So I said, "I've never really gotten the "9 x" table, so, if I asked you what 9x12 was, how would you figure it out?"
See, this is a question I cannot possibly answer for them. There is no "correct" answer possible.
"I'd say," one student quickly responded, "that 9x9 is 81 and 9x3 is 27," he paused, you could see him looking at the addition in his head to check himself, "and that adds up to 108."
"That's not the way to do it," a teacher sitting at his table told the student, forcing me to intervene instantly. "That's great," I said, "perfect. But I can never remember that 9x9 thing like you can, so, does anyone have another way?"
|This connects, just keep reading... |
Newt Gingrich says that every nation shown here (in color) is "invented"
and thus has limited rights. Do your students agree?
For me one of the critical ideas in education comes on page 138 of the Neil Postman and Charles Weingartner 1969 masterpiece, Teaching as a Subversive Activity, "Prohibit teachers from asking any questions they already know the answer to," the authors recommend, "This...would not only force teachers to perceive learning from a learner's perspective, it would help them to learn to ask questions which produce knowledge."
The teacher who asks, "what is 9x12?" teaches nothing. The question I asked, among other things, introduces the concept of algebra. For the "9x9" kid, x = (9x9)+(3x9), finding the unknown via knowns, and he is thinking, not parroting.
Why critical? You should never ask any question for which you will not allow unexpected answers. If you don't allow unexpected answers, you are declaring that you "know everything," and, as I told some UConn grad students last month, all saying, "I know everything" does is tell students that you are a liar, a bad way to begin a learning relationship.
Now, if you are an American, I understand that your nation prizes simplistic, expected answers and efficiency over learning and democracy, so this is difficult, but it makes it doubly important if our kids are to build something better. Do you, do your students, know that most governments in the United States begin every election by declaring that they have absolutely no intention of counting every vote? They do this - refuse to count write-in votes for "unregistered" candidates - because they can't handle anything unexpected, because it might take too long, whatever. Of course, the unexpected answer is invention (we don't need an improved gas lamp, we need something else), and it is democratic, and it forges new cognitive paths, but yes, it is slower (In Ireland it can take many days to count votes in an election, which would really mess CNN up). OK, maybe a vote for Mickey Mouse is odd, but say 10% of the electorate chose to do that, might we not learn something?
What works in math, in elections, works everywhere. The reason I brought the Andersonville Trial to sixth graders last week was that this is a question impossible to answer definitively. Did the United States government really insist that it was an obligation to take up arms against it if that government behaved immorally? And if so, what does that mean? What did it mean at Nuremberg? What does it mean at Zuccotti Park for Occupy Wall Street?
It was why I asked students, "Where does 'space' begin?" because, well, we've been arguing over that for years.
Newt Gingrich gave us a fabulous history question this week... does the fact that your nation was once part of an empire mean that you have no rights? So, because the United States was part of the British Empire, is it an "invented nation" with no rights? Because England was part of the Roman Empire, is it an "invented nation" with no rights? Because Greece (like Palestine) was part of the Ottoman Empire, is it an "invented nation" with no rights? Obviously the nation of Israel was part of the Greek Empire, the Roman Empire, the Ottoman Empire, the British Empire, is it an "invented nation" with no rights?
Is there a "correct" answer to any of this? Gingrich thinks so, do your students? How might they research this, how might they argue their opinion with real information?
|British Empire in 1700, is the United States an "invented nation"|
and what exactly does that mean?
So the next time you start to ask what 2+2=, or when the Civil War began, or the formula for some physics thing... Stop! and ask a question you do not know the answer to, a question you can't possibly know the answer to. It will liberate your students and it will liberate you.
- Ira Socol