Fun with Numbers
In his important 1988 book, Cultural Literacy, E.D. Hirsch warned that “children in the U.S. are being deprived of the basic knowledge that would enable them to function in contemporary society.”
Two decades later, we see the tragic results of our near-total failure to heed Hirsch’s alarm. The basic information that most high school and college graduates don’t know continues to astound those of us of all ages who managed to receive a pretty decent, often non-public education. In the Intercollegiate Studies Institute’s 2008 test of civic literacy, gauging citizens’ “knowledge of America’s founding principles and texts, core history, and enduring institutions,” 71% failed. (The 33-question test is here. It isn’t that tough.)
That there has been a steep decline in basic math skills during the same time period is no secret to anyone who has taught classes to young adults and quietly gasped upon seeing many of them reach for their calculators so they could perform a division as easy as 72 by 9. Many of them literally cower in fear at the thought of completing a math “word problem.”
In 1989, the year after Hirsch’s book appeared, according to a November 14, 2006, New York Times article, the National Council of Teachers of Mathematics, the nation’s leading group of math teachers, introduced “standards” that “let children explore their own solutions to problems, write and draw pictures about math, and use tools like the calculator.” This move, properly derided as “fuzzy math,” contributed mightily to the nation’s basic skills decay. One parent quoted by the Times reported being told by a teacher that “we don’t teach long division; it stifles their creativity.”
Though it would be easy to exaggerate its significance, it seems that there has been a bit of a rebirth of interest in basic math. If so, it’s coming none too late, because nature abhors a vacuum. Those who wish to capitalize on a math-ignorant populace are only too eager to fill it. Many of the void-fillers work in government or for “advocacy groups.”
Applying basic math to recent news reports can unearth very useful information. Here, phrased as those dreaded “word problems,” are four such examples (numbers are rounded in some cases to make calculating the results easier).
Problem 1: Chrysler sold 79,000 vehicles in May during 26 selling days. During the month, before 800 dealers were terminated, it had 3,200 dealers. How many cars did the average Chrysler dealer sell per selling day in May?
Answer: Less than one (79,000 ÷ 26 ÷ 3,200 = 0.95).
Comments: That really makes you wonder what your billions of tax dollars are subsidizing, doesn’t it? Even with the dealer reductions, if overall sales volume stays the same, the average Chrysler dealer will be selling about 1.27 cars a day. Big whoop.
It gets worse when they start talking about energy. Before they even have an opportunity to screw up the arithmetic, the media, as often as not, confuse energy with power. They’ll say something like “the windmill produces 50 kW/HR”. If I threw something at the monitor every time they did that, I’d have a back yard stacked up 20′ high with broken monitors.
Then, a supposedly reputable magazine says something like a new nanotech device will produce 135 gallons/day of petroleum fuels by artificial photosynthesis from 4 SQ IN of solar area.
Something that breathtakingly implausible sails right past the editors because they have no sense of numbers at all. It’s all magic, and anything’s possible. Thermodynamics is so…20th century.
This is a much bigger and broader problem than even you indicate.
Strawman: Everyone who understands thermodynamics is a climate change and alternative energy sceptic. Which means that everyone in Washington does not understand thermodynamics. Stupid does as stupid is.
Innumeracy: Mathematical Illiteracy and Its Consequences by John Allen Paulos is a fantastic book on the subject
Mr. Blumer,
You find the a lack of basic knowledge merely astounding? Personally I find it appalling! I attribute the lack of math understanding to the use of calculators in our elementary schools. Kids are no longer taught their multiplication tables, only how to enter data into a machine. We tend to get our incoming seventh graders at my school no better than 15% proficient in math as measured by the SBA tests. The horror stories I could tell you would fill a book!
And did you know about half of the readers of this article are above average?
The Precedent showed that his own math skill don’t even rise to those of the average 8th grader when he ad-libbed about markets and spoke of “profit and earnings ratios”. In that one little, idiotic phrase, The Precedent showed that he:
1) Didn’t know what the “P” in P-E ratio stood for
2) Didn’t understand that “profits” and “earnings” are the same thing
and, most importantly, and most disturbingly,
3) Didn’t understand that factors in a ratio are never described with “and”, which is something that any 8th grader knows and that everyone who has ever tried mathematical word problems (as can be found on the SAT, for example) must be learned. This little phrase of The Precedent’s is pretty clear prof that the moron didn’t break 500 on the math section of his SATs (which we never see, undoubtedly).
And yet, such a mathematical ignormaus is lecturing the rest of us about finance and economics and global climate models … What sort of morons is this country filled with to accept such idiocy?
For those who don’t get the above, think of it this way; The Precedent’s idiotic phrase is exactly comparable to someone discussing speed limits as “65 minutes and hours”. Such a fool would be laughed out of any respectable company … but we have just such a person dictating policy to us and spending trillions of our money and our credit. Insane.
I believe this is an intentional feature of our government educational system. The ignorant are easily led victims who will believe anything.
How else does one explain Social Security and the Federal Budget Deficit?
By the spring of 1953, when I was in third grade, we had to memorize the multiplication table up to 12 x 12. Sister had a clock face chalked on the blackboard; she would write a number in the center, pick a victim — excuse me, pupil — and as fast as she pointed to the numbers on the circumference, the pupil would have to give the product of that number and the number in the center. And if you flunked 3rd grade arithmetic (or anything else), you didn’t go to fourth grade. That simple. On the other hand, there was one kid in fourth grade who wasn’t good at arithmetic, and couldn’t get division. Sister had him come in now and again over the summer, and worked with him so he could pass arithmetic and move on to fifth grade with the rest of the class. By eighth grade (1958), we had to know fractions, decimals, percentages, the fundamentals of algebra, plane and solid geometry (the volume of a sphere is 4/3 * pi * r^3), and how to extract square roots by hand.
And what did you expect? The whole system has always been run mostly by lawyers, people trained to listen to the numbers only when they speak in their favor, and if they don’t then to dismiss them or try to make it look like they are speaking in their favor. In general, the people that runs the government are not even trained to solve problems, but to live out of the problems. People that are trained to solve problems, and to understand the numbers, for the most part stay out of public service. So this is as much the fault of those in the government as it is of those who chose to stay out of the way.
Problem 1 is a good example of why people hate those word problems. The correct answer is .79 based on 31 days in May. The number of “selling days” is not relevant to the question asked. I guess you could get a pass for the “less than one” approximation.
#6–the word is “President”. Unless you are being sarcastic, and if so, I apologize.
The lack of basic grammar and spelling skills displayed by the American public are as appalling as the lack of math skills.
Actually, I seriously doubt that that’s true, but I’ll leave it as an exercise to explain why.
And yes, statistical illiteracy is yet another dimension to this. Even when Americans were good at math, that was a problem.
All sad but true. Without an adequate education you might think there are 57 states. You might think the Constitution should be changed to protect the rights of the federal government.
11. Shawna:
#6–the word is “President”. Unless you are being sarcastic, and if so, I apologize.
Shawna, he was elected for no other reason than to be a “precedent” – the first black President. This was obvious as none of his supporters could identify any reason to support him. As he has no other skills or talents, and actually lacks just about every imaginable one that would even qualify him to be a President, he is nothing other than what he was elected to be – The Precedent.
When you have educated idiots educating people to be idiots,they will vote for idiots.
Numeracy is the single most important characteristic I look for in politicians. The only two national figures that seem to be packing here are Mitt Romney and Bobby Jindal. They may not always make the right decisions (see Massachussets health care), but at least they will understand when they are making tremendous leaps. Tim Geithner hasn’t proved to be too sharp, Nancy Pelosi is anti-numerate, and Obama can’t even count to 50 – or should I say he overcounts to 57.
I was told there would be no math.
I have a newphew who passed high school calculus, but who couldn’t add/subtract fractions when I had him help me re-roof a house.
Go figure!
Math is the most overrated subject and the least valuable. The fixation on math since Sputnik has been the ruin of the US. Pay attention please:
The US was not founded by math majors. Henry Ford, Andrew Carnigie, Howard Hughes, John Paul Getty, Henry Kaiser, Bill Gates, and dozens of others I could mention were NOT nerdy little math whizzes. Invention and creativity and a devotion to quality manufacturing, good music and so on made the US strong.
Math majors make it weak: GM started its downhill slide under CPA’s with a cost saving mentality that is typical of math majors who are passionless penny pinchers. CPA’s nearly doomed Ford until they remembered they were in the car business. Slickster hedge fund managers with math on the brain have done more damage than ana rmy of poetry majors in charge of the Fed could have done.
The US is based on invention and creativity, not dull math majors. Math and an emphasis on statistics has done more to tilt business schools away from an emphasis on quality manufacturing than anything else: the idea that a business can be run by reviewing computer charts has doomed a lot of US businesses.
I’d take a smart english major or a history major with an appreciation of US history and an ability to inpsire workers over a dull math major any day. And I’d come out ahead too.
Until go to the store, and swipe your card, and they call the security guard.
Blackwell, I somewhat agree with you. Some kids just aren’t gifted at math. I homeschooled my 2 oldest daughters, who were artistically gifted. I used THEE best math program (Saxon) and they managed well until we hit quadratic equations. It was just too abstract for them.
For my son, aged 14 now, I used Singapore Math in grade school, which excelled at teaching mental math. I am blown away when he does long division and complicated fraction problems only in his head. He is obviously gifted at math.
He will start Saxon Algebra 1 this fall.
What makes Saxon so great?: The constant review and the built in drills. It builds to the hard stuff slower than public school math curriculum, but it does a better job of creating automatic mathematical thinking. So when the student starts Algebra, his brain is wired, so to speak, to excel.
Our neighbor’s son, who attends public school, tells me they never finish the math books, or other text books for that matter. I think public schools push students to do ever higher math before they have had time to really absorb it.
A CPA is not a math major. A CPA is an accounting major. While it’s true that accountants use math, they specialize in being bean counters.
Engineers use math to create things. Scientists use math. The Wright Brothers, while they never graduated high school, used a great deal of math to make their airplane. So did many of the early inventors like Bell and even Edison.
Basic math skills enhance understanding of current events. Too bad many of today’s high school — and college — graduates don’t have them.
Too true. Take Mark Sanford. I once heard him say that marriage is between one man and one woman.
Here’s what you get when you have people ignorant of math running the government and trying to run everything else. Reportedly from a senior person at Chrysler.
Monday morning I attended a breakfast meeting where the speaker and guest was David E. Cole, Chairman Center for Automotive Research (CAR and Professor at the University of Michigan. You have all likely heard CAR quoted, or referred to in the auto industry news lately. Mr. Cole, who is an engineer by training, told many stories of the difficulty of working with the folks that the Obama administration has sent to save the auto industry. There have been many meetings where a 30+ year experience automotive expert has to listen to a newcomer to the industry, someone with zero manufacturing experience, zero auto industry experience, zero business experience, zero finance experience, and zero engineering experience, tell them how to run their business.
Mr. Cole’s favorite story is as follows:
There was a team of Obama people speaking to Mr. Cole (Engineer, automotive experience 40+ years, and Chairman of CAR). They were explaining to Mr. Cole that the auto companies needed to make a car that was electric and/or run on liquid natural gas (LNG) with enough combined fuel to go 500 miles so we wouldn’t ‘need’ so many gas stations. (A whole other topic). They were quoting BTU’s of LNG and battery life that they had looked up on some internet website.
Mr. Cole explained that to do this you would need a trunk FULL of batteries and a LNG tank as big as a car to make that happen and that there were problems related to the laws of physics that prevented them from…
The Obama person interrupted and said (and I am quoting here) “These laws of physics? Who’s rules are those, we need to change that. (Some of the others wrote down the name of the laws so they could look it up later.) We have the Congress and the Administration. We can repeal that law, amend it, or use an executive order to get rid of that problem. That’s why we are here, to fix these sort of issues.”
24, I smell satire. Even the rather lame crop of trolls here wouldn’t be that brazenly stupid. Do you have a link?
It was sent to me via email. I know, it may well not be true. However, given the massive combination of arrogance and stupidity throughout the Obama Administration and the Democrats in Congress, I wouldn’t be at all surprised to find out it’s true.
SusanLC: And i agree with you too, that public schools do a miserable job at teaching math (I am example #1.) Perhaps if math was taught in an applied as opposed to a theoretical setting it might be better received and used. The idea that “you have to know” immense amounts of math before you can use it for anything other than balancing a checkbook is part of the problem. Most kids are not math prodigys, and for them, math in the abstract is stultifying.
Larry J: well put: I meant to say that the impetus for most great indutrialists was a dream, not math: math was a means to an end and its taught now as an end–”learn this and it might be useful one day.” Schools insist on “learning math” in an abstract way that accounts for the failing of students to master it. Most liberal arts kids want nothing to do with math. The Obama example you give is almost too good to be true (c’mon-they really said repeal the laws of physics?) The people who are pushing these deficits are even more ignorant of economics and history than of math. The math-oriented CPA’s–math based pople as opposed to me–are still a problem: they ought to be kept away from policy decisions and used as support: they should never be CEO’s.
Blackwell:
You have a very good point, but still math is definitely not overrated.
Mathematics is like any tool, it needs to be understood to be used effectively. Focusing in just numbers and formulas is like focusing on the speed meter without paying attention to the road ahead. That’s why they make us solve word problems in school, so that we learn to understand what the math means.
Those people you mentioned, math mayors or not, I’m sure they understood well the meaning of the numbers, their businesses depended on it. There are even more people, not so famous but as important, whose creativity was stimulated by their understanding of mathematics. Just look around you and you’ll find many devices (like your computer monitor) that couldn’t exist if the math wasn’t there.
The sad thing is that most critical decisions that ordinary citizens have to make require them to understand just addition, substraction, multiplication and division; and way too many people can’t even understand that. Just look at how many people, even educated people and especially in the governmet, make so many silly decisions based on flawed (or convenient) interpretation of the numbers.
Schools insist on “learning math” in an abstract way that accounts for the failing of students to master it.
Part of the problem (and I base this as a former teacher) is that most teachers lack the experience to relate math to the real world. They were students in school, then they were students in college, and now they’re teachers. My math teachers couldn’t explain how the concepts were used. It wasn’t until I studied to become an electronics technician that I learned to really apply math in a meaningful way.
Most liberal arts kids want nothing to do with math.
That’s why I consider many of them unemployable, at least for the kind of work I do (software engineer/enterprise architect). Math is far from overrated but like anything else, it can be abused. Ignorance of math and science is one of the factors that drives the Democrats running Congress to make such stupid policy decisions. Ignorance of economics and non-PC history are contributing factors as well.
The Stimulus raised the same questions
http://corner.nationalreview.com/post/?q=ZWMwMWI4YWUzYmU0MTYzNWE1ODNlNjU1ODk1NDI4OTc=
1) President-elect Obama claims that spending approximately $800 billion will create 3.675 million new jobs. That comes to $217,000 per job. This doesn’t sound like a very good value, especially with the national average salary around $40,000. Wouldn’t it be cheaper to just mail each of these workers a $40,000 check?
And we know how well the Stimulus has worked
http://michaelscomments.wordpress.com/2009/06/08/correction-to-the-may-unemployment-chart/
Seriously those 40k checks are looking pretty smart in retrospect.
So, is the mass media that weak on basic analysis that they can’t question the magnitudes of how much these policies really cost? Or are they being deliberately incurious?
Strawman, a little off topic. Last week I heard a professor of engineering at the University of Michigan say that the batteries she was working on would be make plug-in automobiles more efficient than their current internal combustion engine design. Um, in generalities: chemical->heat->kinetic->magnetic->electrical->~~~trasport~~~->chemical->electrical->magnetic->kinetic=8 gross energy conversions+leakage during transport, vs. chemical->kinetic (Ok, maybe, chemical->heat->kinetic). I may stop saying I studied engineering there…
Tom – I live in Los Angeles and not long ago, having some small talk with a young store clerk about something, he offered this: “[...] but people back east, like Oregon, you know [...]”
Math, geography, geometry, history…. man, that’s oppression!
Uh, Blackwell #19, while some of these men were self educated, Howard Hughes was an aeronautical engineer, Getty had a degree in economics, and Bill Gates was a computer science major before dropping out of Harvard to start Microsoft. So these three at least actually were “nerdy little math whizzes”.
#32, not surprised.
#19, Blackwell, the column is about the ability to do addition, subtraction, multiplication, and division, and the informative value inherent in being able to do it. We’re not talking calculus or physics here.
Dang I got 87.88 % on the test. That’s what I get for taking it while at work. :p
Honestly though it’s sad that the average is so bloody low! O.O!
My brother is a Math teacher and he (and my Uncle who’s a retired Math teacher go fig.) goes on and on about how inept and completely behind his students are at math. It’s hard to teach advanced techniques when you have to teach the basics that should have been learned in Elementary and Junior High school. Oi…
Our Govt is run by people so smart that 2+2=5
This is the basic problem in our govt today, we have individuals that dont understand basics, they try to justify solutions with nonsensical equations that belong in theory,not the real world. Then they wonder why the accounts never balance.
Investing is pretty straight forward; buy low sell high. But our securities houses hire mathematical that use advanced derivative based equations to explain why investing 1.00 today will be worth 1.50 next year ( or as happened, 0.50).
The next great shoe to drop will be the FED. When the Fed gets audited, the game is over. So far they have been able to keep their books and accounts secret and away from your government Officials. When the Day comes that the FED must finally reveal its accounting methods and where trillions of dollars actually went, that is the proverbial nail in the coffin.
Ben Bernanke;
“My concern about the legislation is that if the GAO is auditing not only the operational aspects of FED programs and the details of the programs but making judgments about our policy decisions would effectively be a takeover of policy by the Congress and a repudiation of the Federal Reserve would be highly destructive to the stability of the financial system, the Dollar and our national economic situation.”
And i agree with you too, that public schools do a miserable job at teaching math
Math requires proofs. We can’t have our kiddies taking that concept and applying it to the liberal agenda now, can we?
/sarc
12. Strawman:
Apparently, statistics aren’t your strong point; (Think about the statement:)
I’ll even go out on a limb and state that about half of the readers here are below average!
Cyber, you flunk. Your mistake is assuming that the distribution of any property among PJM commenters is the same as among the general population.
As I said, statistics is tricky even for people who can add.
31, OMG. That’s an engineering professor??? These are the wizards who are going to leapfrog the American auto industry ahead of the Japanese?
We’re cooked.
Key point (Larry J, #29):
Absolutely true. What we have is akin to drivers ed instructors who have never been behind the wheel of a car, but can tell you all about every little detail about every court decision regarding traffic law.
A related problem is the well established fact that teachers’ colleges are, as a group, not the hardest institutions around to get in to.
42. Strawman:
Is your real name Inestine? (sic)
According to your logic flight simulators are a failure.
31. What we have here is a slight of hand. True, batteries and electric motors can accomplish a nearly 100% of energy transformation from electricity to kinetic, but current batteries lose 90% of the energy that is used to charge them. Now, it may be that this design intends to cut those losses in half, which would make all the energy transactions CONNECTED TO THE CAR more efficient than an ICE. However, that does not take into account the thermodynamic energy losses AT THE POWER PLANT, which cost 60-70% of the energy from the fuel. Now, if the issue is eliminating fossil fuels, then that can be accomplished by switching to batteries, but only if we use nuclear power.
David 33:
Not exactly.
Hughes never graduated from college and dropped out of Rice when his dad died. His dad (a lawyer) founded Hughes Tool Co and patented the Hughes drilling bit that made Hughes a fortune when he was young. Hughes liked engineering and was a tinkerer in the best Henry Ford tradition.
Getty’s father, another lawyer, founded the Getty Oil Company: John Paul Getty studies government at Oxford, never got a degree and was going to enter government service when his dad induced him to become an oilman. He was another lifetime tinkerer, even devising granite shafts to clear drillig bits stuck in a shaft.
Neither were college grads. And while both were competent at basic math, neiher were math nerds; neither ever referred to calculus etc in their writings. Both were inspired inventors and dreamers, not students flogged with endless math courses.
My point is not to denigrate math for those that want it: it’s to lambaste the horrific way its taught and now forced on people with no aptitude for it or interest in it. In school today, Hughes or Getty might easily flunk calculus and be dropouts.
Sorry, gotta take issue with the author on his first problem and solution. Using pure math doesn’t give you all the answers, either, just clues.
Car dealerships are open every day, so the number of cars sold per dealership per day is .796. Wiping out 1/4 of the dealerships will not increase the sales per dealership, because the cars simply will not receive the same market penetration. Not only will the closed dealerships not be selling in their markets, but the lack of available dealerships makes the cars less valuable, as it becomes harder to have a warranty honored across the country.
If somehow, magically, they maintained the same amount of sales, then it would be a big whoop. With 1/4 of the dealerships eliminated, the car sales would go to the other three, resulting in a 1/3 increase in sales. 79,000/3200=24.679 cars/mo/dealership. 79,000/2400= 32.92 cars/mo/dealership. 32-24=8 8/24=1/3 At an average of, say, 2k/car (old data, may be more now), that’s an increase of $16k/mo. That is a very big whoop!
Never gonna happen, of course. Sales of Chryslers will only go down as the decrease in market penetration occurs. Further, the devaluation of the cars will decrease sales more. The idea of buying from a company flirting with bankruptcy makes the sales projections yet more problematic. In the car industry, much of the profit is actually made in service and warranties. Not gonna happen, now.
The correct answer, of course, was to declare bankruptcy in 2008, with a commitment to their dealerships and to servicing their warranties. This was the only way to ensure long-term profitability (read: survivability) The UAW would have been thrown under the bus by the bankruptcy judge. The wheels on the bus go bump-bump-bump!
With the UAW legacy costs reduced via abrogation by bankruptcy, as well as the cost reduction of the no-work jobs and the inflated pay structure, Chrysler would have become immediately profitable again. Everyone would have been better off, including the workers, excluding the UAW itself. With the current deal, everyone eventually loses.
“That there has been a steep decline in basic math skills during the same time period is no secret to anyone who has taught classes to young adults and quietly gasped upon seeing many of them reach for their calculators so they could perform a division as easy as 72 by 9. Many of them literally cower in fear at the thought of completing a math ‘word problem.’”
my kid’s school here in Illinois allows students to use calculators as early as the 3rd grade. I told my kids that I will not allow them to use a calculator until they reach high school. I was also stunned to see that the school teaches “estimation” in math instead of calculating for the correct answers. “estimation,” as my kids put it, is simpy guessing, now kids correlate guessing with math – in math, it’s ok to guess instead of working for the correct answer.
when the school districts starts allowing calculators instead of making teachers teach the math tables in their class then it is to be expected that students will not have math skills.
when the schools stop teaching phonics then it is to be expected that children will not have reading skills…and without reading skills, there goes the enthusiasm for reading.
the learning of basic knowledge includes the technical aspects of the subject being learned and in reading the technical system for it is phonics, in math, it’s the arithmetic tables. skip those two and children will never catch up with what they need to learn at every grade level the school bumps them up to.
I and my wife literally FORCED our kids to read by learning phonics. we go to the library every week and have them pick out up to five books that they would like to read. we force them to practice phonics, reading, and math tables during the summer vacation and it works wonders. those who think that memorization shouldn’t be a part of learning are totally mistaken. learning the basics starts with memorization – learning the alphabet is memorization, learning the phonetic sounds of the alphabet is memorization, and it’s the same with numbers and arithmetic. if memorization is taken out, you have kids with slow dull minds as a result.
I grew up in a different country where education (at least during that time) was taken seriously. where calculators are banned in primary education and only allowed in high school, where kids learn phonics (in both english and our native language) as early as kindergarten, and where school hours are much longer than what we have here in the US.
The education system in the US is a failure, sadly though, I doubt that the people as a whole has the will to fix what needs fixing. I often hear parents complain that their children have too many homeworks (my kids’ school only give maybe a half hour’s worth of homework and does not give homework during the weekends, compare that to my old school where we’re given multiple chapters and problems that would take a full day during the weekend to complete) and not enough playtime (good grief). I also hear parents complain that the school (my kids’ school) is mean since they make the children line up in front of the school doors so they can come into school in an orderly way (imagine that).
Parents and their complaints factor into the failure of the school system as well as the teachers’ union and the lack of government resolve to fix school funding, may it be lack of money or simply lack of insight on how to use funds properly – frankly, I don’t believe that all schools are underfunded, I believe that schools are inefficient.
I’m 110% behind improving the teaching of math in this country.
#10, added the word “selling” at the end of the question to be crystal clear.
Larry J has the correct approach on the math folks, my brother the millionaire bean counter is good at what he does, count beans, but he is also convinced that he can put anything in business in his graphs and modeling, he is confused, though it obviously paid well.
He is also a liberal and does not begin to grasp what drives a Conservative. He thinks that Bill O’Reilly is a Conservative. Oh well, we shall no longer prosper.
I don’t think that was the point. The point is that if you don’t have the math basics, you don’t have the wherewithal to resist any BS of any sort.
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