Drinking the Kool-Aid

Closing the Teach For America Blogging Gap
Feb 10 2011

The World’s Hardest Easy Geometry Problem

I’ve always believed in rigor and Bloom’s and teaching higher-order thinking. Of course! Of course I want to teach my kids to think at a level higher than the state tests require. But today, the Mirror of Teaching revealed some assumptions I can’t wait to shed.


This particular Thursday morning, I was feeling guilty about Bob. Responsible, analytical, unassuming Bob. He came in just before school started to turn in some missing work, and seeing him reminded me of how much I’m not doing for him in 2nd period. He finishes everything early, plows through the extra stuff I give him, and often asks to go to other classes to finish other projects or assignments. Half the time, I’m so caught up with my low kids and feel so guilty for neglecting him that I just let him go. I want so much to challenge him and push him harder—he’s the kind of kid who needs to be stumped.

So, on a whim, I posed this problem to 2nd period. I was gone for half of the period finishing up an ARD (Yes, this is the THIRD day this week that I’ve been pulled out of first period—don’t EVEN get me started) and couldn’t fit my lesson in, so I figured I would give my two or three high, bored kids something to chew on while the rest of the class had a review/makeup/refresh day. I told them three things: One, the first person to solve it would get $10; Two, I spent two full days on it over break and didn’t figure it out; and Three, they already knew everything they needed to know to get the answer.


They ate it up. All of them. What I had intended to be a five-minute introduction of the problem turned into a 30-minute whole-class brainstorm session—the first of its kind, mind you. There were side conversations, sure, but the class was generally involved, and kids did things like addressing each others’ misconceptions, taking notes because they thought an idea might help them later, and asking each other “why?”

The best part was seeing my medium and medium-low kids get really into it (“really into it” here means they were following what was going on and asking a question or making a suggestion every once in a while). And! My Silent student, who makes every effort to only speak when she absolutely must, stopped me as I was whizzing by with a “miss! [wait… wait…] … it’s 10.” It wasn’t 10 at all (and her reasoning was that it looked kind of like the 10 degree angle just below it), but I was thrilled that she was so confident in her answer that she’d put herself out there like that. She didn’t even say it with a question-mark.


It was really, really cool to see my kids try something hard. We had FUN! … But what today revealed to me is that I never really harbored the expectation that my kids would be capable of sticking with a problem like that for long enough. I’ve seen them give up on so many lower-level tasks and leave so many higher-level problems blank that I started to assume they just didn’t have enough of a skill base yet to do much critical thinking on their own.

I hope y’all readers know how hard that is to admit. (Hello. I am a 2010 Teach For America Corps Member, and I have low expectations).


Turns out everything they say about higher-order thinking is true:

1)      “Higher-order thinking creates a more lasting memory of what is learned,” they said. Watching my Gangly girl use what I told her about triangles’ interior angles to solve a larger, harder problem makes me more confident she’ll remember that skill than any perfect exit ticket would.
Assuming kids need a skill base in order to think at a higher level is exactly my problem. This geometry problem is perfect, because it requires very few skills but a LOT of thinking—precisely the opposite of what I’ve been asking my kids to do. Right now, everything is screaming at me to make them think in order to gain the skills, not to do it the other way around!
2)      “Lower-level objectives have very little use on their own,” they said. I realized the reason my kids give up on the low-level problems might have less to do with their low skill level and more to do with the fact that there’s just no point to problems on worksheets. (For me, the point was always “the teacher said to, and I want a good grade.” If those things didn’t matter to me, I would have simply refused to practice). The skills we teach don’t matter until they require kids to think.

It was just so JARRING to see my kids—my math-phobic, work-phobic, thinking-phobic kids—really putting their minds to something for a sustained period of time. And it was difficult to realize that it was my fault—the reason I hadn’t seen them work like this before is that I never gave them the chance.  I’ve been feeding them skill-and-drill, basically, and wondering why they’re not learning. Pushing deeper thought isn’t a luxury—it’s a necessity. I’ve been harboring this misunderstanding for months, and blaming my kids for my own mistake. They do know how to think. I just don’t yet know how to pull out their thinking and use it.


Anyway. I have way too much to say about this (as you can see). This probably could have been split into a high expectations post and a higher-order thinking post… but today, they’re very meshed.

6 Responses

  1. You. MUST. Read. Glasser. The Quality School. The Quality School Teacher. Choice Theory in the Classroom. In a nut shell: Kids (People) reject what they perceive as having no value. They won’t invest in it. You valued grades and the approval that you received for getting them so you were willing to invest energy in tasks that otherwise you would not have perceived as meaningful. Some people (and loads of middle and high school students) don’t value adult approval as highly as peer approval, and don’t value approval that is based solely on willingness to comply AT ALL. So even if they aren’t overtly non-compliant, they definitely won’t be motivated to do things they think are “lame” by a driving desire to please. Create value, ie “quality” (based on what THEY value) in everything you do or ask them to do and they’ll invest. SO much fun. If you never listen to me about anything else again, read Glasser. I love this blog.

    • Wess

      Glasser Glasser Glasser, he’s on my list! Man, seeing all the new 2011 blogs and thinking about reading lists makes me wish I could spend my time reading. I need a long plane ride, like to DC or something. Oh wait. :P
      Hope you’re feeling better!

  2. Ms. Math

    This is wonderful! The same thing happened in my classroom when I gave that problem. I realized that what I was teaching them was way too easy most of the time. One of the main points of the book the Teaching Gap is that kids in the US have a hard time because we only do easy routine problems and they would actually like to do something harder and find it more interesting. There are plenty of researchers who pull kids and do hard problems and the kids eat it up too. If only math books were filled with such cool problems. So, did you solve it over break? I never did, just watched my kids work on it.

    • Wess

      Nooo, I never did it! Bob came back into my room at lunch thinking he’d done it, and he really had me going for a while–but he made one too many assumptions.

  3. adrilicious

    I hope one day I can be as reflective as you – I feel like that makes a truly successful educator. Also – thanks for sharing because I’m totally inspired to be reflective and to think about higher ordered thinking. You’re great! Also – I think anyone thinking about their students on your level is incredibly invested in them. Well done!

    • Wess

      Thanks! Blogs definitely help on the reflective front. Don’t stop writing! :)

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