Joe works too fast.
Joe doesn't show his work.
Joe ends with the beginning in mind.
Today Joe took a test on being able to identify the graphs of quadratic and cubic equations. He bombed it.
Joe came back to my desk while the rest of his class was finishing their tests and had some good questions. He said he didn't know how to set up an input-output table so I showed him. I plugged in one x and found y. I plugged in a second x and asked Joe what the y-value would be. Joe did the rest himself.
Joe and I graphed his results. I asked Joe to graph a simple parabola with coeffieient of 1 on the same set of axes.
Joe said, "Hey Mr. Cox, if the number in front is bigger than 1, then it grows faster."
"And what if the number is a fraction?"
"Then it grows slower?"
"Are you asking me or telling me?"
"It grows slower."
"What if the number is negative?"
We turned the paper upside down.
Joe gets it.
His grade is different than he thinks it is.
Update (can I update a post I haven't published yet?)
Joe just informed me that a cubic with a positive coeffiecient will end up in the 1st quadrant and one with a negative coeffient will end up in the 4th. Yeah, better get on that grade change.