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 number P.
2. Show where -P is 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."
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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...
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