“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."

“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."

Margaret Mitchell the writer was having a horrible day. She just completed her latest novel when the tornado sirens went off. Fast, she rushed down into the basement, barricaded the door, and she sat in a corner of the dank dusty room to wait for the storm to pass. The winds howled noisy and increased in intensity until it sounded like the tornado was right above her. Suddenly, a gigantic bang echoed throughout the basement and Margaret dropped to the floor in terror. Then just as suddenly the noise vanished. Margaret got up and dusted her off before moving hesitantly toward the basement door. She opened it, and found the house above her was completely gone. Despite the horror of the site, she sighed and muttered, "Oh, well." A neighbor came running up to her and said, "Margaret! Thank goodness your alive! But what happened to your house, and what about your new book?" Margaret gave a rueful smile and replied, "Oh, that's Gone With The Wind."

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

Replace the underlined portion with the answer choice that results in a sentence that is clear, precise, and meets the requirements of standard written English.

The questions have only been seen by myself.

The cat made it clear to Jeremy whom was the boss around the house. The only time it showed him any affection was when it was time for the cat to be fed, the moment at which it would rub up against his legs and purr loudly enough to be heard. But as soon as the food hit the cat dish, it would run to the dish, gorging itself, and then ignore him the rest of the day. If he attempts to pet the cat at any other time, it will hiss and spit at him trying to bite him. Playing with the cat was even worst because it would wait until Jeremy was dangling something over it's face and then leap up to sink its fangs into his' hand. Eventually he would give up trying to be affectionate toward the cat and simply interacted with it every morning at feeding time. It was safer that way.

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."

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."

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."

During the final months of 2007, the prices of basic grains nearly doubled in Northern Africa, Latin America, and much of Asia, the high prices caused a global food crisis. The catastrophe sparked and incited an international debate regarding the licensing of new technologies to developing nations. One economist warned that because of the risk of unforeseen price shocks, officials should proceed very cautiously. The construction of private farms pose a serious financial threat to farmers in the United States; nevertheless, of the five most industrialized nations, the United States exports more crops.

How do some countries cope with food crises better than others. It is technology that accounts for the majority of the difference. The rate at which countries adopt innovations depends significantly on environmental factors. These environmental factors include climate, soil and elevation. The variability in environment inhibits new technologies from gaining worldwide popularity that are suited for one particular region over another. For example, the pesticides used in Europe are much more acidic than North America. Without the different levels of acidity, pests would prevent the crops to grow.

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