“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."

"Our Family Trip to Hawaii" by Jennifer Mings (2013)

Last summer, my mother, sister, brother, and me took a trip to Honolulu, Hawaii. We were excited to see everything, and couldn’t wait to arrive. After our lengthy plane ride, we stepped off of the plane in a daze. There was two flight attendants who immediately greeted us, putting flower wreaths around our necks. We then met up with our tour guide; and he told us that we would be going straight to Pearl Harbor.

On our way to Pearl Harbor, there was a largely immense amount of traffic, something that aggravated my mother. Luckily, the tour guide was a native of the island, and he was able to calm my mother down.

When we finally arrived at Pearl Harbor, there was many tourists and natives of different nationalities. The first thing we did when we arrived was watching a movie about the history of Pearl Harbor, which included the story of the USS Arizona. During the movie, everyone had been excited to see the USS Arizona Memorial and wanted to get on the boat. After, we all got on a boat and we were driven to the USS Arizona Memorial. It was an amazing, beautiful, gorgeous, and great experience for everyone.

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

"Our Family Trip to Hawaii" by Jennifer Mings (2013)

Last summer, my mother, sister, brother, and me took a trip to Honolulu, Hawaii. We were excited to see everything, and couldn’t wait to arrive. After our lengthy plane ride, we stepped off of the plane in a daze. There was two flight attendants who immediately greeted us, putting flower wreaths around our necks. We then met up with our tour guide; and he told us that we would be going straight to Pearl Harbor.

On our way to Pearl Harbor, there was a largely immense amount of traffic, something that aggravated my mother. Luckily, the tour guide was a native of the island, and he was able to calm my mother down.

When we finally arrived at Pearl Harbor, there was many tourists and natives of different nationalities. The first thing we did when we arrived was watching a movie about the history of Pearl Harbor, which included the story of the USS Arizona. During the movie, everyone had been excited to see the USS Arizona Memorial and wanted to get on the boat. After, we all got on a boat and we were driven to the USS Arizona Memorial. It was an amazing, beautiful, gorgeous, and great experience for everyone.

Choose the answer that best corrects the bolded portion of the passage. If the bolded 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."

"Our Family Trip to Hawaii" by Jennifer Mings (2013)

Last summer, my mother, sister, brother, and me took a trip to Honolulu, Hawaii. We were excited to see everything, and couldn’t wait to arrive. After our lengthy plane ride, we stepped off of the plane in a daze. There was two flight attendants who immediately greeted us, putting flower wreaths around our necks. We then met up with our tour guide; and he told us that we would be going straight to Pearl Harbor.

On our way to Pearl Harbor, there was a largely immense amount of traffic, something that aggravated my mother. Luckily, the tour guide was a native of the island, and he was able to calm my mother down.

When we finally arrived at Pearl Harbor, there was many tourists and natives of different nationalities. The first thing we did when we arrived was watching a movie about the history of Pearl Harbor, which included the story of the USS Arizona. During the movie, everyone had been excited to see the USS Arizona Memorial and wanted to get on the boat. After, we all got on a boat and we were driven to the USS Arizona Memorial. It was an amazing, beautiful, gorgeous, and great experience for everyone.

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."

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."

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. One of the answer choices repeats the underlined portion as it is written.

Few domesticated animals have the ability to fend for themselves without humans providing for themselves.

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."