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Let’s Make a Deal with Paul the Octopus

As summer reaches its midpoint, we come to the end of another rousing year of World Cup soccer. As with any international sporting event, fans all over the world have undoubtedly had their share of ups and downs. Of all the countries in this year’s tournament, however, I think Germany may be receiving the most attention, for even though they didn’t make it into the finals, the Germans have one thing no other country has: a precognitive octopus.

At least, that is what the media would have us believe. For the past several weeks, Paul the Octopus has captured the hearts, minds, and stomachs of people around the world. He’s a charming octopus, to be sure, but it isn’t his good looks that have gotten him this far. Instead, it’s his seeming ability to correctly predict the outcome of soccer matches. As time has gone on and Paul’s predictions have . . . → Read More: Let’s Make a Deal with Paul the Octopus

A New Birthday Problem

Last week, Slashdot posted an interesting link to a problem posed at the most recent Gathering 4 Gardner, a mathematical (or perhaps I should say mathemagical) convention created in honor of the late Martin Gardner. The question, posed by Gary Foshee, is as follows: you have a friend with two children, one of whom is a boy born on a Tuesday. What is the probability that the other child is a boy?

Forget about the Tuesday fact for a moment – if you have a friend with two children, one of whom is a boy, what is the probability that the other child is a boy? You might expect that the answer should be 50%, since the sex of one child shouldn’t affect the sex of the other. But this is not quite right, because you’re not told whether the boy is the older or younger child.

There are only . . . → Read More: A New Birthday Problem

Martin Gardner and the Three Way Duel

As you may have heard, last week Martin Gardner celebrated his 95th birthday. Gardner, who authored the “Mathematical Games” column in Scientific American for a quarter of a century, is often credited for introducing generations of young students to the beauty and charm inherent in mathematics. My favorite quote in this vein comes from professor Ron Graham, who is quoted in a recent New York Times article on Gardner as saying that “Martin has turned thousands of children into mathematicians, and thousands of mathematicians into children.” A warm brain is the key to mathematical dexterity.

Both Scientific American and Wired ran articles on Gardner last week, and each one used a different expression to represent his age. Scientific American congratulated him on reaching an age of 25 x 3 – 1, while Wired proclaimed that Gardner had turned 5! – 25. Upon reflection I think I prefer the latter expression . . . → Read More: Martin Gardner and the Three Way Duel

Restructuring the Math Pyramid?

A friend recently shared with me the following video from TED (see below). In it, mathematician (or, in this case, mathemagician) Arthur Benjamin gives a brief argument for eliminating calculus as the top of the “mathematical pyramid” in high school education, and replacing it probability and statistics. The main reason for this shift is that unless you are planning to have a career in a technical field, it’s unlikely you’ll find a use for calculus in your everyday life, but an understanding of statistics can benefit you no matter what you do. For example, it can help you to build an intuition about day to day decision making when risk and uncertainty are involved. Here’s the video (it’s short, only a couple of minutes):

A noble goal, to be sure, and it’s certainly a solution that wouldn’t cost a whole lot. There is an argument to be made for such . . . → Read More: Restructuring the Math Pyramid?

Math Gets Around: On Birthdays and Trading Cards

Today marks the 1 year anniversary of Math Goes Pop! I started on somewhat of a whim after reading an article about compulsory Algebra I education for all California 8th graders (although what with our finances down the toilet, who knows what the current status is here). When I started writing I wasn’t sure there was enough content out there to sustain a blog with this one’s focus. Once I started digging, though, I found that the rabbit hole went quite deep, and so here I am a year later with plenty left to talk about (the recent obsession with pointless math holidays certainly has helped with my output). Given the date, it seems fitting to begin by mentioning the birthday problem. This is a standard problem given in any introductory probability course, but many people find the result counter intuitive at first.

The birthday problem asks a simple question: . . . → Read More: Math Gets Around: On Birthdays and Trading Cards

How Low Can We Go?

I’m not sure, but this seems like a good candidate for a new bar. According to a recent study out of the University of Washington, as many as half of the population may fail to understand simple probability statements, in the context of weather forecasts.

Here’s the summary:

If, for example, a forecast calls for a 20 percent chance of rain, many people think it means that it will rain over 20 percent of the area covered by the forecast. Others think it will rain for 20 percent of the time, said Susan Joslyn, a cognitive psychologist at the University of Washington who conducted the study.

Coming out of Washington, one would think that the participants would have a better than average understanding of rain forecasts, but now I certainly hope that’s not the case.

That’s American math education for you. Maybe everyone should just move to LA – . . . → Read More: How Low Can We Go?