Oy what a day, but I think by working through the struggle, I had a new and improved idea I want to try.
Before school started this year, I pondered how to get my "average" students to start going beyond the homework problems that they could INSTANTLY understand and do because they remembered from class, or we did something EXACTLY like it or it was EASY. So my initial thought was this idea.
Then as things do, I made sure to pass it through to my department chair, and it sort of morphed to a "homework completion grade rubric" that the whole department was strongly encouraged to follow (which included my original questions, but my main idea was embedded in other things).
Flash forward to 4 weeks into school. I've had hit or miss success with it. Some kids (literally a handful) buy into it and use it to their advantage and make progress on problems they can't originally do. Most kids either ignore it or just pay lip service to it.
One conversation I had a week ago:
Average Girl In Class (AGIS) while we're going over the previous day's hwk: I didn't get that. We didn't do anything like that in class.
Me: Okay, so what did you do about it to make progress?
AGIS: I wrote the answers to the "extra" questions.
Me: what did you write?
AGIS: "I didn't know how to start. We didn't cover this in class."
Me: okay, so then what did you do.
AGIS: blank stare.
AGIS: still staring.
Me: It doesn't help you just to answer the question, you actually have to put forth an effort to make progress beyond your original stumbling block.
AGIS: wide-eyed and silent.
Me: (I got nothing!)
So, flash forward to today. I taught 3 classes of "average" geometry students. During the 1st class when they started in on the "those last problems were hard", and "we didn't do anything like that in class", I gave them an analogy. I said, suppose you wanted to run the mile and had never run it before. Do you think you'd be successful your 1st time out? No. You'd fail and fail again, but you'd keep trying and eventually your progress would eek you towards your goal. With the hard problems in math, if you just look at a hard homework problem and then give up immediately, then it's like you're taking off your running shoes and not even practicing on the track. You can never do hard problems unless you attempt hard problems.
Okay, so then I was all strutting my stuff and proud of myself for my little motivational speech. Then my 2nd class comes. I trot out the same story (except for some reason it morphed to a 10K race, but ....). Then my subconscious must have been working because I added while we were going over a hwk problem that they did NOT get: okay, say you are at home and attempted this problem. I'm guessing you just sit there and stare at it with big question marks. Here's the question I want you to ask yourself: okay, I may not know how to solve the problem, but what DO I KNOW about ANYTHING in this problem? Then I had them discuss in their groups and brainstorm about anything they knew. Then I just called on people, and we got a ton of ideas down. Then with a wee bit of guidance, and me continually prodding them about what they knew, they started to be all, "OHHHHHH, then I can do this, or this....", and we eventually solved the problem.
Then my 3rd class came. This spiel morphed into not just the 10K, but potentially throwing free throws or playing the guitar or whatever. Did the same questioning and such with 3 problems. But now I added the story of: even I'm continually learning. I wanted you to be able to do hard problems on your own, and I attempted something, and now I see it's not working well, so I have to go back to the drawing board and ask myself, what do I know? what can I change? etc.
Bla bla bla. Who knows if it'll get through, but maybe I'll soon have a homework for them that includes 5 HARD problems. And I'll stipulate that I don't even want them to solve them if they can't, but to get ANY CREDIT beyond a ZERO, they have to brainstorm and answer the questions:
well, what do I know about this?
what do the words mean?
what formulas might apply and why?
here are some calculations, I don't know if it'll work, but I'll do them anyway .....
FYI here were the stumping 3 problems for them:
1. AB is parallel to CD. A, B, C points are given. D is on the x-axis. Find D.
2. EF is perpendicular to GH. E, F, and G are given, and H is (5, y). Find y.
3. J,K,L are given points. Is triangle JKL a right triangle?
To be continued...