While I was out, I left a few distance/rate/time problems for students to solve. Upon my return, I was asking students about the problems and many students had similar responses.

S: "The

**Dirt Triangle**."

Me: "?"

S: "Look, Mr. Cox it's like this... | "...You cover up the one you're looking for and if the other two are
next to each other, you multiply. If one is above the other, you
divide." |

Me: "Really? That's strange. I never learned the

**Dirt Triangle**. I learned ...

**The Turd Triangle**

S

_{1}: "No, that won't work. That's not what he told us."

S

_{2}: "He said it didn't matter how we wrote it."

Me: "So which is it; does one work or are they the same? Make your case and be ready to defend it."

As long as I don't have to be some kind of Will Hunting and actually understand one of the most basic and intuitive equations possible, either one works. But if I can't spend a few class periods making some kind of construction paper triangle glued onto posterboard and present my discovery to the class, I still probably won't remember the turdriangle.

ReplyDeleteHere is a perfect example of the difficulty we have with definitions of words in English and in Math. Hours/mile is indeed a rate, but it is not *the* rate that kids are assuming you mean. If you are working with 6-7-8th graders, the trD triangle does NOT work, unless you are consciously upending their understanding of the basic terms *with* their full co-operation ... and that is counterproductive at this point.

ReplyDelete