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Tag: "math"

5

Ripped off because we don’t do well at math

I’m in the process of reading Stopped Getting Ripped off: Why Consumers Get Screwed, and How You Can Always Get a Fair Deal, by Bob Sullivan (2009). He starts off by asking you to pretend that you are in a restaurant and you are presented with a menu that he illustrates on page 5 of his book. You are asked to assume that you ordered the onion soup (the price is clearly listed on the menu as $.60) and the “Lancaster Special Sandwich” (the price is clearly listed on the menu for $1.95).

The question he asks is this: “How much should you leave for a 10% tip?

I’ll wait for a bit while you do your calculation in your head. No calculators, please.

What did you come up with?

[more . . . ]

The answer is 25.5 cents, so either 25 cents or 26 cents would be an acceptable answer.

What Sullivan next states is shocking:

If you answer this question correctly, consider yourself part of an elite group, because when the US Department of education asked US adults to answer it as part of a nationwide study, only 42% answered correctly. Less than half of American adults were able to pick two numbers from the list, add them, then perform the most basic of all percentage calculations–simply moving the decimal point one column to the left to calculate 10%.

Innumeracy is literally killing us. Try to think of a major issue facing our country that does not require a basic proficiency in mathematics that most of us don’t seem to have. Think of the environment, energy, national budget, climate, health care, evolution being taught in public schools, space exploration, public health issues (e.g., the importance of vaccinations), the true cost of the “war on drugs,” reform of financial institutions or taxation policy. Since most Americans cannot understand how to calculate a 10% tip, there is little chance that they could meaningfully participate regarding most of the big issues facing our country. These are truly painful words to write.

Just think of the many math-related claims that got math-ignorant voters excited during the last presidential election, including Sarah Palin’s claim that American could live long and prosperously on Alaskan oil (when straight-forward calculations based on known reserves showed that there is only enough Alaskan oil to supply America’s current rate of use for six months). Imagine how different things would be if most Americans could actually calculate the minimal chance that they would be affected by an act of terrorism, and if they were able to compare that risk to the immense numbers of lives that could be saved by much more modest expenditures. But it’s not even clear whether most Americans can benefit from further training regarding statistics. It’s certainly true that many health care professionals don’t adequately understand basic problems involving risk. The reasons so many of us are innumerate are not easily addressed. We desperately need proficient math skills to tamp down our fears.

I know it has been tried (and abused) before, but a sinister thought enters my mind. The information presented by Sullivan makes me wonder whether we should make voters take and pass a rudimentary math test before allowing them to vote. How indignant could a rejected voter be if he/she can’t figure out a ten percent tip? Understanding the many math-based claims asserted by candidates is sometimes the only way to see past their slick acting abilities.

I’m not seriously suggesting a poll quiz, though I’m sure that my frustration is showing through. What we really need to do is provide better math education all the way through school. It appears that we are paying dearly for the many grade schools that fail at math education, individually and as a country.

2

Quote time

I love to collect quotes. Such a high ratio of thought-provocation per word! I’d even bet that there is a the seed for a novel in most well-honed quotes. I collect these from many sources, though more than a few of the following were presented to me by The Quotations Page, which I use as my homepage. Some of these quotes have made the rounds (the oldies-but-goodies), though I’d bet that you’ll find more than a few that you’ve never seen before. Enjoy.

In mathematics you don’t understand things. You just get used to them.

Johann von Neumann (1903 - 1957)

Doing a thing well is often a waste of time.

Robert Byrne

It’s not the voting that’s democracy, it’s the counting.

Tom Stoppard (1937 - ), Jumpers (1972) act 1

The great thing about being the only species that makes a distinction between right and wrong is that we can make up the rules for ourselves as we go along.

Douglas Adams , Last Chance to See

“It is not acceptable to have a religion where the alternative to faith is punishment — that’s how you train dogs, not develop people.”

Deng Ming-Dao

When ideas fail, words come in very handy.

Johann Wolfgang von Goethe (1749 - 1832)

I was working on the proof of one of my poems all the morning, and took out a comma. In the afternoon I put it back again.

Oscar Wilde

A physicist is an atom’s way of knowing about atoms.

George Wald (1906 - )

Furious activity is no substitute for understanding.

H. H. Williams

15

Just run the Monty Hall experiment and get it over with

Monty Hall was the host of a TV game show called “Let’s Make a Deal.” I watched it when I was a boy and it was quite entertaining. One of the specific games on the show involved offering to allow a contestant to pick one out of three wrapped prizes. Some of the prizes were valuable, but one was often a worthless gag. After the contestant chose one gift, Monty invariably removed one of the two wrapped gifts that the contestant did not take. He then asked the contestant if he/she wanted to trade the box he/she originally chose in return for choosing the other remaining gift. Should the contestant stay put or should he/she switch? My gut feeling says that there is nothing to gain by switching, but there are many experts who disagree with me.

Frankly, I’m tired of hearing about the Monty Hall problem. Many mathematically-inclined experts insist that you should ALWAYS switch after Monte takes away one of the three hidden prizes. There’s all kinds of high end mathematics involved in many of these analysis (see here for instance).

The dispute gets really high-pitched sometimes, which is usually a clue that experts are claiming to be certain when they really don’t have any right to be.

What I’m wondering is this: why don’t some social scientists simply gather empirical data in a lab? Assign someone to be Monty and let college students play the roles of contestants. Set the experimental parameters precisely (this needs to be done carefully because there is some question as to what, exactly Monty knows and does) and run the test over and over, until you’ve got LOTS of data. Have some students always make the switch. Have others never make the switch. Then tally the results and tell the mathematicians that you have the real answer.

So that’s my thought: allow real-world trials tell the theoreticians the answer. Then let’s move on, please.

Or has someone actually run the Monty Hall skit over and over in a lab yet and added up the results? I haven’t seen it yet, if this has been done.

0
Gray Matter at Wolfram Research

Gray Matter at Wolfram Research

As I promised, I have visited the Periodic Table Table on the penultimate floor of the Wolfram Research building. This is a fairly tall building for Champaign, IL and contains some serious brains. We walked in, rode up to the top floor, and asked to see “The Elementary Mr. Gray.”

The receptionist chuckled, made sure that I claimed to have an appointment, and called down to the co-founder and interface designer for Mathematica Software, Theodore Gray. We were escorted down to his spacious office area, in which samples of every element in the universe are kept. Many on open display.

One Corner of the Office

Big SamplesI had budgeted 2 hours, and had to tear myself away after 3. There were huge samples of some things like 99.999999% pure silicon and a massive block of magnesium. There were pretty and ingenious samples of others. The pictures he took for PeriodicTable.com are excellent, but seeing them and holding them is an order of magnitude more impressive.

I got to hold a nice chunk of depleted Uranium (kept in the safe with the gold and platinum and antique samples). Heavy stuff, and almost as big as my sample of equally heavy tungsten. Maybe I should mention the layers of security and cameras, in case anyone gets acquisitive.

PeriodicTableTable and its creator

Notice the lead pipe over by Hydrogen? It was last seen on my patio, and now is part of this collection.

I hadn’t realized that this brain trust is where Hollywood went to get correct math for the TV show Numb3rs. Wolfram staff may not criticize the inaccurate applications, but at least they make sure the formulas written by the actors match what they say they are doing and look cool.

I often regret not having gotten a job at a brain trust back when I was young and quick. It was nice to visit such a place and to be made to feel a collegue.

So, how shall I spin this as a serious post? Real science is a matter of playing with reality and seeing what makes it tick. To understand matter, one should see what there is of it. To understand the mathematical models on which our standard of living depends, it is good to know some real math. I find comfort in knowning that those who really know the math have fun with it.

1

Attitudes toward gender affects math performance by girls

It is often observed that girls do not perform as well as boys in mathematics. This difference is often overstated and it’s cause is often highly debated.  Many people have suggested that the basis for this difference is essentially biological.
It is now well established that a society’s attitude toward gender will significantly affect the performance [...]