## Posts tagged ‘gender’

### Prime Number Problem and Gender Bias

This morning, my friend AJ called to ask for help in solving a problem from his ten-year-old daughter’s homework. When he explained his dilemma, the first thing I did, of course, was laugh. “Wow,” I said. “You really aren’t as smart as a fifth-grader, are you?”

AJ and his daughter are both intelligent, and his daughter loves math. The problem they were trying to solve was this:

What is the units digit of the product of the first 21 prime numbers?

You can use this list of prime numbers if you need some help. As a hint, the 21st prime number is 73 (which, incidentally, is the Chuck Norris of numbers).

Once you solve the problem, of course, you realize that the problem would have the same answer if asked as follows:

What is the units digit of the product of the first n prime numbers, for n > 3?

This made me think that this could be a good problem for the classroom. Have all students randomly generate a positive integer, and then have them solve the problem above using their random number to replace n. It would be impactful for students to see that everyone gets the same answer; and those who multiplied things out might be compelled to look for a pattern and figure out why everyone got the same answer.

But then I realized: this problem is gender biased. Well, maybe. The problem asks for the units digit of the product of the first 21 prime numbers. The choice of 21 was very deliberate, I’m sure. It’s small enough that an industrious student might actually try to calculate the product. In my experience, female students are more industrious than males and therefore more likely to do the computation. But the number is large enough that male students, who are lazy like I am, will think, “That’s too much work. There’s got to be a trick!”

I mentioned to AJ that if a larger number were chosen — for instance, if it involved the product of the first 1,000 prime numbers — then it might be more obvious that students ought to look for a pattern. “You haven’t met my daughter,” he said. “She’d still try to compute it.”

You may think my assertion is crazy. There is nothing in the problem that appears inherently biased against females.

A few years ago, the AAUW published a report about gender bias in math questions. One of the selected questions was something like, “What is the value of n if n + 2 = 7?” Despite the neutrality of the content, girls scored significantly lower than boys on this question, so it was deemed to be biased. (Sorry, I wasn’t able to find a reference to the report. If anyone knows the report to which I’m referring, please share in the comments.)

Further, FairTest claims that the gender gap all but disappears on all types of questions except multiple choice when other question types were examined on Advanced Placement tests. What is it about multiple choice questions that makes them implicitly unfair to females? I have no idea.

### The Gender Gap — Even in Online Dating

Women have it rough. The following is a typical — and valid — lament of most women:

I want to add to my income,
subtract from my weight,
divide and conquer,
and try like hell not to multiply.

As if it isn’t bad enough that the average female makes only 75.7% of her male counterpart (source). Now this.

According to OkTrends, the blog that provides dating research based on data from OkCupid.com, a profile about 130 words is fine for a man, but a woman will do better if she creates a profile that is closer to 800 words in length. And a woman should try to sound less intelligent — while there is no difference in the number of responses a man will get if his messages are written at a 4th-grade or 10th-grade level, the number of responses a woman gets will drop precipitously if her messages are written at a college level. What’s more, the analysts actually display the following advice for women:

If someone doesn’t think you’re hot, the next best thing for them to think is that you’re ugly.

The mathematics behind this statement is fascinating. The number of messages a woman receives can be estimated by the following formula:

M = 0.4m1 – .5m2 – .1m4 + .9m5 + k,

where M is the number of messages received, mn is the number of men who rated this woman n stars (on a scale of 1–5), and k is a constant.

Now take a look at that formula. The .9 coefficient for m5 implies that a woman will receive approximately one message for each five-star rating that she receives, but notice that the .4 coefficient for m1 implies that each one-star rating will also garner some messages. On the other hand, two- and four-star ratings actually decrease the number of messages she receives. (Since m3 is not included in the formula, three-star ratings apparently have little effect on the number of messages.)

Fascinating, no?

But a little game theory might help to explain this. Suppose you’re really diggin’ a woman’s profile, but most men give her a one-star rating. Well, that’s good news for you — it means less competition. On the other hand, a four-star rating may incorrectly imply that a woman is in high demand, so a typical guy — who thinks she’s cute (4 stars) but not hot (5 stars) — may not be willing to throw caution to the wind for a woman with whom he suspects he has little chance. (Sure, he may have even less chance with a five-star hottie, but it’s worth a try because she’s so hot!)

But, buck up, ladies. Despite all this depressing data, there is a silver lining: messages of just 50 words from a woman are most effective for soliciting a response from a guy, but a guy will have better luck with messages that are closer to 200 words in length. So, women may have to type more to create their profile, but at least they can type less when trying to make a connection.

All this objectication of women reminds me of a middle-aged mathematician I knew. When he walked into the house one afternoon, the following conversation occurred.

“I went to the doctor today, honey,” his wife said.

“Oh. How’d it go?” the mathematician asked.

“Well, he said that I have the spine of a 40-year-old,” she said.

“Oh,” he replied.

“And he said that I have the bones of a 30-year-old,” she continued.

“Hmm,” he replied again.

“And he said that I have the heart of a 20-year-old,” she said.

“Really?” asked the mathematician. He took all of this as unnecessary bragging, so finally he asked, “And did he say anything about your 55-year-old ass?”

“Actually, no,” she said. “Your name never came up.”

The Math Jokes 4 Mathy Folks blog is an online extension to the book Math Jokes 4 Mathy Folks. The blog contains jokes submitted by readers, new jokes discovered by the author, details about speaking appearances and workshops, and other random bits of information that might be interesting to the strange folks who like math jokes.

## MJ4MF (offline version)

Math Jokes 4 Mathy Folks is available from Amazon, Borders, Barnes & Noble, NCTM, Robert D. Reed Publishers, and other purveyors of exceptional literature.