Saturday, March 31, 2012

Say What?

In a story on the giant Mega Millions lottery this weekend:
Accountant Ray Lousteau, who bought 55 Mega Millions tickets Friday in New Orleans, knows buying that many tickets doesn't mathematically increase his odds, and that his $55 could have gone elsewhere. He spent it anyway.

"Mathematically, it doesn't make a difference, and intellectually we know that. But for some reason buying more tickets makes you feel more lucky," Lousteau said. "Even people who know better are apt to feel that way."

Um... having more tickets in a lottery doesn't increase your chance of winning? How the hell does that work? And how did this get by both an accountant and the journalist writing the story?

Friday, March 9, 2012

Google Divide by Zero

You know that Google automatically acts as a calculator, right? Type in any kind of math expression, and it automatically simplifies it in response -- including unit conversions of all sorts (very useful for that latter part, in my experience).

But here's something I discovered the other day: The calculator won't respond at all to any kind of division by zero. It won't say there's an error; it won't say it's undefined or not-a-number (NAN); it just won't trigger the calculator facility at all. It goes straight to a regular web search like it wasn't math at all. (I realized this after my first basic math class; carefully defined division and considered divide-by-zero, compared to a calculator error response, and then I asserted the same would happen in Google. Turns out that's not quite correct.)

This is true even if you try to hide the division-by-zero in some kind of very complicated expression (that's otherwise obviously math). Consider these:

And then contrast with the following:

I'm not sure if this is an oversight, or some tremendously subtle winking in-joke by our friends from Menlo Park. (Like: The calculator has to get triggered, do quite a bit of work before determing there's a divide-by-zero, and then decide to run away and hide itself from appearing.) Can you make Google Calculator admit to a divide-by-zero in any way?

Wednesday, March 7, 2012

Going Commando

Yay, got my Commando-brand chalk holder with anodized aluminum barrel/handle in the mail. Hopefully this keeps me from shattering the chalk in my clenched fist every day from my math rage-outs. If this doesn't work, then I'll need to step up to some kind of military-grade titanium or somesuch...

Monday, March 5, 2012

Times Tables

So first the first time this semester, the community college where I work gave me a class in remedial prealgebra (fundamental operations on integers, fractions, decimals, percent, etc.) to teach. Thinking that the class would be largely review, and not knowing where a good starting point would be (you can't always tell if a textbook starting location is good or not for the students in your program), I decided on the first day of class to give a sample pretest of 20 questions to see what stuff was generally easy for the class, and what stuff hard. That turned out to be an excellent idea, and I got some good data I can use to structure the class going forward.

Here's one thing I noticed as the class took the pretest: At least one girl was doing counting on her fingers: like a lot of it, and pretty rapidly, too. So I started wondering about that, because while they were certainly add/subtract problems, that was maybe less than half the test, and I was a bit puzzled at what she could be doing with all that counting.

So later, I asked a more senior adjunct lecturer about it, and here was his claim: A lot of schools now don't bother to teach "times tables" anymore. I guess this would be in the context of the corrosive "concepts vs. operations" argument in basic arithmetic: someone decided that it's most important to know that multiplication is the same as repeated addition, and so the only way students from a program like that know how to simplify 7×3 is to perform 7+7+7 (or worse, 3+3+3+3+3+3+3). And I suppose that would also be consistent with only understanding addition as repeated counting (i.e., perhaps not even memorizing addition tables). So possibly that would explain in this case why so much finger-based adding/counting was going on.

True or False?