also makes from little to no sense (6) why those whom (7) play the sport gets (8) paid the exorbitant amounts that they do, even though he is (9) in effect doing the same thing that high school and college students do on a daily bases (10). But as the French would say, "Chacun à son goût" (11) though its (12) highly doubtful that most football fans (or even people who are not fans) would know what that means.

Choose from the following four options the answer that best corrects the underlined mistake preceding the question number. If there is no mistake or the original text is the best option, choose "NO CHANGE."

After the unbelievable fame of J.K. Rowling the author of the Harry Potterseries hundreds of idealistic authors struggled to achieve similar success. Because of Rowling's legendary accomplishments, we have invited the author, herself to the book signing so that she can share her experience to anyone that wants to listen. Whether you're an amateur writer, expert author, or simply an eager fan, all kinds of people can benefit from her insight. After all, if a person wants to be successful, you have to be willing to listen to the advice of others. If anyone are interested in attending, please contact the office before the end of the month.

Choose the answer that best corrects the bolded portion of this passage. If the bolded portion is correct as written, please select NO CHANGE.

“On the Nature of Belief”

Belief and faith often are critiqued in a scientific culture. It can seem that mere belief is a replacement for science made available to soothe the ignorant masses. There is some truth to such accusations, and many people do use belief as a screen to cover their own ignorance about the truths of reality. Everyone should be aware, however, that almost every single human being have these kinds of “blind spots.” We all live with many things that we merely believe, all of which are so central to ones world view.

Even if we set aside all such types of beliefs, there still remains a broad terrain of human life in which faith and belief remain—even if we ignore all religious matters whatsoever. Imagine the scientist who’s work on brain neurons depends upon many discoveries made by many other people. Yes, if it were possible, it would be better for such a person to know all of the details that they accept merely at the word of other scientists. In all cases, seeing directly is more fulfilling than merely hearing about something.

However, is the scientist better off when he or she knows only what they have experienced directly. Although it is preferable that he or she knows such facts. However, it is impossible to investigate everything. Sometimes, one must extend one’s own vision with the vision of someone else. In a way, the person who thus “takes it on faith” gains a further vision.

Such faith always relies upon the credibility of the person who shares the experience, of course. For one person to believe on faith what another person says, it is presupposed that the other person is not a liar and actually could have experienced the matter in question. This means that even the “scientific believer” must take the risk of placing credibility in someone who has witnessed things that he or she has not seen. While this does not vindicate every kind of faith that people have had, it does provide a telling sign that faith, as such, is not always the refuge of the ignorant. Indeed, it is an important part of all of our lives, even the lives of scientists, who’s daring and investigative work is rarely criticized as being a refuge for ignorance!

Choose the answer that best corrects the bolded and underlined portion of the passage. If the bolded and underlined portion is correct as written, choose "NO CHANGE."

Adapted from The Autobiography of John Adams (ed. 1856)

Not long after this, the three greatest measures of all were carried. Three committees were appointed, one for preparing a declaration of independence, another for reporting a plan of a treaty to be proposed to France, and a third to digest a system of articles of confederation to be proposed to the States. I was appointed on the committee of independence and on that for preparing the form of a treaty with France. On the committee of confederation Mr. Samuel Adams was appointed. The committee of independence were Thomas Jefferson, John Adams, Benjamin Franklin, Roger Sherman, and Robert R. Livingston. Mr. Jefferson had been now about a year a member of Congress, but had attended his duty in the house a very small part of the time, and, when there, had never spoken in public. During the whole time I sat with him in Congress, I never heard him utter three sentences together. It will naturally be inquired how it happened that he was appointed on a committee of such importance. There were more reasons than one. Mr. Jefferson had the reputation of a masterly pen; he had been chosen a delegate in Virginia, in consequence of a very handsome public paper which he had written for the House of Burgesses, which had given him the character of a fine writer. Another reason was, that Mr. Richard Henry Lee was not beloved by the most of his colleagues from Virginia, and Mr. Jefferson was set up to rival and supplant him. This could be done only by the pen, for Mr. Jefferson could stand no competition with him or any one else in elocution and public debate.

Which is the best form of the underlined sentence?