Category: News Clips

Am I Going to Die This Year?

Here’s an unexpected application of exponential growth that I only learned about recently: the Gompertz Law of Human Mortality. It dictates that “your probability of dying in a given year doubles every eight years.”

Here’s the article that I read from NPR: http://www.npr.org/blogs/krulwich/2014/01/08/260463710/am-i-going-to-die-this-year-a-mathematical-puzzle?sc=tw&cc=share.

39 Ways to Love Math

From Math with Bad Drawings:

Last week, 6,000 mathematicians met in Baltimore. They crowded in conference rooms, swapped gossip over beers, and wherever free food appeared, they lined up like ants.

On a table in the hallway of the convention center, I stationed paper, markers, and the following invitation:

I got 39 replies, 39 tributes to math’s power—in short, 39 ways to love mathematics.

See the results here: http://mathwithbaddrawings.com/2014/01/22/39-ways-to-love-math/

From “Reshaping High Schools”

A colleague pointed out the following article to me: Put Understanding First, by Grant Wiggins and Jay McTighe. A sampling:

Unfortunately, the common methods of teaching and testing in high schools focus on acquisition at the expense of meaning and transfer. As a result, when confronted with unfamiliar questions or problems (even selected-response problems on standardized tests), many students flounder. Consider a high school algebra question that was included on state tests in New York and Massachusetts:

To get from his high school to his home, Jamal travels 5.0 miles east and then 4.0 miles north. When Sheila goes to her home from the same high school, she travels 8.0 miles east and 2.0 miles south. What is the measure of the shortest distance, to the nearest tenth of a mile, between Jamal’s home and Sheila’s home? (Students were provided with a grid they could use to plot the answer.)

Fewer than 40 percent of New York 10th graders correctly answered this item, despite the fact that the requisite knowledge is “covered” in every Algebra I class in North America. Test results such as these reveal not a failure of coverage but a failure of transfer.

Out-of-context learning of skills is arguably one of the greatest weaknesses of the secondary curriculum—the natural outgrowth of marching through the textbook instead of teaching with meaning and transfer in mind. Schools too often teach and test mathematics, writing, and world language skills in isolation rather than in the context of authentic demands requiring thoughtful application. If we don’t give students sufficient ongoing opportunities to puzzle over genuine problems, make meaning of their learning, and apply content in various contexts, then long-term retention and effective performance are unlikely, and high schools will have failed to achieve their purpose.

From high school math teacher to quarterback for the Dallas Cowboys

I’ve never been a fan of the Dallas Cowboys, but Jon Kitna remains one of the good guys of the NFL. After retirement, he went to work as a math teacher and football coach at his high school alma mater, getting students with learning disabilities to understand algebra (and thus be prepared for higher-level math classes in later years).

After the unfortunate injury to starting quarterback Tony Romo, the Dallas Cowboys called upon Kitna for emergency service. He plans to donate his one-game salary back to the high school.

Reference: http://bleacherreport.com/articles/1901693-jon-kitnas-salary-decision-proves-his-return-is-noble

The Monty Hall Problem

In 1990 and 1991, columnist Marilyn vos Savant (who once held the Guinness World Record for “Highest IQ”) set off a small firestorm when a reader posed the famous Monty Hall Problem to her:

Suppose you’re on a game show, and you’re given the choice of three doors. Behind one door is a car, behind the others, goats. You pick a door, say #1, and the host, who knows what’s behind the doors, opens another door, say #3, which has a goat. He says to you, “Do you want to pick door #2?” Is it to your advantage to switch your choice of doors?

She gave the correct answer: it’s in your advantage to switch. This launched an avalanche of mail (this was the early 90’s, when e-mail wasn’t as popular) complaining that she gave the incorrect answer. Perhaps not surprisingly, none of the complainers actually tried the experiment for themselves. She explained her reasoning — in two different columns — and then offered a challenge:

And as this problem is of such intense interest, I’m willing to put my thinking to the test with a nationwide experiment. This is a call to math classes all across the country. Set up a probability trial exactly as outlined below and send me a chart of all the games along with a cover letter repeating just how you did it so we can make sure the methods are consistent.

One student plays the contestant, and another, the host. Label three paper cups #1, #2, and #3. While the contestant looks away, the host randomly hides a penny under a cup by throwing a die until a 1, 2, or 3 comes up. Next, the contestant randomly points to a cup by throwing a die the same way. Then the host purposely lifts up a losing cup from the two unchosen. Lastly, the contestant “stays” and lifts up his original cup to see if it covers the penny. Play “not switching” two hundred times and keep track of how often the contestant wins.

Then test the other strategy. Play the game the same way until the last instruction, at which point the contestant instead “switches” and lifts up the cup not chosen by anyone to see if it covers the penny. Play “switching” two hundred times, also.

You can read the whole exchange here: http://marilynvossavant.com/game-show-problem/

For much more information — and plenty of ways (some good, some not-so-good) of explaining this very counterintuitive result, just search “Monty Hall Problem” on either Google or YouTube.

Source: http://www.xkcd.com/1282/

Complex knowledge

I took a statistics course at MIT. I would go study and do problems, and have high confidence that I understood the material. Then I’d go to the lecture, and be more confused than I was when I entered the classroom. Thus, I discovered that some teachers were capable of conveying negative knowledge, so that after listening to them, I knew less than I did before.

It was also clear that knowledge varies considerably in quantity among people, and this convinced me that real knowledge varies over a very wide range.

Then I encountered people who either did not know what they were talking about, or were clearly convinced of things that were wrong, and so I learned that there was imaginary knowledge.

Once I understood that there was both real and imaginary knowledge, I concluded that knowledge is truly complex.

– Hillel J. Chiel, Case Western Reserve University

Source: American Mathematical Monthly, Vol. 120, No. 10, p. 923 (December 2013)