## 11 December 2011

I was working on a lesson with sixth graders and middle school teachers in doing math without any tools, just in your head. Not memorization, but logic.

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?
The teacher had her answer, and she was thinking of traditional school questions, which are really not questions at all, whether asked on paper, or verbally, or via computers, or via clickers, but traps. 'Gotcha' devices to train kids to respond exactly the way they've been taught. When we ask real questions, kids stop repeating and start thinking, and learning.

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?
Even Christmas offers amazing inquiry opportunities... Was Scrooge redeemed or just frightened into behaving well? Does the Bible require taxation for income redistribution? Why do so many northern hemisphere cultures have holy days around the Winter Solstice? and why is the gift of food so common? Who created our Christmas stories and rituals, and why?

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

Anonymous said...

I remember back in elementary school, I was supposed to memorize the times table out to 12x12. I couldn't do it, in no small part because it was just a big array of numbers without any context, but also because people kept telling me I'd fail the class, and life, without it. So, you know... No pressure.

Finally my dad said if I could get to 7x7 that'd be enough. Why 7? Because it's the largest prime in the 1-10 set. Once he said that, I understood that it was OK to derive the other values, and all was well.

--HTB

jsb16 said...

How would you deal with students who dig in their heels and refuse to answer questions the teacher doesn't know the answer to? For example, if, as a physics teacher, I give a student a graph of how high a ball is as a function of time and ask "How would you figure out what the ball's acceleration is?" and the student says "I dunno" or "You tell me how to find it"...

narrator said...

Homer, indeed, framing it in an understandable way, a way which makes sense, not to the teacher but to the student. I hated school math (which is really arithmetic and not math at all), but I was fascinated by primes and the fibonacci sequence, and if it explained engineering, you could suck me in.

jsb16, think of exactly how hard your schools have worked to train that kid to say, "I dunno" or "You tell me how to find it," and you'll understand the problem. Even at third grade Mike Thornton - @mthornton78 http://youtu.be/_2jaayzp_0o talks about the six or eight weeks of "unteaching" he needs to do to free students from just 3 years of previous schooling which makes them incapable of choice or critical thinking (and that's in a very good elementary school).

You need to unteach aggressively. And we need to rebuild our education system from pre-K up.

- Ira Socol

@malynmawby said...

Good post.

Questioning can be used as assessment of and for learning. I have no issues about asking questions students [should] know the answer to...they may not and this informs my teaching.

I do have issues with limiting possible answers or questioning being the sole domain of the teacher. Kids should be taught this skill as well. Rather than re-hash, I'll just add a link here: Questioning Facts + "addendum" in the comment area. Your thoughts on that would be most appreciated too.

narrator said...

malynmawby -

These kinds of questions inevitably create sttudent questions, they have to. Just the "space" question generated a dozen almost instantly, focusing on how we might define "space" (includes, doesn't include).

Students need to doubt it all, question it all, if education is to be anything but socially and intellectually reproductive.

- Ira Socol

Kylie Roberts said...

In line with the title of this post, I get really pissed off at people who have this attitude wherein they're just total showoffs - thinking that they can manipulate their classmates and make them feel like they don't know anything.

These people (the type I don't like) felt the need that if people think they know a lot of stuff, they're high and mighty.

Sorry for ranting it out here, but, really, I've met countless of people who have this kind of attitude and seriously, it's just annoying.

Don Hudson said...

Yes! I find this same consternation with writing. I have given workshops, speeches, and taught classes where I had to work on how to "unteach writing" before we could really get started writing. Participants, including long time teachers demand, "No! No! Tell me what you want and in what way, and I will do it for you!"
Here's the difference, for example, Did you know that good writing never starts at the beginning?
Huh? What are you talking about? Where else can it begin?
Garrison Keillor put it humorously this way with this lead in - "I want to die peacefully, in my sleep, like my grandfather; not kicking and screaming like the others in the car!"
I can only imagine what the rest of the story was like. But I know it did not begin with this line. After the story was told then this line was added, it's called a lead. Leads catch a readers attention through hymor, startling dfetails, seeming impossible conundrums, insightful questions, impossible questions, quotes, famous quortes, riddles, oxymorons, dialogue, etc but leads are usually the last thing written for a piece of good writing. No matter how factual, or how clearly a story starts out in your head, it will never get on the page the way you think or intend. That means the lead needs to be the last thing you write for the story.
By the way, writing possible leads for stories is great fun and opens up doors of inquiry and questions students do not even know are there.
And this is just one element of writing I have to "unteach".