Imagine, if you will, 32 seniors who all need Algebra 2 to graduate. A problem is presented... find the slope of the line through the two given points. There are three answers posited. A quick Plickers poll shows a pretty even split between two of the answers.
Who will come work it out on the board? I ask.
Aren't you going to tell us the answer?
I will not.
Four hands shoot up.
I hand the stylus to a quiet girl from the back row. You know, I say, that I have no idea what your answer is. You might be about to put up the wrong answer.
I'm ok with that, she says, and gets to work. Much yelling ensues, over subtracting a negative number, but we are all finally convinced. The girl was right.
I owe Tracey ten dollars, says another girl.
17, 18 years old. Working hard to figure out 3-(-1). But working. Which gives me something to work with. We're going to be ok.