Sometimes the misconception isn't their fault.

Take the "-" symbol for instance. Are we talking about subtraction? Negative numbers? How about "the opposite"? Or inverse; maybe it's inverse.

I gave students this number line today with the prompts.

1. Tell me everything you can about the numberP.2. Show where-Pis on the number line. Tell me everything you know for sure about-P.

They did very will with the first prompt. Lots of responses like:

"P is on the negative side."

"P is a negative number. It's between -2 and -3."

"P is probably about -2.7 because it's closer to -3 than it is to -2."

Ok, I'm loving this. Then they drop the hammer on me.

"-P is negative."What are your first steps when you encounter thing like this?

"-P is also on the negative side."

"-P has a negative sign in front of it so it's also negative."

## 3 comments:

Ask them about -(-3)? Ask them what opposite means, and to show you pairs of numbers that are opposites?

Ask what you get when you add P and -P. Then bring it back to the number line by looking at where other pairs that sum to zero go.

Love question and love the comments. I had a convo with math T the other day and she was confused about (sinx)^-1.

She wanted it to be inverse sine as in I give you a ratio and you give me an angle. "That would be true if you wrote it sin^-1(x)"

She was having a hard time with difference and she said, "that's stupid (!), why not just say arcsin) and leave the notation out of it. Hmmm...

Post a Comment