The Problem with Creating Problems

Words of warning, I have no answers here. I'm just thinking out loud and wanted to post a quote for future reference.

The third chapter of The Art of Problem Posing begins with an anecdote of a speaker relating the following observation to a group of math teachers:

There are nine Supreme Court Justices. Each year, in an act of cordiality the Supreme Court session begins with each judge shaking hands with every other judge. (p. 19)

He then asks what the question was for this setup.

What would you ask?

If you're like me you asked the, "How many handshakes..." question. The book states that the question was so obvious the speaker treated it as rhetorical, stated the question himself, and moved on with his talk. The authors then drop kick me in the head with this:

Many of us are blinded to alternative questions we might ask about any phenomenon because we impose a context on the situation, a context that frequently limits the direction of our thinking. We are influenced by our own experiences and frequently are guided by specific goals (e.g., to teach something about permutations and combinations), even if we may not be aware of having such goals.

The ability to shift context and to challenge what we have taken for granted is as valuable a human experience as creating a context in the first place. (emphasis added because it's so awesome)

I had a strong reaction to reading Ashli's experience working with Dan Meyer's Boat in the River problem. When I sat in to watch Dan present this video (IIRC, there were about 20 of us and presumably, most of us were teachers), the "right"question was asked by nearly all of us. I recall being shocked that Ashli's students were so all over the place and only one group got the "right" question.  In her shoes, I can imagine myself being mildly irritated at what appears to be kids shouting out random questions in attempts to be, ummm, kids.

Look at this question - "Why does he put the headphones in?"

I would definitely get this question. I would get it from the kid who is always trying to not-so-smoothly listen to his ipod by resting his head on his hand and running an earbud through his sleeve. He'd probably follow up the question with a statement about how Dan's ipod is old and the newer gen is much better. I'd be dismissive and move on.

Except.... I'm the one at fault here. It's actually quite interesting why he needs headphones and is certainly worth investigation. Discovering that Dan needs to maintain a constant speed only enriches the problem that I had intended for us to investigate originally. If you want to get crazy, the followup question, "What if he didn't maintain a constant speed?" opens up a whole new, and perhaps more interesting, investigation.

My tunnel vision is only exacerbated when I've taken the time to develop and create the problem myself. It's fairly easy for me to divorce myself from a lab I found on google. On the other hand, when I've taken hours to create a lab or demo in order to launch a specific investigation, I find myself invested in the idea that this demo so wonderfully elicits the question I'm hoping my students will ask so I can teach the thing I wanted to teach.

Stepping back and allowing the process of problem solving and problem posing to grow organically is something I struggle with daily.

It hurts my brain to think about how often I've limited questions because I've imposed my own context.

Stuck in the Middle

In my last post, I wrote about the books by Atul Gawande. I'm going to give an extended quote here, so if you're a representative of Henry Holt and Company, I apologize for trying to get people to read your books:

The hardest question for anyone who takes responsibility for what he or she does is, What if I turn out to be average? If we took all the surgeons at my level of experience, compared our results, and discovered that I am one of the worst, the answer would be easy: I'd turn in my scalpel. But what if I were a B-? Working as I do in a city that's mobbed with surgeons, how could I justify putting patients under the knife? I could tell myself, Someone's got to be average. If the bell curve is a fact, then so is the reality that most doctors are going to be average. There is no shame in being one of them, right?

Except, of course, there is. What is troubling is not just being average but settling for it. Everyone knows that average-ness is, for most of us, our fate. And in certain matters - looks, money, tennis - we would do well to accept this. But in your surgeon, your child's pediatrician, your police department, your local high school? When the stakes are our lives and the lives of our children, we want no one to settle for average. 

If you've ever heard any of the many version of Killing Me Softly With His Song, you know what I felt like reading this passage. I'm not worried about being a bad teacher. I'm worried about staying an average one.

The view from afar

There's this science fiction movie trope where the scientist, after seeing the carnage that his creation has unleashed, cries out,"What have I done? What have I done?"

An email correspondence with a fellow teacher made me start thinking about my "What have I done?" moment. My reason for having gone assessment crazy. It happened three years ago.

I can still picture her. She had dark brown hair and brown eyes. She usually had a pony tail and was on the small side. She liked to sit on the left with a table of 3 other girls. She smiled a lot and made me laugh. She brought me some dollar store ginger cookies for Christmas. She was on the basketball team but wasn't very good. It didn't bother her. She just liked being on the team. She turned every assignment in the entire year. She took every note. She even annotated them at home like I taught. She finished the year with an A every trimester. And she didn't learn a single thing.


Two things.

One. She wasn't gaming the system. She was a product of it. We created her. We asked her to sit in her seat and do what we say and turn in stuff on time. She was simply following orders.

Two. I knew she hadn't learned anything. I knew the whole year. I felt trapped though. I gave points for notes. She took them. I gave points for neatness. She was neat. I gave group grades for labs. Her friends were all A students and her lab reports were always formatted just the way I taught. Her test grades were never great, but I always gave test correction points. I gave extra credit for going to a science museum and writing about it. She did that. All the time, I knew she never really got what was going on. If I asked her something, she'd smile and parrot back what I'd just said or flip through her notes or let her friends whisper answers to her. Or she wouldn't know. She'd listen very carefully and echo it back. I justified her grades by telling myself there was nothing I could do. Points were points. If she got 90% of them, she deserved an A.

June came, then July. She was going to start high school soon and all the time I couldn't shake the feeling that I had done a huge disservice to her. I lied to her. Her grades told her that she had learned science. My grades. My lies. I think about her often. She comes back and visits. I feel conflicted when I see her. She's doing well in high school. I don't know how I feel about that. I wish her well and want her to succeed. I don't know how have the courage to tell her she's been living a lie. So I smile and give her a big hug. I ask about her classes. Her teachers. Her family and boyfriend. We laugh over a story that begins,"Remember that time you set the ceiling on fire...." As she's walking away I stand back, look at her, and ask myself, "What have I done?"

Why industrial designers understand education more than we do

I was watching Independent Lens yesterday on KQED. The film was called Objectified. In the beginning a designer named Dan Formosa said this: (not quite word for word but the spirit is intact):

We have clients come to us and say here's our average customer: female, she's 34 years-old, she has 2.3 kids....we listen politely and nod and say well that's great but we don't care about that person. What we really need to do to design is look at the extremes: the weakest or the person with arthritis or the athlete or the strongest or the fastest person. Because if we understand what the extremes are, the middle will take care of itself.

Again with feelings..if we understand what the extremes are, the middle will take care of itself.

An industrial designer has summed up very nicely my feelings on both educational research and teaching in general.

So much in educational research goes to the average kid. We look at the effect size. We do meta-analyses. We care about how a giant lump of kids does on average against another giant group of kids. What we should care about are the extremes. A .4 effect size is nice. What I really care about is the outliers in the group. What type of student did this treatment make a HUGE effect on? It gets washed out because of our love of averages. When we look at research, we shouldn't care so much about the stuff that makes the group move a little on average (although that's still good to know). What we should be looking at is those students or groups of students in the treatment that were extremely positive and negative. What conditions existed for this specific student to make such an extreme gain? We can move towards truly individualized education only when we can say what works for this specific student under these specific conditions.

As for teaching, I don't know how many times I've been told by a principal/other teacher/staff developer that I should choose 3 or 4 kids in the middle and design my instruction around them. I've done that for a long time and had pretty good results. I'm becoming convinced though that I need to be more like Dan and design for the extremes. I need to take care of the really high and the really low and the middle will take care of itself.