Fifty Percent

Last night I did play mah jongg--there was a group of four of us only, which is good because you play the whole night, but it is also bad because the four in question, Mary, Janine, Trisha, and I, were all totally fried from our week and therefore we had more wall games (nobody wins) than anything else. But it was a nice break from baby and family and house. Yes.

I got there first, and Trisha was busy making chocolate chip cookies. Except she was using a different kind of oil and a different kind of flour. She was worried that they wouldn't bake up right, and we debated what temperature and time changes she might need to make. She lowered the temperature and decided to increase the time--but by how much?

"Should I go up to 12 minutes?" she asked. "The recipe calls for 8, but the last time I made them, it went longer than that--"

"But that's an increase of 50%," her husband pointed out.

"No it's not," she corrected. "It's not 6 minutes going up to 12, it's 8 going up to 12."

I did the math in my head. "Actually, he's right," I told her.

"Whatever," was her casual response.

It got me thinking about that phrase: fifty percent increase. It doesn't mean "double" but rather "half again," or, algebraically, 1.5x. In Trisha's cookie case, 1.5(8) = 12. But Trisha isn't the only person who confuses fifty percent increase with doubling--I have heard this error in conversation often.

I think part of it is bad math education (duh), but a good chunk has to be blamed on the opposite function--if you want to go from 12 to 8, you don't say "decrease by 50%" because that would indeed get you to 6. 8 is 2/3 of 12 (or 66 2/3%). "Half" and "decrease by 50%" mean the same thing, but when increasing, the language doesn't hold up.

This sort of thing is why, when I taught middle school math, we learned via word problems. The homework wasn't a sheet of rote work with one applied word problem at the end--it was a page of word problems, and if you had trouble with the rote math, there was a section in the back that could help you work that out. Life is filled with applied math--it is not often that one is asked to divide polynomials, but one might find cause to work out compound interest with one. It only makes logical sense to learn how to translate math into English, and back into math. Teachers who don't do this do a disservice to all the future cookie bakers sitting in their classroom.

The cookies were good, by the way. Turned out just fine at 12 minutes.