My kids can do anything

Today I gave my second quiz. My first I gave about a week and a half ago, although it seems to be already in the far distant past. I had only taught two lessons at that point, and the quiz I gave them was far to easy (granted, it is seventh grade math). It didn't seem right. Assessment as a motivating factor should act either as a reward and a consequence. A high grade, praise, a spot on the wall of fame, or Ace Award (an award given to a student who gets a perfect score on a test or quiz, something my calc teacher did in high school) should be a reward for putting in the time and studying, and if students can come in and get great grades with little effort, like the two students who scored 103 on my first quiz did, the reward starts to seem meaningless, since it was achieved with little or no exceptional effort. A poor or failing grade should act as a consequence, but if everyone is already far from failing, then the negative aspect of assessment as motivation is also failing.

For my second quiz, I decided to make it quite a bit harder. I made it a good three pages, with no goofy extra credit points (I offered one extra credit point out of 140 for finding the square root of 1369). I tried to set it up in such a way that I had several questions on each of the topics we covered, and a little more than 4/5 of the questions could be answered pretty easily if you knew the concepts, and the last fifth were questions (one or two on each subject) that required a little more thought than just "I remember rule X so I just need to write Y".
The class was not happy. One of the girls was frustrated and feeling like she didn't know anything. Another, Samantha, was more angry about the quiz, and probably also about the detention she got yesterday (which I overheard led to her mom grounding her- yeah parents). Regardless of whether she was still steaming over the detention or whether she was mad at me for making such a hard quiz, she was close to tears after about 20 minutes of it. A third girl, Megan, who is about three feet tall, with glasses and the cutest little southern voice, had been at a funeral the day before and thus had been absent (excusably) and also seemed to be under a lot of outside stress today, with the funeral being an obvious source. This girl had missed all the information about prime numbers, GCF and LCM, which made up significant chunks of the quiz. Now, Megan is generally a really responsible, although really shy, little girl, and she was getting really upset about the quiz. Her hand was up several times, asking me what to do about the questions relating to the stuff we covered when she was out. For one definition, I told her to just write "I wasn't here" and for the others, I told her I understood, that I would remember when I was grading that she hadn't been here, and that she should think of them like bonus problems, but she was still flipping out. I told her to look at all the other questions she had been able to answer, and told her that she would be fine. I told her to take deep breaths.
About 3 minutes before the bell, everyone but Megan had finished the quiz, and I had them all trying, individually, to figure out the Fibinacci sequence. I pulled Anthony, our class joker, to the side. He's actually one of the smartest guys in the class, and he was actually getting pretty close to figuring out the sequence. I asked him if he would do me a favor. "What you want?" "Anthony," I said " Remember the fraction song?" Nods head. "I want you to do an interpretive dance to the fraction song for me." Eventually, with a bit of convincing, he and another student, Terrance, agreed to do a dance. The whole class sang, and those two clowns got to dance, and I thought it made everyone lighten up a bit, so they'd have that out of their system and be ready for next period.
It didn't work for Megan, however. After the bell rang, she finally hands me the quiz, and says "Golly Mr [blank]" and just shakes her head. I assured her it would be fine, but I could tell neither my reassurances or the interpretive dance had lifted her spirits.
At the end of the day, Samantha asked me what she had scored on the quiz. I told her I hadn't finished grading them yet and that I'd bring them back on Monday. Megan, Leaning against the wall, blurts out, in her little voice - You probly flunked it like I did - and she slid down a little lower along the wall. I felt bad about the quiz. I felt like I had made it way too hard for them, that they'd all failed, and that all I had accomplished ammounted to a big kick in the teeth for their confidence.
I was even more upset when another teacher, during the test, told Megan she would go over the questions with her after lunch. Fine idea. My class. Go through me first. I wasn't really excited about getting pulled into a good cop bad cop game. Then, when they were working on it after lunch, the teachers says, in front of the class, "Mr. [Blank], this test is hard." Implying, obviously, that it was too hard for my kids. No one should ever tell my kids that something is too hard for them. Ever. They are not smart kids, and they have enough people telling them they are too stupid, too uneducated, too far behind. Aside from that, I felt like it undermined my authority in the classroom. I gave a quiz. That's it. I was mad. I understand that it's hard to see a kid be frustrated and upset, and we're all here because we want to help kids, but this was the wrong time and the wrong way to try to help. My kids can do anything, and in private, I'll talk about things they struggle with, or things that that I will really need to pound in to their brains, because they won't get them at first. But they can do anything.
Turns out, I was right. I just graded the quizes. The mean and median scores were 81. No one failed. The range was from 74 to 95. Megan got an 80. So maybe it was too easy. The way I grade, pretty much every problem is worth three points, you get one point if you try, two if you're on the right track, and three if you get the right answer, which keeps things sane for me as a grader and gives the incentive to show work, which keeps them from slipping up on the dumb stuff. If I didn't give partial credit, kids would have failed, maybe all of them, but I really believe that the grade should be based on what they know, and if they know how to do a problem, but momentarily forget how to subtract 4 from 7 (it's amazing how often this happens), they should get half-credit for it.
So, that is my rant. I haven't figured out about assessment yet, about what it should be. Kids should take a test and feel smart. Kids don't feel smart when they do easy things. I spoke with a kid from someone elses class today in lunch. Says he doesn't learn anything, says he knows everything they learn. He doesn't feel smart when he gets taught it again, even if he gets 100s on the test (especially if everyone else would be getting hundreds as well). Kids want to be challanged, they want to twist their brains around problems. That's the reason why kids crowd to the board after lunch to try to find the roots of some huge squares (I think 5041 is the biggest one I've given them yet). I have taught them some dumb things, and assigned them some stupid work, and gave them that first dumb quiz, but I'm learning. I still don't have a clear philosophy about assessment, but I'm finding out a few things about it. Success has to be just within reach, and failure should be always snapping at your heels.


(All names are ficticious. My students are way too cool to appear in this blog.)

The Great Seventh Grade Pie Eating Contest

Thursday was a day of firsts for me. It was the first time I taught two lessons in a row, the first time I had students work in groups, the first inductive lesson that I taught, and the first time I used cold calling, a questioning strategy that Anne introduced to us in class the other day. It was a good lesson, despite the fact that I had some unexpected twists, and I think there are a bunch of ways for me to learn from what happened in that class.

The Objective

The primary objective was for students to add and subtract mixed numbers. The secondary objectives were for students to improve their social skills by working in groups, for students to take responsibility for their own education and the education of their peers, and for students to feel like they themselves are capable of determining the rules of math without having these rules explained to them.

The Task

I divided the students into two teams, and told them to imagine that they had just finished a pie eating contest. I gave each student a slip of paper with a mixed number - representing the number of pies that student had eaten - and I asked each group to find the total number of pies that their group had eaten, so that we could determine which group had eaten more pie. Then, I told them that the winner of the contest would be the group that was best able to explain how it found its answer to the other group. They were introduced to mixed numbers the day before, but never told how to add them. I told them the winner of the contest would be the team taht was best able to explain its answer. As an added twist, I threw in the cold calling idea and told them taht I would pick one student at random from each group to explain how they came to their answers. I told them it was their responsibility to make sure everyone in their group understood and was able to explain their solution.

The Result

Both groups were able to find the answer, with some, sometimes substantial prompting. The prompting was often more about how to work in a group than about how to actually do the math, so I think in the future I need to give out more instructions about how to work in a group before I get them started. The biggest problem I had with the structure of the exercise was that one group finished much, much quicker than the other, despite the fact that when I had chosen the groups the night before, I had tried to split the kids up as evenly as possible, both in terms of math intuition and group-working skill. To the group that finished first I gave a bonus problem to keep them busy, which worked decently enough, and at least kept them quiet and academically occupied while the other group finished.
Both groups found the answer in different ways, which was exactly what I had hoped for. It was also obvious that knowing they woudl be chosen randomly to explain forced them to try to teach each other, but when it came time for the randomly chosen students to do their explaining, the results were less than impressive, and it was clear, at least for one groups, that they weren't sure what they were doing.
Overall, though, I feel like the lesson was a success. I made sure to remind them that they all figured out how to add mixed numbers themselves and emphasized that I never taught them how to do these kinds of problems. Sometimes, although I wanted them to struggle through the problem, the struggle seemed to be too much for them, and I felt like I was losing a lot of the kids to frustration.
The other problem I had was time. The lesson spilled over into the next period, so it was a good thing I was teaching both; however I rushed through the material I had planned for the second lesson (multiplying and dividing mixed numbers) and I ended class with the feeling that the students weren't really clear on any of it. Like my mentor teacher said afterwards, "It's better to teach one thing well than several things poorly."
As for the cold-calling, it kept everyone involved and kept everyone interested not only in the problem but in their classmates' understanding of it, which was great, but I ended up calling on students who clearly struggled to explain the material in front of the class. If I were to teach the same lesson again tomorrow, I would keep the cold calling, but I'm not sure how I could have helped the process along so that everyone really developed a good understanding of what was going on. I could allow a second person to help explain if the first couldn't, but that would remove a lot of the incentive for the group to make sure that everyone gets it.

Charter Schools Focus Paper

So, as an assignment for class, we all had to read on the focus papers that the second years wrote last year and write a response to it in our blogs.

I read a paper written by a fellow Eph and math teacher about the efficacy of charter schools and vouchers. While the paper succeeds in illustrating many of the important positive results that have come about through the use of vouchers and especially through charter schools, it leaves out many of the prominent concerns with such programs.

The paper follows the basic economic idea that competition and market forces are the only way to efficiently produce improvements, and that both charter schools and vouchers provide such competition. One often ignored point that the paper makes clear is that the competition benefits not only those in the charter schools or using the vouchers, but it benefits those who remain in traditional public schools as well, since these schools, after the introduction of competition, are faced with new incentives to improve.

The paper also says that there are questions involving the constitutionality of voucher programs, but never mentions the source of these concerns or the ways in which vouchers might be unconstitutional. I would speculate that these questions arise from problems with the separation of church and state when government funding is used to pay for religious education, but that isn’t really clear from the paper.

Overall, however, the paper gives the impression that these two programs put public education on the verge of big changes, and I have to agree with that sentiment, and can only be happy about it. Public schools have failed too many of our children for far too long, and if these programs are as beneficial as the paper suggests, then they are certainly worth trying. However, the negative aspects of these programs, specifically the loss of funding to schools that need it the most, cannot be ignored.