## Wednesday, September 7, 2016

### Stupid Math Notation

Sometimes students show a misconception that makes me pause and wonder how we can continue without clearing this up.

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."
"-P is also on the negative side."
"-P has a negative sign in front of it so it's also negative."
What are your first steps when you encounter thing like this?

Sue VanHattum said...

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

CalcDave said...

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.

Amy zimmer said...

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...