# Mathematical Illiteracy And Its Consequences Pdf

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Innumeracy: Mathematical Illiteracy and its Consequences is a book by mathematician John Allen Paulos about " innumeracy ," a term he embraced to describe the mathematical equivalent of illiteracy : incompetence with numbers rather than words.

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## Innumeracy : mathematical illiteracy and its consequences

Pick up the key ideas in the book with this quick summary. For most people, mathematics is a difficult and tedious subject and even a feared one. Mathematics is generally considered a challenging discipline which is why so many of us shy away from it. In our society, it is quite common for people to boast that they were always bad at maths. Consequently, it is safe to say that innumeracy has become a major issue.

From our summary, you will learn about the negative effects of innumeracy and why it has become a major risk for our society. You will also see how people who are not familiar with maths struggle with simple day-to-day situations and how understanding basic mathematical concepts can be extremely helpful. There are many negative consequences that being innumerate has, including not being able to make correct judgments and not having appropriate reactions in circumstances that involve probability and numbers.

Because they are incapable to determine whether the figures that are given in different contexts are small or big, innumerate people will often personalize. Thus, their own experiences will often prejudice their numerical intuition. For example, the odds of being eaten by a predator are quite low, although alligators do sometimes eat people. The most common reaction that an innumerate person will have when reading about such an event in the news will be to develop a crippling fear of alligators.

This fear stems from the fact that they will ignore the statistics that indicate how rare such alligator attacks are. Another disadvantage of being innumerate consists of not being able to grasp simple maths principles and their implications. According to this principle, we have m ways to make a choice and n distinctive ways to make a subsequent choice.

So, we have m x n combinations of choices. If a woman has three pairs of trousers and five shirts, she has fifteen 5 x 3 different outfit combinations.

This means that she actually has a whopping ,, different options! Is this a coincidence? But in order to discuss this concept, we need to define it first. A coincidence is an event that is extremely improbable but that happens very often. Coincidences are so common that people even expect them to happen. Coincidences have become such a well-established concept that they were even used in court. For example, in , a woman with blond hair and ponytail stole a purse in Los Angeles.

She then sped off with a bearded black man in a yellow car. Two suspects who fit this description perfectly were quickly apprehended and brought to the Supreme Court of California. Interestingly enough by using math, the court was able to make the argument that in a very large city like Los Angeles, there were many similar couples and all except one were innocent.

Lucki the court used math to argue that in a city as large as LA, it was probable that there were many such couples, most of whom were innocent. So, the suspects were allowed to walk free. The likelihood of coincidences can sometimes be explained by probability and statistics. But, because innumerate people will have a hard time understanding these concepts, they will confuse simple nuances and ignore the statistical evidence.

For example, they are often shocked by the fact that while some coincidences are extremely likely to happen, to them, it seems extremely unlikely that a specific coincidence will happen. If 23 people are attending a party, the chances that at least two of them have the same birthday is a good fifty percent. However, the chances that two people will share a birthday that has been specifically selected are slim.

In order for two people attending the party to be born on September 21st, the party should have at least guests for the chances to reach a level of fifty percent. Although absolute truths are the foundation of mathematics, its applications are not always one hundred percent correct. In fact, there are entire industries that misuse mathematics in order to build pseudosciences.

According to some of the basic concepts of astrology, each one of us is affected by the ways in which gravity pulled the planets when we were born.

Astrologists claim that our personalities, our everyday lives, our moods, and pretty much everything that happens to us can be explained through this pseudoscience. In other words, as the square distance between two bodies increases, the gravitational pull between them decreases. The doctors and the nurses who helped your mother bring you into the world have a much greater gravitational pull than some planets that are millions of miles away.

A Gallup poll revealed that more than fifty percent of young Americans believe in astrology, which indicates that this topic is extremely alluring.

Even Freud himself, who was a great psychoanalyst, fell into such a trap when his close friend Wilhelm Fliess managed to convince him of the special properties that the numbers 23 and 28 had. Fliess argued that these numbers were special because if you add and subtract their multiplies, you can obtain any number. The calculations that Fliess made were correct, but not because those numbers have anything special.

So you can replace 23 and 28 with 11 and 24 or with 2 and 3. Unfortunately, because math gives the impression of universal truth, it can be very easy for tricksters to use it in order to manipulate those who are not familiar with maths. So what are the leading causes of innumeracy? An important factor that leads to innumeracy is the way in which the subject of mathematics is thought in schools.

Although students become familiar with the basic principles of maths such as substracting and adding, they do not learn how these concepts can be applied in real life. For most students, this problem might feel completely irrelevant. But if they were asked to solve the following problem: Calculate the percentage of Indian global population if of the total world population, one quarter is Chinese and one-fifth of the remaining population is Indian. Much more students will get the answer to this question right than the answer to the equation.

It would be much easier for students to understand the importance of maths if maths teachers would use more examples like the one above. Understanding how maths can be applied is much more effective than mechanically learning abstract concepts.

A second issue that can lead to innumeracy consists of the psychological blocks that can be paralyzing for many people, especially for those who already think that they are bad at maths. This fear of mathematics is also known as math anxiety and it can be triggered when emotional scarring and intimidation is associated with the subject.

If a person has math anxiety, the first step towards becoming friends with maths is becoming more confident. Even if it seems silly, becoming friends with mathematics can be quite easy. Once your confidence has been boosted, the only thing that needs to be done is solving many simple problems. Slow but steady progress will surely follow. Innumeracy can also result from the misconceptions that are perpetrated by people who have a natural aversion towards it.

Saying that maths prevents us from being good at humanistic studies is like saying that eating salty foods prevents us from liking sweets. It is actually closely related to many different activities that people do in their daily lives.

Take the concept of trade-offs for example. When faced with making a decision, we often need to make a trade-off between two or more different concerns.

There are two types of statistical errors that need to be taken into account when we make a decision: type-1 and type-2 errors. The errors that happen when we reject a true hypothesis are type-1 errors. A good example of a type-1 error is not believing that smoking causes cancer. When we accept a false statement as being true, we are dealing with a type-2 error. Believing that the earth is flat is a great example of a type-2 error.

When people need to answer a question or to make a decision, they will have a unique understanding of what the error actually is. For instance, when it comes to capital punishment, people who have a more liberal approach would focus on avoiding type-2 errors because they want to avoid any unfair suffering. However, a conservative would probably gravitate towards avoiding the type-1 error because they want to make sure that the criminal gets what he deserves. Not only can math provide fascinating insights about our society, but it can also be used to make more informed decisions.

For instance, just a basic understanding of statistics and probability can prevent people from wasting their money on fake discounts. If you find a dress with a forty percent discount, and the store makes and additional forty percent discount, you might jump at the occasion to buy it, thinking you just scored an eighty percent discount.

In truth, you only got a sixty-four percent discount from the original price, as the item was already reduced by forty percent once, and an additional forty percent is equal to just twenty-four off the original price. The key message of the book is that having a good understanding of mathematics can improve our everyday lives.

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Summary: Why do even well-educated people understand so little about mathematics? And what are the costs of our innumeracy? John Allen Paulos, in his celebrated bestseller first published in , argues that our inability to deal rationally with very large numbers and the probabilities associated with them results in misinformed governmental policies, confused personal decisions, and an increased susceptibility to pseudoscience of all kinds. Innumeracy lets us know what we're missing, and how we can do something about it. Sprinkling his discussion of numbers and probabilities with quirky stories and anecdotes, Paulos ranges freely over many aspects of modern life, from contested elections to sports stats, from stock scams and newspaper psychics to diet and medical claims, sex discrimination, insurance, lotteries, and drug testing. Readers of Innumeracy will be rewarded with scores of astonishing facts, a fistful of powerful ideas, and, most important, a clearer, more quantitative way of looking at their world. With the emphasis on laboratory use, these volumes represent a comprehensive and practical guide to modern synthetic organic chemistry.

Semantic Scholar extracted view of "Innumeracy: Mathematical Illiteracy and its Consequences." by Lisa J. Evered et al.

## Innumeracy Summary and Review

Pick up the key ideas in the book with this quick summary. For most people, mathematics is a difficult and tedious subject and even a feared one. Mathematics is generally considered a challenging discipline which is why so many of us shy away from it. In our society, it is quite common for people to boast that they were always bad at maths. Consequently, it is safe to say that innumeracy has become a major issue.

Беккер попробовал его обойти, но парень ему не позволил. - Я сказал тебе - подними. Одуревшие от наркотиков панки за соседними столиками начали поворачивать головы в их сторону, привлеченные перепалкой. - Не советую тебе так себя вести, парень, - тихо сказал Беккер. - Я тебя предупредил! - кипятился панк.

Беккер покачал головой. Панк пристально смотрел на. - Вы похожи на полицейского.

- Это уму непостижимо. - Я видел алгоритм. Уверяю вас, он стоит этих денег. Тут все без обмана. Он стоит десять раз по двадцать миллионов.

Это шантаж. Больше всего похоже на требование выкупа. Слова Сьюзан прозвучали слабым, едва уловимым шепотом: - Это… Энсей Танкадо.

Сьюзан не любила бывать в шифровалке в неурочные часы, поскольку в таких случаях неизменно чувствовала себя запертой в клетке с гигантским зверем из научно-фантастического романа. Она ускорила шаги, чтобы побыстрее оказаться в кабинете шефа. К рабочему кабинету Стратмора, именуемому аквариумом из-за стеклянных стен, вела узкая лестница, поднимавшаяся по задней стене шифровалки. Взбираясь по решетчатым ступенькам, Сьюзан смотрела на массивную дубовую дверь кабинета, украшенную эмблемой АНБ, на которой был изображен могучий орел, терзающий когтями старинную отмычку.

Люди на подиуме не отрываясь смотрели на экран. Агент Смит начал доклад. - По вашему приказу, директор, - говорил он, - мы провели в Севилье два дня, выслеживая мистера Энсея Танкадо. - Расскажите, как он погиб, - нетерпеливо сказал Фонтейн. Смит сообщил: - Мы вели наблюдение из мини-автобуса с расстояния метров в пятьдесят.

По профессиональной привычке поправив съехавший набок узел галстука, он повернулся к писсуару. Он подумал, дома ли Сьюзан. Куда она могла уйти.

Хейл пожал плечами и направился к буфету. Буфет всегда был его первой остановкой. Попутно он бросил жадный взгляд на ноги Сьюзан, которые та вытянула под рабочим столом, и тяжело вздохнул. Сьюзан, не поднимая глаз, поджала ноги и продолжала следить за монитором. Хейл хмыкнул.

Estas ya muerto, - тихо прошептал он, двигаясь по центральному проходу.