An opinion piece:
In chapter 4, John Allen Paulos discusses reasons why he thinks many people are innumerate. Pick one of the reasons that John Allen Paulos mentions and agree or disagree with it. Make sure that you give reasons for why you agree or why you disagree.
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Thursday, March 12, 2009
Chapter 4
Posted by Mr. Wille at 1:56 PM
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38 comments:
Christian J.
In Innumeracy, Paulos states that one of the causes of Innumeracy is poor education. He used the example of himself as a young boy, calculating the ERA of a pitcher on a team he liked. When he told his teacher, his teacher completely shut him down. Later he realized that he was right, told his teacher, and once again his teacher ignored him. In some cases i have to agree with this theory. In schools with low budgets, its hard to afford a good teacher who is highly qualified. Schools with money to throw around, such as private schools, they can afford teachers with great teaching backgrounds and amazing recommendations. Now I'm not sayings its all the teachers faults, sometimes its just a psychological block. However, if one is getting paid barely enough to pay his rent and one has to teach 100's of kids if not more, they would not be very motivated to teach these kids.
Trevor Lindner
In chapter 4, John Allen Paulos discussed how today's youth is not motivated or disciplined. Many students could care less about math and it's importance. I know what it feels like to give up on something I didn't understand. Grammar just would not work for me, I just could not get it. The difference between me and them is that even though I felt I could give up, I kept trying. I had the motivation. Children need to be motivated to do their work and not just answer blankly. One of the questions that is always asked in a class is "when are we going to use this in our lives?" Most teachers never give a straight answer so if you want to become a writer, you don't get turned off to math. And this is not math anxiety or a math-phobia, it is pure indifference to the subject. And if someone doesn't care, they can't learn.
Candy L.
I love his idea about the safety index thing. I think it will be helpful to stop innumeracy. The safety index work like this: on a scale of one to ten where one is the most dangerous, rank different activities that people do. Here's a example: The number of deaths cause by car accident annualy in America is 1/5300, the safety index for it will be 3.7, because 10^3.7=5300. I like that idea alot, because it tells the risk of doing something. Usually when you tell people to becareful when doing something, or tell them to stop doing things that are dangerous, they don't listen, because they are "innumerate". If there's a safety index like this, then people will start being careful by themselves when they saw how low the numbers are. For example, 1/800 Americans die every year due to heart, lung, and other diseases caused by smoking. So the safety index for it will be 2.9, that's even lower than a car accident. It will be pretty impressive for the smokers if we present these numbers to them. And I bet this number, 1/800, will decrease rapidly, if people knows about it.
Brooksr
Innumeracy is the result of many different possible factors. The one most blatant factor of innumeracy is the filtering of vital information from regular media excerpts. Filtration is tantamount to censorship because usually only positive information is seen in the news. It is seldom that we see such figures as the amounts of death associated with smoking is the equivalent of crashing three fully loaded jumbo jets each day of the year. Despite these numbers, terrorist bombings, local shootings, and the money spent on the war are still talked about on the television more than even deaths caused by smoking per year. This serves to distract the populace from the more imminent problems; problems that can be easily changed. Instead, the television networks broadcast information that is not as important as the number of deaths due to smoking. The average person will not know the number of deaths per year due to smoking. That is exactly why the average person is innumerate; he does not understand what is the most important and should be given the top priority.
Amanda Z.
Innumeracy is not only widespread, but it is also accepted much more than it should be which is why so many people don’t mind being innumerate. Paulos states the most obvious reason for innumeracy is poor education. One of the most prevalent scenarios typically involves a cash register. Although, it is assumed that a cashier would know how to count change and calculate tax, the truth is that a great number do not. The advancements in technology are continuing to help these people by providing the answers, yet in reality, the advancements are anything but- in fact, they are encouraging ignorance.
Jeffrey L.
John Allen Paulos states that one of the possible reasons for innumeracy is a lack of education. I completely agree with this fact because innumeracy can start at a very young age. It is a proven fact that people of younger ages retain and learn more information than adults. If a child is given a proper education, innumaracy would be avoided. If a child were to recieve an above average education, innumeracy is almost guaranteed to not occur in that child. It all starts at a young age and innumeracy can be prevented at that time. When it comes to the later years in life, it will be very difficult and almost nearly impossible for a person who is innumerate to become a numerate person once again.
Amanda Z.
Innumeracy is not only widespread, but it is also accepted much more than it should be which is why so many people don’t mind being innumerate. Paulos states the most obvious reason for innumeracy is poor education. One of the most prevalent scenarios typically involves a cash register. Although, it is assumed that a cashier would know how to count change and calculate tax, the truth is that a great number do not. The advancements in technology are continuing to help these people by providing the answers, yet in reality, the advancements are anything but- in fact, they are encouraging ignorance.An example of this that can be found in the book is when Paulos describes his experience when ordering a hamburger, French fries, and Coke in which comes to two dollars and one cents. Yet the cashier who has worked there for months still fumbles at the side of the cash register calculating the six percent tax, unable to realize that six percent of $2.01 is $0.12. Now accomodating for thier innumerate help,larger franchises have now cash registers that have pictures of the ordered items on the kets and it automatically adds on the appropirate tax.
(Please ignore previous comment, it was incomplete)
Tony L.
In chapter 4, John Allen Paulos believes Innumeracy is one main problem in todays society. many people do not understand concepts of math, numbers, statistics, etc. He believes this is true since poor math educastion is taught in schools or poor material are being utilized. One example which may support this argument is the one about the cashier calculating six percent sales tax. the cashier clearlys has expierence with his/her job but still calculates it wrong. most likely the elements of mathematics were taught insufficently or taught fautly.
John Allen Paulos says that the reason many people are Innumerate is because of poor educational skills. I agree because if teachers attempt to make math a more interesting subject, children would appreciate it more. He also explains that teachers should teach how Math can help in real life siituations otherwise children will beleive it is useless and give up on math. Hence the fact that Innumeracy depends on how math is taught.
The example that i chose from the story was the one about school system being very poor. He states that although many students graduate knowing their simple arithmatic tables. most do not know the answers to sipmle arithmatic word problems such as if a car was traveling at a speed of 35 miles per hour and it was traveling for 4 miles per hour, the tatol distance that this car has been on the road was a total of 140 miles.
John Allen Paulos states that the one to blame is the educational system, the ones who teach us at young age. He gave another example when John Allen Paulos was ten years old he calculated the ERA's of the batters, and his answer was 135. the teacher shot him down by saying that the highest ERA that the batter could have was about 21. A few days later the ERA was just as Paulos had stated. Exactly 135 was the ERA of the batters. The teacher was upset and told him to sit down.
the poin that Paulos was trying to make was, that teachers often suppress the thoughts of numerate people at a young age. I completely agree with this fact I think that most teachers if not all slowly desolve the minds of the students that show much promise in the feild of math. This is a sad but true fact.
John Allen Paulos says that one of the reasons that people are inumerate is because of the lack of teaching and understanding of math when you are in Elementary. I agree with this fact because the majority of kids, at a young age, aren't interested in school so they don't pay attention in class. Teachers don not make math fun for the kids (as stated by Paulos) and therefore, when math is needed in the future, the person lacks that knowledge.
Rudy O.
Benjamin G.
The biggest reason Paulos states that contributes to innumeracy is lack of education. He explains how High School is when students need to be taught especially well, and how many don't get the correct education and therefore understanding of mathematics. This leads them to become uninterested come college, and not take any math courses, leading to more and more innumeracy. I agree with this concept, as if somebody's teacher didn't teach them well or correctly, the student would probably lose interest; this leads to them becoming unaware of all of the concepts of mathematics, and not bothering to go on and learn more about it in college, which leads to them becoming innumerate.
The one that I want to talk about is the ones about education and i am going to mix it with other stuff and things. I think that the reason why most people are inumerate is because as John A. Paulos says most teachers do not know how to teach math/or are complete jerks who make it so BORING you want to just leave. There is also the "i don't care what you say because i have a masters and u don't" type of teacher. All of these play a great role in why we have a great amount of inumerate people. If some teachers where not as snobby many students will fell better in there class and will ask for help more often if they need to. That's an example i agree with.
John Allen Paulos believes that a vast percent of generation X is innumerate. He cites several reasons for this, but the most pressing is the lack of teacher to student cooperation. If a student is not willing to learn then they will not learn the subject. You have to be willing to learn in order to learn. Another reason is that teachers are unwilling to teach. If you were a teachers teaching many many hordes of noisy rude smelly teenagers (Oh wait...) a day would you be happy and willing to teach? Maybe you would feel reluctance to educate the indifferent ones who refuse to learn. Either the student, or the teacher, or both, are responsible for society's Innumeracy.
Emily S.
When Paulos writes about the connection between innumeracy and elementary school students made me smile because for ONCE I could relate with what he's talking about. The teacher's not intergrated methods of teaching is not all their fault. After teaching 20-40 rowdy, immature, unmotavated students, its okay to not always be motavational when one of them some to you with a question about what math has to do with the amount of pizza they ate last night. I've had a teacher that would have bimonthly simulations where she would dress up as different characters that "hired" us to solve everyday problems that pertained to what we were learning in class. From a design plan for a party that a snotty rich girl wanted, to finding the scientific notation of the distance of things such as from the school to the closest Hard Rock Hotel, it may sound kiddy-ish but we never forgot the lessons learned. Although convetional, the average teaching methods of underpaid, underapprieciated urban elementary teachers are boring and make math seem like a chore that most be done ander over with as soon as school's out.
Clara S.
An example that John Allen Paulos brings up in the fourth chapter, that I agree with, is the very first one. It describes his ordering of a fast food meal and how it took the cashier too long to look up the tax for his meal. He describes how innumerate our community has become by being given so much, like a tax chart. I completely agree with Paulos' opinion. It's a little sad when people can't do simple math in their head(like calculating tax), but it's just pathetic when you need pictures of the food on the cash register. The people used to memorize the prices and then just add them up. Nowadays, they need to search for the picture of the fries and large Coke.
Rondelle B
In Chapter Four, Paulos talks about his recent time in a suburban fast food restaurant. His bill came up to $2.01 and the cashier fumbled with the register to find $2.01 on the tax chart to figure out how much tax was owed. Then he talks about how the larger franchises have little pictures of the orders on the registers and the register adds on the tax automatically for them. Paulos is saying that people don't have to calculate anything anymore, everything is already there for them, canceling out the option to think, which also contributes to the aspect of innumeracy. I totally agree with Paulos on this one. If people don't have to think anymore, then why should they? That's what is causing all of this innumeracy. If we gave people the option to think nowadays then maybe America would be a smarter nation once again.
In chapter four John Allen Paulos describes that one reason why people are innumerate is that they personolize things. I agree with this, because I relate it to myself. I always ask myself what does number or equation or problem have to do with me & my life if im not planning on working with math or numbers and how much am I going to get paid. Paulos explains how people do not realize how math affects their lives. People personlize other things like astrology, because it can give them clear answers without work. I can't say math has ever been my favorite subject, but I try to understand it because I know I'll need some of it later.
In chapter 4, John Allen Paulos discusses reasons why he thinks many people are innumerate. I agree with Paulos in that the quality of education one receives in their early years is what makes all the difference. The teachers aren not sufficiently capable and they often have little or no appreciation of mathematics. Therefore, the kids grow up into innumerate adults who think mathematics is a waste of time and has no use in the real world. The teachers do not attempt to make mathematics fun and instead portray it as extremely boring. Even on page 97, Paulos describes a situation where he ordered at a fast food restuarant and the experienced cashier was still having trouble using and locating information on the six-percent tax chart. So innumerate people are the reason cash registers at many restuarants now have pictures on the cash register. That way, the cashiers won't have to use their brains and calculate the tax for the food themselves. Not that they would know how to, considering their innumeracy.
Keith M.
One of the reasons Paulos claims why people are innumerate is Math Anxiety. One claim that Paulos makes is that females are more subjective to Anxiety. Due to having very little understanding of the subject and intimidation, they become fearful of it. Because of this fear, it is a powerful cause of innumeracy. I agree with Paulos because when you don't like learning about a subjuct, you start to avoid it. This makes it even more difficult to comprehend when you come across it again. There are, however, many ways to learn it. So I believe that it is very possible to develop such a fear to a subject, that the mentioning of it doesn't induce the slightest enthusiasm. What makes it worst is that anxiety could cause disinterest in subjects other than math.
One of John Paulo's opinions is that the reason that so many people are innumerate today is because proper mathematics is not being taught in elementary school level. This is due to the lack of good secondary school teachers in elementary schools, which then gives the math the appearance that it is boring and almost useless. I agree with this because in anything, you need a strong foundation, a strong starting point to slowly build up not just your skill but your interest. If you are not properly taught or motivated when you begin, you will lose interest and this activity will quickly become a drag, and easily found as boring.
Nada G.
In the book, John Allen Paulos says “If mathematic education communicated this playful aspect (humor) of the subject, formally at the elementary, secondary, or college level or informally via popular books, I don’t think innumeracy would be as widespread as it is”. By saying this, I believe he is saying that innumerate people really never connected math to the real life so they never saw any fun in it; it was always a boring subject for them. I agree with Paulos on this because I too believe that if one could connect math to reality and have fun with it, then it would be more understandable to them. I believe that some people just don’t see the use of math in reality so they really don’t care about it.
Sergio G.
One of the major reasons that John Allen Paulos mentions that causes innumeracy is the teaching methods worldwide, which don't really show how much Mathematics have to do with real life, instead spouting theory at student. The result is a subject that is deemed irrelevant to many students, and will not really be invested much in terms of time in the future of those students, thus producing a mildly innumerate student, who will not keep his mathematical skills in use as he/she grows, leading to greater innumeracy as he/she grows older and/or further up in society.
That's how we get Innumerate politicians.
Chapter 4: Whence Innumeracy?
In Innumeracy, John Allen Paulos has been telling the reader the conditions of being an innumerate. He’s been telling them what it’s like, and how that affects how they see the world, or how they don’t see the world. In chapter 4, Whence Innumeracy? Paulos begins to tell us what he thinks the origins of this madness to which he’s given the pseudonym ‘innumeracy’ are. Basically, he starts off accusing math teachers of not doing their jobs correctly because they aren’t committed to teaching arithmetic, or mathematics in general, correctly. What stood out to me was when he said that an innumerate could’ve caught his innumeracy by his own negligence. Paulos said that some math comes naturally when one transcends to one’s self, family, and friends. For example when one asks himself: How many? How long ago? How fast? What links this to that? Which is more likely? Numbers and science for this type of innumerate comes from the fact the he only familiarized himself with them because he was tied to them personally. This sort of innumerate will be the one that believes in tarot cards and claims he doesn’t believe in astrology because Geminis don’t believe in astrology. I agree with this explanation because I know for a fact that there are people out there that won’t give a damn about something that is important until it affects them personally. For example (relating science with math), the earth formed, supposedly, several billion years ago. Why would the innumerate even care about this? He’s probably living in the moment – taking in all the technology and magic the world has to offer but he doesn’t realize that math and science are what got him the fun gizmos and gadgets he plays with. I agree that if this innumerate (and all of them that are like him) had applied math to something other than his own personal life, he would work better with numbers and instead of using him as an example of an innumerate right now, we’d use him as everything that an innumerate isn’t. Also, if he didn’t apply math only when it applied to him, he probably wouldn’t grow up to say, “I never really liked math,” or, “math was always my worst subject.”
Unfortunately for us, he grew up as an innumerate and therefore is subject to ridicule by people like us who are reading Innumeracy, a book that was made to poke fun at his disease and make us glad that we’re in the specialized high school for MATH, SCIENCE, and Engineering (which also includes a LOT of math).
Kelly Y.
John Allen Paulos discusses reasons why he thinks many people are innumerate. One of the reasons that John Allen Paulos mentions is that estimation is usually not taught. I agreed with him because we rarely see teacher asking us to estimate about things in real life. Like what Allen says about teacher rarely ask the students to estimate "the number of bricks in the side of a school wall, or how fast the class speedster runs, or the percentage of students with bald fathers, or the ratio of one;s head's circumference to one's height, or how many nickels are necessary to make a tower equal in height to the empire state building, or whether all those nickels would fit in their classroom." I was never asked to do any of these and even if try now, i would probably not be able to do so. It is hard for people to imagine things like a thousand of paperclips most likely because we never saw it before, so it is hard to picture it.
Aleksandar P.
John Allen Paulos (who only uses his middle name so people don't confuse him with the Pope) states reasons why he thinks that so many people are innumerate and possible ways of fixing them. One of the reasons that Paulo states is our teachers. He states that math teachers lack interest or are insuffienctly capable to teach properly. I disagree with this statement because teachers that may not be "capable" might just be new teachers who are inexperienced, or other situations may be that the teachers have too many students or the school does not have enough resources for the teachers to use, or worse, a combination of these circumstances. For the changes that Paulos is suggesting would require much more money then is given to schools currently.
A major problem in today’s society is the widespread innumeracy that seems to be hidden. John Allen Paulos describes the different forms of innumeracy in daily tasks, and he blames it on education. I agree with this because most schools do not teach their students to excel in math and be interested in it. Most students just think it’s another class, blow it off, and the teachers let them. However the students do not understand that it is part of everyone’s daily life. To be a cashier seems to be quite a simple task. All you really have to know is how to add and multiply to find the total sum and the added on tax. However even this task is not completed entirely by the daily worker. With the advancing technology computers are doing more and more of the work. It seems to make it “easier” for everyone by putting stickers with all the answers already there, however this shortcut is making the global population more innumerate then they already are.
-Monika C.
Bix K. W.
In chapter 4 of Innumeracy, John Allen Paulos points out how vastly widespread Innumeracy is and why this is so. One of the reasons for this, says Paulos, is the over-personalization of dangerous events. This has caused an innumerate paranoia to sweep our nation. Whenever there is a terrorist attack in the United States, which is unbelievably rare, the families of the dead are shown on national television sobbing and telling stories about their dead loved one. However the number killed in the U.S each year due to terrorist attacks pales in comparison to those killed from smoking. Despite these numbers, some people will stop taking airplanes and continue smoking and expect to be less likely to die.
Grissel G.
In Chapter 4 of Innumeracy, John Allen Paulos believes that innumeracy is caused by poor teaching habits in elementary schools. This hypothesis makes sense to me because that is where, in fact, the fundamentals of math are taught to you. I have noticed that everything I learn one year in the field of mathematics, I will apply to my studies the following year. It is very difficult to understand , say, exponents, if you do not fully understand multiplication. I vividly remember when my second grade class was learning long division which I could barely grasp. Simply subtracting the divisor from the dividend over and over again until I reached to zero came to more avail than to try and comprehend what my teacher was teaching. I said to myself, "If only she would stop giving steps, and explain why this works." The steps I could rememebr easily, but it always confused me as to whether I actually remembered them, because at the time, they made no sense. The first year I noticed that any teacher was teaching mathematicas alongside with reasoning was the eith grade. To explain what I mean by reasoning, let us continue with the example of long division. I now see that is works because it is the same as diving 100 by 6, then 90 by 6, then 2 by six, if the problem were 192/6. Just yesterday tasia, Victoria, and I were in Duane Reade and Tasia has a craving for lollipops. She had just bought one in the store for 15 cents and a bag with sixteen was $3.99. I quickly realized that this would be a waste of her money because 16 lollipops should cost $2.40, excluding tax. I did the math in my head quickly, with multiplication, the same way I would divide $2.40 by 16, by taking the number apart. I multiplied 16 by 1 then by .5, and added the sums together and knew the cost would be $2.40. I didn't think the cost would be $24, however, because estimation with reasoning was taught to me quite well.
Shomir U.
In chapter 4 one example of innumeracy given by John Allen Paulos is when he calculates the earned running average of a relief pitcher which is 135. His teacher tells him that this is wrong. The teacher asserts that ERA,s can never be higher then 27. He says the reason this happened is because early mathematics education is poor. The elementary do good jobs teaching how to do addition or subtraction but not so well on when to apply them.This causes many students to have not as great of a understanding on math when they get past elementary schools.
Tasia Hawkins
One of the reasons Paulos believes people are innumerate is because of a lack of eduction. I agree with this because if in elementary schools students are taught more about applying math to real life, it will make it easier for them to use math in every day life and make it easier for them to learn more difficult kinds of math like calculus
John-Corey M.
One if the reasons and personally the one that i feel is the major is just lack of math education. People are not taught math in some courties or like in sometimes in hour not taught it well. If people are not taught of course the they will be innumerate. Also teaching math poorly is even because if you teach it poorly esspecially in the easier math like algebra and arthemtic how can you expect someone to excell in geometry or calculus.
John-Corey M.
Another reason is Math is inpersonal. Math is Math, always has been always will be. There is nothing spiritual or to analzye about. Take for example 2+2=4 this will always be no matter what there is nothing to analyze, hmm... why does 2+2=4 because it does unlike history or language or science where you analyze documents and evidence, to come to a conclusion, then, you can analyze it in different way to get different conclusions. But seem inhuman in a way something aboslutly true like some of the example in this book that seem to be based on chance, the example in chapter 2 about the order of the choice for dates a girl would pick. I have an even better example, flip a coin 1000 times it can land on heads 1000 times or 999 and the propability of that coin fliping on heads or tails is 1/2. Mr.Innumerate says,"This mind boggling shouldn't be 500 heads, 500 tails." My answer odvisioulys not! learn your math the 1/2 refers only to each individual flip not as a whole.
Earl J. I agree with Paulos' idea that innumeracy derives from people not caring about math or its conventional uses. One of the age old-if less popular than it initially was-questions heard is "Why do I need to know math if I'm not going to use it." I think this question Illustrates how extreme this aspect of innumeracy is; people don't seem to realize that a majority of everyday life is related to math. Also, Paulos basically says that a cause of innumeracy was just the lack ability or background to comprehend numbers, however people with this problem seem to have more of a chance at becoming numerate because they would at least be more likely to put in the effort. People who just don't care, however just do a half-hearted attempt at math because they have to, and therefore will stay innumerate (perhaps willingly) longer than those who simply cannot understand numbers the way others can.
Sadichchha A.
John Paulos gives the reason for innumeracy that kids are not taught well to begin with. They are not taught to love and appreciate math and thats where innumeracy all begins. Also he shows math teachers as bad people for not teaching kids the right things. I completely disagree with this and i think that is not the problem. If you like math, youre gonna want to learn more about it and explore other things and if youre not into math or interested in other subjects, then youre simply going to do only the math you have to and not be as numerate as some other people may be. Being innumerate doesnt mean that you had a bad education as a kid or that the teachers arent doing a good job. It simply means that this particular person is not as amazed by math as others. I also think that what kids are taught today in school is perfect for their age because maybe their brain cannot handle more information than their being taught. You cannot overwhelm kids with exxess amount of knowledge.
One reason John Paulos gives for people's innumeracy is that people tend not to think things through fully and instead jump to conclusions. For instance, when given a scenario of 600 soldiers and two paths, one of which will leave 200 alive and the other will either leave all of them alive or none of them alive (the latter of which is more likely), people will choose the first path. However, when given the same soldiers and one path that will kill 400 soldiers and one path that will either kill all of them or none of them (the former of which is more likely), most people will choose the second path. Personally, since this proof was based on a real experiment, I would have had to agree with this theory – 20 years ago. However, this book was first published in 1989, and many things must have changed by now, so I would have to disagree. Furthermore, my math education has been top-rate, so it's impossible for me not to be prejudiced. Was I writing this blog comment 20 years ago, I would probably agree with John's theory, but today, I have to disagree.
-Louis L.
In this chapter John Allan Paulos gives alot of reason as to why so many people are innumerate these days. He gives lots of examples as to why this could be. One of his suggestions is that as growing children kids have poor math education and are not taught to love and cherish math. Also he says that math teachers are bad for not teaching the kids the right things. I completley dissagree with his theory. Being innumerate has to do completely with the selected individual. I have had an extremely good math education and I am far from good at math. Math clicks with some peoples brains and does not click with other peoples brains. There is nothing that a math teacher can do about this, and it isnt fair to blame them. Therefore I disagree with John Allan Paoulos's theory that innumeracy is cause from a bad or lack of math education.
Nina A.
Evan Y.
One of the reasons for innumeracy John Allen Paulos illustrates is the unwillingness to learn on the part of the student. Many students will not pay attention to a subject or subjects because they don't believe them to be useful or that they will ever use them again outside of the course. One of these subjects is math and because so many people don;t think math beyond arithmetic is useful they don't pay attention and get the wrong ideas about it, This causes them to become innumerate. I believe that John Allen Paulos is correct in this statement. I myself have experienced this with the grammar course. I didn't believe that I would ever need to know what an adjective phrase, or complex sentence was because I was using them correctly anyways without knowing what they are. However I am not able to see the future so maybe grammar could be useful for me then.
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