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What the Numbers Say: A Field Guide to Mastering Our Numerical World

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This book offers examples of quantitative reasoning, including the topics of compound growth and statistics. Their perspective is that without the ability to work with numbers, people can easily be misled. One of the examples is a statistic used by defense attorney Alan Dershowitz to mislead the jurors in the infamous Simpson trial.

As I was reading the book, I wondered who the audience ought to be. Although the tone is breezy and the examples are presented without the use of algebra or higher mathematics, I am not sure how a math-phobic person would react. My experience with math phobes is that they would feel threatened by the book and be resistant to picking it up.

A better audience for the book might be math educators. As a teacher, I found numerous examples in the book that will be helpful. Moreover, the last chapter, in which they discuss ways to reform math education, is a gem.

What the authors are saying is that people need good basic intuition about numbers in order to understand a world that is increasingly dominated by numerical data. The traditional math curriculum tries to prepare a student to study Newtonian physics. Instead, I think that the authors would argue that the curriculum ought to be aimed at enabling a student to understand stock market ratios and statistical research.

One random note is that the authors attribute the phrase "independence from irrelevant alternatives" to John Nash. I may be wrong, but I believe that it was Kenneth Arrow who brought that concept to the fore.

By filling the book with interesting examples that illustrate the type of quantitative reasoning that they consider important, the authors make a compelling case for the math education reform that they advocate. However, if their primary audience is math educators, that fact is obscured on the book jacket, which makes the intended audience unclear.

Authors Niederman and Boyum articulate that we live today in a new Quantitative Information Age. Strange then, that they did not entitle their book, "Ten Habits of Highly Effective Quantitative Thinkers" (actually the title of Chapter Two) - this book would have sold twice as much.

Ahh! Twice as much as what? As Stephen Covey's books? As much as this book's actual sales? What's the base? Now that I've read this "Field Guide to Mastering Our Numerical World" (actually the subtitle,) I am trained to ask the pertinent questions about numerical comparisons. I have learned to simultaneously "only trust the numbers" and to "never trust the numbers" - habits #1 and #2.

In this entertaining tour of today's quantitative landscape, the authors expose our collective inability to cope with numerical reasoning. From humorous pot shots at "our favorite punching bag, the International Skating Union," whose farcical scoring systems are easily exposed, to a better method of comparing safety between small plane flying and automobile safety, to famous courtroom misuses of statistical data, Niederman and Boyum demonstrate a growing gap between our increasingly data dependent decisions and our nation's declining numerical literacy.

"What The Numbers Say" provides a layman's look at mathematical skills required by everyone. It is a book for non-mathematicians, liberal arts students, teachers of all subjects, political and educational leaders, and above all, parents. To anyone struggling with children struggling to master the multiplication table, and wondering what became of the rote memorization and textbooks from earlier days, the authors make sense of the new teaching techniques. Traditionally, it seems, mathematicians have been Euclideans, "deriving truths, in step-by-step fashion, from first principles or axioms." But, "good quantitative thinkers are Babylonians. They understand that quantities can be measured and expressed in many different ways, and that looking at something from multiple viewpoints enhances perspective and fosters creative thinking." Finally, we understand why our kids can't complete the 9-times Table, but are whizzes at stacking Lego blocks.

Niederman and Boyum embellish their hypotheses deriving wonderful examples of easy-to-comprehend quantitative situations involving baseball, weather forecasting, popular movies, roulette odds, consumer tips, home finance and stock market analysis, timed swimming contests, fair games, and more. Readers cannot fail to understand how simple some of the recipes (Pareto's Law, The Rule of 72, how to interpret Zagat's Restaurant Guides) are for understanding quantitative measurement. Mathematics, long misunderstood as "uncool" for its complicated formulae and notation, in fact, is often a beautiful and handy tool with which to find "the easy way out."

Though the authors uncover highly political ramifications of misunderstood data and twisted statistics (e.g., environmental debates), the book is apolitical save for the last chapter that cries out for educational reforms. Niederman and Boyum sum the book up neatly with suggestions for educators regarding curricula, calculators, and competitiveness. They propose ending the "math wars between Progressives and Traditionalists," and put forth solutions. The authors' main salvo: differentiate between mathematics and quantitative reasoning, and offer training on a separate track for each.

Put this on your 'to-read' list for the coming year. If only to find out how many combinations a 2 X 3 Lego brick can form.

Premised on the idea that we now live in a "quantitative information age", in which a person can hardly get through a day without reaching some conclusion based on numerical data, but that most people are poor quantitative thinkers who routinely make poor decisions because they are unskilled in analyzing numerical data, authors Derrick Niederman and David Boyum offer us "What the Numbers Say", a guide to spotting the most common kinds of data manipulation and determining what those numbers really mean. I should say that you do not need to know any mathematics beyond a 6th grade level to understand this book or to successfully decipher the numerical data that one encounters in everyday life. "What the Numbers Say" is engaging, clear, and easy to read. There are interesting examples taken from the stock market, business world, and current events for every subject that is discussed. And the examples don't have a pervasive political bias.

"What the Numbers Say" starts off by explaining "The Ten Habits of Highly Effective Quantitative Thinkers" and then dedicates each of six chapters to a different type or facet of quantitative data. "For Good Measure" explains the importance of understanding what unit your numbers are expressing, the problems inherent in distilling an assortment of data into a single number -such as an index, and troubles with rounding numbers. "Playing the Percentages" explores the traps of adding fractions, dealing with negative returns, percentages of percents, and ordinals, i.e. rankings. "Gaining Perspective" talks about very big numbers, very small numbers, and very sensitive numbers -especially denominators. "Throwing a Curve" is about non-linear relationships, including quadratic relationships and exponential relationships (growth and depreciation). "Taking Chances" discusses the three schools of probability: classical, frequentist, subjectivist and various methods of expressing probability. "The Proof is in the Numbers" is a chapter about Statistics that addresses the confusion of correlation and cause, sample sizes, data mining, and surveys. In "A Peace Offering for the Math Wars", the authors offer a critique of the current mathematics curricula and the lack of quantitative thinking instruction in U.S. schools, including their suggestions for remedying some of the problems.

In the book's last chapter, the authors get up on their soapbox about mathematical and quantitative education in American schools, so I trust they won't mind if I get up on mine. I wholeheartedly agree with most of what they say, but I find the authors' reaction to American students' performance in the Trends in International Mathematics and Science Study puzzling. U.S. students are always "smack in the middle of the pack" in those studies, which leads Mr. Niederman and Mr. Boyum to conclude that American students are bad at math and that American schools are bad at teaching it. I don't know why anyone gets bent out of shape about the TIMSS results. Americans do better than average. There are always some anglophone nations that do worse and some that do better. I think the results for American students are rather good considering that we have a significant population of non-native-English speakers in our schools and a very heterogeneous population -culturally, ethnically, and geographically- in general. In any case, the authors acknowledge that "mathematical knowledge and quantitative reasoning are quite different things". So why the fuss?

Speaking on another subject, the authors lament the elementary school mathematics curricula, which is full of useless stuff. That's a hopeless cause, because it doesn't take 6 years to cover basic mathematics. So most of elementary school education is filler and repetition -in all subjects. Junior high school and high school mathematics could be improved though. Not really, but at least in theory. There is nothing in a "pre-algebra" class that anyone needs to do algebra; there's nothing in a "pre-calculus" class that anyone needs to do calculus; and there's nothing in a geometry class that couldn't be memorized in 10 minutes. Ditching those courses would allow school systems to require that all students take a quantitative reasoning course and one year of calculus without placing any more burden on students or budgets. In the meantime, why not design a quantitative reasoning curriculum that could be made available to high school students taking internet or correspondence courses and publishers of homeschooling materials? As for all those students who reach for a calculator when their brain would do just fine... I recommend Isaac Asimov's short story "The Feeling of Power".

In a way, I feel very frustrated with this wonderful book, it remainded me when my father recommended me the 7 Habits of Covey and told me " Its sad I found this at 60 and not a your age"... well, its sad to be 42, a mechanical engineer and someone who studies math as a hobby to suddenly realize that I have been using numbers without a guide to their context..

All I can say that this should be required education material at all levels of schooling..

For some reason I purchased this book, started reading it, and got side tracked for about a year. At the time that I put it aside I guess it hadden't made a big impact on me to the point that when I picked it up again last week I wasn;t expecting much. How worng i was, I now have to go back and re-read the beginning. Chapters 4 through 8 are some of the best writings I have read on numerical thinking, probability and staistics in a long time. The last chapter is outside of my area of expertise, but i resonate with a lot of what the authors are talking about. innumeracy is rampent.

This book, by a friend and former colleague, is a wonderful introduction to the ways that numbers are used, and misused, in our work and everyday lives.

If you are uneasy with quantitative reasoning, you will never read the business page, or your medical chart in quite the same way after reading this book. If you fancy yourself more sophisticated, you will still learn a lot, and you will swoon with joy at the emphatic debunking of much humbug: predictable flaws of Olympic judging, hidden messages in the Bible, and so on. the chapter on measures is my favorite. I never understood the difference between an acre and a hectare.

I have assigned Chapters 2 and 3 to my masters' level students in policy analysis. I think this is a nice addition to the bookshelf of any manager, investment manager, or reader of the sports page.

Various topics are discussed, such as percentages, units and measurements, probability, statistics, etc., with a strong emphasis on rounding numbers to perform quick calculations in one's head in order to get ball park estimates of the desired results. It is also emphasized that producing results to n decimal places is rarely necessary in day to day calculating. Although this book is clear and well-written, it may, nevertheless, instill fear into the minds of those people who are uncomfortable with numbers. I therefore agree with a prior reviewer that the book may be aimed at the educators; the book's last chapter would seem to support this.

This is an outstanding book, describing in detail, yet in layman's terms, many of the problems regarding the public's understanding of mathematics. Mathematical reality is what it is; hunches and intuition are just that, sometimes true, which is what is fondly and emphatically remembered, but most often false and conveniently forgotten. The authors discuss topics such as:

*) What mathematics should be taught in the public schools.
*) How mathematics should be taught in the public schools.
*) The reality of regression to the mean and how short-term high achievement is natural.
*) The myth of being in a hot streak.
*) Why the average can be open to more than one interpretation.
*) Pareto's law.
*) How much conditional probability can change the odds.

All are presented in language and terms that anyone can understand.
The most interesting point they made is that most of the quantitative skills needed in life are taught before one exits the sixth grade. While skills such as trigonometry and logarithms are widely used, the majority of people will survive just fine without them. Therefore, the key to making sure that the greatest good is done for the greatest number is to make sure subsequent math education does not reduce those critical quantitative skills.
There have been many popular books written in the last few decades lamenting the lack of number skills in the American populace. This book is one of the best, not only does it point out the problems, it also is written at a level where those with the problems can understand it. And that is no easy task.

"What the Numbers Say" offers readers an engaging overview of the importance of mathematics and numerical literacy in today's increasingly complex and technologically advanced world.

Utilizing a light and readable style, Niederman and Boyum make a convincing case for the need for more mathematical skills and knowledge for everyone. The mathematics covered in this book are not advanced but are important.

The book is subtitled "A Field Guide to Mastering our Numerical World"...it fits that bill and is well worth a read. Quantitative reasoning is highlighted as an important skill in today's world and, if nothing else, this publication provides a good basis for stimulating readers to hone their mathematical and quantitative reasoning skill sets.

This book, co-written by a friend and former colleague, is a surprisingly fun read.

For all the wisecracks about Olympic judging and the Lakers, this book presents a sophisticated roadmap to the use and misuse of numbers in work and everyday life. You won't listen to the business report--or your doctor's advice--in quite the same way after a careful read. If you are already numerate, you will laugh at the careful but emphatic debunking of frustrating humbug that goes uncorrected on the local news, the sports report, and more serious venues.

I especially like Chapter 2, "The 10 habits of highly effective quantitative thinkers." Investors who read their chapter "For good measure," might still have gotten ripped off in the Enron scandal. At least they would have understood what happened. I will use both chapters in my Masters'-level courses in policy analysis.

All in all, this is a valuable addition to the bookshelf of any policy analyst or private-sector consultant.