existential acrobat: Study Mathematics |

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?Why Should Anyone Study Mathematics??

Everyone should master basic mathematics.

Everyone should at least master algebra.

Mathematics helps you to understand the world around you.

Basic mathematical principles are used everywhere.

Everyone should master trigonometry.

Mathematics is needed for problem-solving and analysis.

Non-technical majors should not be required to take mathematics.

All majors should take a relevant college-level mathematics course.

Calculus I should be required of all college students.

Higher mathematics requirements would reduce the number of people with degrees.

Mathematics courses should require mastery before proceeding to the next level.

Lack of mathematics skills reduces your career options.

Mathematics is more difficult than other subjects.

Mathematics standards should be set by mathematics teachers, not by politicians.

If mathematics were not required, most people would not take it.

Mathematics helps in pattern recognition.

Mathematics is the language of nature.

Society depends on mathematics.

Non-technical majors should require mathematics courses, because engineers have to study humanities, etc.

If the other majors didn?t have to study mathematics, then engineers wouldn?t have to study humanities, etc.

People should study mathematics, so they can help their children with school.

You study more mathematics to really understand what you learned in previous mathematics courses.

Non-technical majors should study a little mathematics so they can communicate with technical majors in the workplace.

Diversity in all education makes you a better person, and more employable.

People should study mathematics because they are weak in it.

A college graduate should be better educated than someone who has not been to college.

Failure in mathematics should be culturally unacceptable.

Mathematics should be taught with more underlying theory.

Mathematics should be taught with more applications.

America needs more educated workers to compete in the global market.

Learning mathematics makes you more intelligent.

Learning mathematics can save you money.

Some people absolutely have to study mathematics, to keep society going, and invent new things.

The study of mathematics teaches discipline.

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Math?s Use in Society ? Joey Harp

Math is present in everyday life; it surrounds a person wherever a person goes. ?It is involved with purchases, computers, and inventions used on a day to day basis. ?People sometimes do not realize the amount of math that surrounds them and the amount of math that they use everyday.

The sort of math that is needed for a person to be competent in our society is not very complex. ?A person should be able to do the basic addition, subtraction, division, and multiplication. ?They need this to be able to handle money, prepare food, and to do simple calculations that are present in all job types. ?Most people are not expected to be able to devise new machinery with complex mathematics, solve physics problems, or engineering problems. ?There are however, people who most do these things.

It is not, in my opinion important for everyone to learn complex mathematics. ?I am not saying that people should not learn some kind of mathematics. ?I think that they should have knowledge of basic everyday math. ?I do not think they should learn math if it is not relevant to their future career. ?If a person chooses to stop learning math then that is their choice. ?If a person is not going to use something later on in life, why should they waste their time learning it? ?If however, a person can not comprehend basic math, then I think they should be taught this skill.

Not everyone wants to obtain a math based major and there are other subjects which are mandatory for non math based majors that math based majors are not required to take. ?I believe an understanding in the subject is necessary, but I do not think everyone should be required to take something that they hate doing. ?I do not really think that a person would care if the doctor who was operating on them was competent in advanced mathematics rather than in advanced surgery.

Mike Leovic

It is my personal opinion that math education should be required at both the high school and collegiate levels to a certain extent. ?In determining the level of math knowledge that should be required, the problem lies in accounting for the differences in intelligence of each unique individual. ?As with every subject, a certain number of individuals will undoubtedly fail and be unable to comprehend the material. ?However, I believe that every individual should be pushed to gain the greatest understanding of mathematics that they are personally capable of obtaining.

The study of mathematics is extremely important for many reasons. ?Most importantly, math surrounds us in many aspects of our everyday life. ?Our monetary system, system of measurement, mechanical objects such as automobiles and many other aspects of life we encounter daily are highly dependent upon math. ?If an individual is unable to perform simple mathematical processes, he or she finds himself in a highly disadvantaged situation that lacks a certain understanding of how things operate. ?These individuals lack beneficial abilities such as pattern recognition and logical reasoning that are developed in mathematical instruction.

For me, math was is useful in teaching discipline. ?This subject requires an individual to constantly make an effort to comprehend new material, part of which requires completing homework on a regular basis to be collected. ?I believe that this methodical technique helps not only to teach the material, but to also create individuals that are dedicated, focused, reliable, and organized (all characteristics that create a more respectable, successful individual). ?Mathematics should be included in this general education for its ability to develop character qualities such as this and the understanding of mathematical processes it provides. ?An individual that is well-rounded is highly valued in our society and our education system must continue to require general education requirements, including multiple courses in mathematics.

People often complain that math is simply too hard of a subject and that they just don?t understand it. ?I think it is ridiculous that I have friends that can fail the same math course twice. ?Being that the math course was Intermediate Algebra and that the student is very capable of academically succeeding, I find that there is no excuse. ?Math is typically a subject associated with geniuses such as Einstein and other so-called ?nerds.? ?Maybe it is the media?s fault for associating math with such an image, but I think that this image of such difficulty makes some students feel inferior from the get-go and that they will be unable to succeed in math regardless of what they do. ? This results in a lack of effort to comprehend the material. ?I feel that removing math education requirements would be greatly detrimental to our society, and that the nagging about math?s difficulty would only be replaced by another subject.

It may be required that our society place a stronger focus on mathematics earlier on in the education process to correct this problem. ?If students are quickly taught that math is important and are correctly taught the basics of the subject, they will be able to succeed with more ease when they reach the collegiate level. ?I feel that more practical application of math may spark the interest of students, and therefore should be incorporated into the curriculum.

(Name withheld by request)

The study and application of mathematics has lead to the invention of almost everything we see and use today. ?The building we live, work, and play in are constructed to specifications based on mathematics. ?The currency we use is a form of mathematics. ?Without mathematics our lives would be very different.

The inventors, and mathematicians are the people that created these things, and most people do not know how, or care how, they work. ?Math in the American society is seen as useless if you are not going into a profession that uses it. ?Why should an English major, who wants to write books, be required to learn math? ?And in being required what level should he or she have to learn?

There is a difference on the other hand, in whether math should be required in high school and college. ?High schools that are teaching college preparatory courses should be required to teach enough math to be able to pass standardized tests to get into college, and for use in basic life skills. ?Higher levels of math should be encouraged but not required.

Dealing with the college education, some math is required just to be able to survive adequately in society. ?If a college had general education credits because they want their students to be well rounded than math is a necessity. ?If there is no general education then depending on the major math should be required. ?In order to graduate from a university a student must have more knowledge than those who have not been to college.

David Neroni

?The great book of nature can be read only by those who know the language in which it was written. And that language is mathematics. (Galileo)? It is necessary for people to study Mathematics for many reasons. The universal language of the world is math, and people have been using it for thousands of years across the world. Today?s society would not be in existence without the application of mathematics.

The application of math can be seen everywhere throughout the world, and without it a majority of things would not be possible. Complicated things such as building a bridge, flying an airplane, or mass producing anything would not be possible. Even simple things such as leaving a tip, paying a bill, or cooking would not be possible without math. Even if someone has no interest in how to build a bridge, or how things are mass produced, to live in today?s society it is necessary for someone to be able to support themselves financially, and money involves math. In order to cook numerous things exact measurements and temperatures, as well as exact times are needed, all involving math. As much as the ?normal person? hates math, no one can escape the need for mathematics in their everyday life.

It is also important to study mathematics because it gives one a different perspective on things. Learning math involves a different type of thinking that is not addressed in other subjects. ?To be a well educated person one need to be able to think methodically and analytically as well as figuratively. People most commonly state that math is hard and they will never need to use math in their majors. However, just as it is necessary for engineering and math based majors to take philosophical courses, other majors not pertaining to math, still need to take math courses in order to be well rounded students. ?Even if math is hard for someone, and they need to persistently work at it to understand it, it will create a good work ethic for them. Math teaches people to recognize patterns in everyday things, and view things more critically.

Whether people like math or not, in order to be a part of today?s society one needs to understand the concepts of mathematics. It is essential for mathematics to be integrated into the school curriculum so people have a better understanding of math in the world today.

Anthony Paulin

Preamble: Given that most people hate mathematics and/or find it difficult, is it appropriate that we make all high school and university students take mathematics courses? The standard cry is that ?I will never use this material!?

As a math tutor for the University of Akron, I have tutored many students who struggle with math. There are several variations, but the comment I hear most often is ?Boy, am I glad that this is my last math class.? Upon further inquiry, I find that there are two reasons for them saying this. First, because they find the material difficult (College Algebra or Calculus with Business Applications) and second, that they don?t see the point in learning math, since they will not ever use it for their major. The students who typically say this are the business majors, or who have majors in areas related to business, such as accounting. I find this ironic, mostly because business and accounting are all about money, which is just numbers, and math is the manipulation of numbers, so it would be reasonable to conclude that math is necessary for business. That and the fact that Calculus with Business Applications teaches math and applies it to business problems makes it illogical to argue that math has nothing to do with business and other related majors.

However, the question is also raised for majors that have nothing to do with business, engineering, or science, such as education, philosophy, geography, etc. Basically, the ?artsy? type majors don?t want to take the math classes, because they don?t relate to their majors at all. A counter argument that comes to mind is that they should have to take it because the engineering majors have to take classes unrelated to their majors (philosophy, humanities, etc.). The reason given for this is that it makes the engineers ?well-rounded individuals?. This should apply to the other majors as well, because math classes would make them ?well-rounded individuals.? However, I feel that a better argument besides ?we have to take their classes, so they should have to take our classes? is needed.

In The Republic, Plato presents a better argument for why math should be required for all high school and college students. He argues that math and geometry teach problem-solving skills and how to analyze and think. In other words, math is necessary for understanding, whether it be in engineering or philosophy (Plato, p. 184). Basically, he is saying that in order to understand and learn any subject, you need to have some basic math skills. Based on this, I recommend that math be required for college and high school students.

The next question that arises is that to what level should the math requirements go up to? I argue that everyone should be at least required to take math up to and including pre-calculus. In my observance, the most important aspect of math that is widely used, and that which people have the most trouble with, is algebra. Even in this class, people still have trouble doing basic algebra, including factoring, completing the square, and solving equations. Requiring people to take up to pre-calculus ensures that not only will they have learnt algebra, but they will become adept at it, because it will be reinforced through pre-calculus. Hence, based on this, high school and college students should be required to take math courses up through pre-calculus, regardless of their major.

Works Cited:

The Republic / Plato. Translated by G.M.A. Grube (Hackett Publishing Co., 1992)

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Nina Katz

It is more than ?appropriate? that high school and college students are required to learn mathematics; it is necessary to their performance in today?s world. ?Every job opportunity, every household responsibility, and most every personal interest involves mathematics to some degree. ?Without it, day-to-day activities become difficult and, in many cases, meaningless. ?Through pattern recognition and application of basic skills, the entire world becomes mathematical, and students who are mathematically adept have a clearer view of a successful future.

As Dr. Norfolk has repeatedly stated, math is about recognizing patterns, and patterns occur in everything from traffic to weather to eating and sleeping. ?It is obvious that these pattern-containing topics affect a person?s daily life. ?According to an article from mathscareers.com, patterns also occur in nature ? in the ripples on the surface of a pond, in the sun?s path across the sky, and even in snowflakes, zebra stripes, and broccoli buds. ?Though these patterns occur in such ways that an understanding of them is not necessary for survival or success in life, it is important to consider that mathematics are essential to even the most overlooked details. ?Math gives order and structure to what would otherwise be random and chaotic. ?Who can deny the importance of mathematics when human genetics rely on them? ?Thus, in these examples, it can be seen that math is everywhere, even if math is not necessary for survival.

Having a general understanding of mathematics yields immeasurable benefits. ?Math can be put to use in the grocery store and at the mall but also while watching television or reading the newspaper. ?For example, without mathematics, grocery shopping becomes much more expensive than it has to be. ?A person without knowledge of mathematics may assume that bulk purchases save money, but this is not an intelligent assumption; according to an article in the Sunday Times, 2004, buying in bulk is often intentionally made more expensive that buying individually. ?Specifically, ?the newspaper found that the difference can be as much as 30%!? When applying for credit cards, many customers do not take into account the interest rates they are being charged. ?Many do not understand where their credit scores come from! ?Similarly, a weak statistics background may mislead an ad reader into believing a faulty success rate. ?For example, the fact that ?eight out of ten women prefer? a specific brand of shampoo is not a valid reason to purchase it. ?What if two of the women surveyed lost all of their hair or developed a skin disease as a result of using this brand? ?How would the statistics look if the reader knew the whole story? ?Even for merely common-sense purposes, a general understanding of mathematics is necessary (?What Use is Maths??).

The vast majority of high school and college students despises mathematics; it is difficult for this majority to realize that various seemingly-unrelated areas of study include math as a foundation. ?Music, art/design, and even athletics are built on mathematics. ?A pianist can benefit from patterns and sequences when composing much the same way that a golfer can benefit from math-based physics, trigonometry, and even statistics when driving. ?As Dr. Norfolk says, the future is in math and science, but what does this mean? ?No matter which avenue a student pursues, math will somehow be present. ?It is not only the responsibility of a nurse, an engineer, or a physicist to know mathematics. ?Rather, it is in each student?s best interest that they apply, or at least consider, mathematics in all areas of life.

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John Thomas

Mathematics is defined as ?the study of the measurement, properties, and

relationships of quantities and sets, using numbers and symbols? (dictionary.com). ?With a definition like that how can a person not be intrigued by this subject? ?Granted, mathematics is not the easiest subject a person could take, and it definitely isn?t the most fun. ?Some people would even go as far as to call it boring, dull, or a waste of time. ?Albert Einstein was once quoted saying, ?Do not worry about your difficulties in mathematics, I assure you that mine are greater? (quotes.com). ?However, there are people who happen to enjoy mathematics and find the problem solving interesting and exciting. ?A prime example of this is the famous mathematician from Budapest, Alfred Renyi, ?If I feel unhappy, I do mathematics to become happy. If I am happy, I do mathematics to keep happy.? ?(quotes.com).

A persons brain has quite a bit to do with their love, or lack of love for mathematics. ?If a person is more developed or more in tune with the left hemisphere of their brain, than they probably find mathematics easier than a person who is more in tune with the right hemisphere of the brain. ?Since the left side of the brain deals more with logic and reasoning, this would make sense that a person who is strong with this part of their brain would like the problem solving of mathematics.

I realize that not all people like mathematics as much as others, when I was younger I hated math and I would do whatever I could to avoid a math class. ?But I discovered that it was only because I didn?t understand some basic principles that are fundamental items a person would need to know to be able to perform mathematics. ?But now that I have achieved mastery of some of the minor things, I find mathematics fun and very easy to do.

I feel that every person in America should be taught at least a minimum level of mathematics, no matter what career that person plans to pursue. ?I feel that everyone should have a mastery of ?basic math such as addition, subtraction, etc. as well as a mastery of algebra skills and some experience in dealing with trigonometry. ?All these skills will be useful in everyday tasks. ?Also if you plan on having children some day, wouldn?t it be nice to be able to help them with their math homework when they bring it home, as opposed to my parents who hadn?t the slightest idea what I was doing.

Like Adrian Mathesis said ?The greatest unsolved theorem in mathematics is why some people are better at it than others.? ?(quotes.com). ?Although this may be true, every one that plans to do anything in their life needs to have a solid base in mathematics in order to succeed in life. ?Even if they don?t plan on using the actual math in real life, they will use the problem solving skills they learned in their math courses to learn how to problem solve other situations in real life.

Works Cited

http://quotes.zaadz.com/topics/mathematics?page=1

http://dictionary.reference.com/browse/mathematics

http://www.morphonix.com/software/education/science/brain/game/specimens/hemispheres.html

Anthony Puntel

Every high-school teacher and even some college professors have heard the repetitive cry that ?math is pointless? and ?I?m never going to use math.? ?It has become a recent topic of discussion as to whether or not require all students to take mathematical courses even if it is against their will. ?The answer is yes! ?There are only a few paths that a person can take after high-school which includes going to a university college, a technical school, the military, or entering the work force. ?Universities require all students to take some sort of mathematics, as do technical schools and the military. ?This leaves the path of directly going into the work force. ?Does this mean that directly going into the work force allows you to get away from math?

The answer is fortunately no. ?Mathematics is the basis for everything in this fast, growing technical world. ?Today, ?less and less labor intense entry-level jobs? are available due to the fact that many of these jobs are being taking over by robotics and machinery that are much more cost efficient (1) ?In the United States, there are approximately 87 million (29% of the U.S. population) people that do not graduate from high-school, making them deficient in mathematics. ?In short, this means that there are 87 million people competing for a small amount of entry-level jobs, making it highly competitive and a rarity to find a job that doesn?t require at least some sort of mathematical basis. ?In fact, many employers will only hire employees that can do a basic mathematics section on their company?s application. ?Their reasoning for this, besides the obvious, is that people who can do math are more logical thinkers and better problem solvers (2).

Many will still argue that it is still a possibility to find jobs where no math is expected and this is true, but other than careers, many people do not realize how often mathematics is used in their everyday life. ?Math is used when mothers go to the grocery store to shop and find the better deal on goods, when homeowners fix their houses, when vacationers are finding the best deal to go on vacation, when cooks prepare their recipes; the list goes on indefinitely. ?Furthermore, some argue that you can ?get by? without knowing any math. ?This is sadly also true, but to be a ?knowledgeable and functional member of [today?s] society,? basic mathematics must be known (1).

If an educator?s job is to prepare their students for the future and to be a part of this growing society then mathematics must be in every lesson plan, because society will never progress forward if math is thrown to the side. Therefore it is vital for all students to take math courses and to be enlightened on its everyday advantages.

Sarah Gedney

There are many people who hate and/ or find mathematics difficult. ?Then should we make them take courses in it? ?I believe that the answer to this question is yes. ?The reason for this is mainly for their well-being. ?Think of all the places where mathematics pops up all around us?prices at the store, tips at restaurants, taxes, bills, bank statements, checkbooks, etc. ?The list can go on forever. ?If people don?t know the basics of mathematics, they are going to be ripped off and taken advantage of on a daily basis (of course then they will complain that it?s the school system?s fault for not requiring mathematics courses). ?If credit card companies and businesses in general knew that they were dealing with someone who knows nothing about mathematics, they could easily show inaccurate calculations of what the customer owes them (by jacking up the bill). ?I think if people stopped learning mathematics, the national debt would soar (not that it already isn?t) due to the fact that people are so dense that they don?t realize what they are going to owe a credit card company.

If grade schools and high schools stopped introducing mathematics, then people would be less likely to pursue careers in fields that involve mathematics. ? This would mean the end to technology and structural advances?let?s face it, math is everywhere. ?Calculations are needed to construct the bridges we drive on, build the houses we live in and develop the computers we depend so much on.

I?m not saying everyone has to be a math whiz, but someone has to do it. ?If not, our whole way of living might as well go back to the days of reading by candlelight and driving horse and buggy carriages! ?If math was important enough to be put into the required school curriculum long ago, then there?s no reason why it should ever be taken out. ?I believe that some form of math knowledge is required for one to be able to take care of themselves in the real world, mostly due to financial purposes?leave the rest to the Engineers?.

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David Prueter

I think that it is short-sighted to assume that an individual can function in today?s society without any mathematical abilities. Almost any job involves mathematics in some form or another, and mathematics is required in many common day to day activities. I believe that it is fair to conclude that without any mathematical ability, an individual will be greatly disadvantaged and will have an extremely difficult time coping with the demands of daily life.

Why should anyone study mathematics?

I think that a reasonable response to this question would be the same response if the word ?mathematics? were replaced with any other area of study or academic discipline. Why should anyone study science, English, history, foreign language, art, music, etc? The simple answer is that knowledge makes an individual better-rounded. Whether it is to gain more knowledge or to simply learn more about oneself, education in any form benefits the entire person.

Is it appropriate that we make all high school and university students take mathematics courses?

No. By requiring more students to study math does not, in my opinion, correlate to more students understanding math. There are some individuals who, no matter what, will not learn mathematics. Either, the entire class will suffer, or grades will simply be inflated.

I think that students must realize the consequences of their decisions. An individual cannot, in my opinion, be competitive in today?s business world without having a decent level of mathematical ability. If a student decides not to learn math, then he or she must be willing to accept the fact that many future opportunities might not be available. Furthermore, by being close-minded to mathematics, one limits the opportunity for success in a technologically focused society.

The same principle can be applied to other disciplines. However, everyone should be realistic about his or her abilities. For instance, at least at this point in my life, I have accepted the fact that, due to my lack of musical ability, I will not be competitive in the music industry. This is a fact that I have accepted and am willing to live with. However, if all musicians demanded that all mathematicians learn music, there would either be a multitude of mediocre singing mathematicians or an overall decline in the quality of musical talent, on the average. Neither of which would be desirable.

In closing, I think that ideally, every student should strive for proficiency in as many different academic disciplines as possible. In a perfect society, everyone would be intelligent and posses the ability to succeed in any endeavor. Realistically this is completely impossible.

With this being said, I think that it is more important to focus on an individual?s strengths instead of attempting to exploit his or her weaknesses. I enjoy math, and have traditionally done well in it. However, this does not imply that others should feel the same. Everyone has different talents and abilities and should not be penalized for a lack of ability or interest in a specific area of study. All individuals must be responsible for their academic choices but should also be encouraged to challenge themselves to reach their full potential.

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Grade 12

Mathematics Practice Questions

& Scoring Guide

Questions begin on page 2.

Scoring Guide begins on page 13.

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This booklet contains sample items from the National Assessment of Educational Progress (NAEP). Additional items can be accessed at www.nces.ed.gov/nationsreportcard/itmrls.

Students were given both a ruler and a protractor for use on this assessment.

The following question refers to the following information. Each of the 12 sides of the figure above has the same length. ?
1.? Which of the following angles has a measure of 90??
?
?	A)	Angle ABI
?	B)	Angle ACG
?	C)	Angle ADF
?	D)	Angle ADJ
?	E)	Angle AEH
? ? ? ? ? ? ? ? ? ? ? ? ? ?
? 2.? Use your ruler to help answer this question. ? Of the following, which is closest to the perimeter, in inches, of quadrilateral LJFD?
?
?	A)
?	B)
?	C)
?	D)	7
?	E)
? ?	?	?


3.	Use your centimeter ruler to help answer this question. Of the following, which is closest to the area of parallelogram ABCD above?
?
?	A)	20 square centimeters
?	B)	30 square centimeters
?	C)	40 square centimeters
?	D)	50 square centimeters
?	E)	52 square centimeters
? ?