Today, in the middle of the geometry warm up, it stopped working. The pen refused to interface with the screen. The technological infrastructure in my district is a bit dated. I do not rely on lightening fast internet for streaming videos. Our firewall often blocks websites for random/no reasons. The network is in such a state that if there is a class of students in the computer lab, my computer runs noticeably slower. All of this is the background to a huge tech push from higher up. They want us to be flipping our classrooms and using Khan Academy (barf) and various other technological services on a regular basis. It's becoming part of what they look for during observations. I don't mind any of that, except that when the tech fails, I'm in trouble.
So when the pen stopped working, and my board turned into a VERY expensive projection screen, I had to improvise! Luckily, I still had a single piece of chalk. I used it to draw graphs on the board to explain the distance formula. I used it to have students go to the board to show off their work. I used it for 6 classes and it didn't run out. It was like the Hanukkah oil of chalk.
In the math 8 classes, I'm focusing heavily on trying to drum out bad habits, like putting too many equals signs in a problem, or writing everything on the same line. In addition, their basic arithmetic skills are quite lacking, so we're also working on numeracy.
When I teach addition and subtraction at this level, I need to remind students that they already know how to do it. There have been several discussions on Twitter lately about trying to move traditional mathematics concepts from being taught in the abstract and then only brought to the concrete later, to the opposite. In theory, I'm all in on this, but in practice, I've been having some difficulty. What I found, however, is that with the concept of reinforcing addition and subtraction, I'm already focusing on the concrete rather than abstract.
My students have tremendous difficulty trying to remember rules like "When you add a positive and a negative, the answer will have the sign of the number that was bigger before you added them." Seriously. Why do we teach it this way?? For example:
(-13) + 8
"So, I subtract 13 and 8 and get 5 and since the 13 is bigger and it's negative, my answer should be negative, so -5."
Yes, but how scary is that?? If you're not a person who sees patterns everywhere (like I do) or is comfortable fitting things into rules or a formula, this can seem like a very confusing way to solve the problem. A few years ago, I stumbled on a way to get kids to do this problem without even thinking about it. Think about it in terms of money.
"If I owe you $13 and I have $8 in my pocket, where am I after I pay you off?" I ask
"You still own me $5," they say without pausing to think about it, and before they realize they have done math in their heads.
I find two things really amazing about this. First, it has worked with EVERY kid that has tried it. There are occasional calculation errors (someone will say $6 or $4) but almost never are there conceptual ones. Most students, by 8th grade, have a very decent concept of money. It's something they understand and are comfortable using. Today, a student talked about it in terms of yards as well. "If I'm 13 yards down and gain 8, I'm still 5 yards down!" Perfect!
The second thing that I find amazing, and baffling, is how quickly this idea flies out of their heads as soon as they pick up a pencil. We can talk about doing addition and subtraction in terms of money for an hour and as soon as I give them some practice problems to do on their own, they go right back to "the bigger number is negative..."
I think part of it is conditioning. They have been conditioned to think abstractly when it's in front of them on the paper, but the conversation we have lifts that veil for duration of our conversation. I'll keep reinforcing it in the hopes that it will stick.
The girl I pulled aside last week (or earlier this week, it has been a long week) was asked to put a problem on the board. She and 6 other students went up, put up their problems and then walked us through them. Hers was almost entirely wrong, but my enthusiasm for it didn't wane. I picked out at least three things that she did that I LOVED, including not having an equals sign anywhere in her work, putting each step on a new line, and drawing lines between numbers that she combined to their result in the next step.
I'm trying to impress upon them several things, but this above all: Mistakes are not failures. They are necessary steps on the road to success. Giving up is the only failure.
Overall, I was very pleased with the class.
The second section of the class, not so much. Their blatant refusal to stop talking over me lead me to turn the lights off and give them drill work. I immediately hated myself for it but I didn't know what else to do. I don't want to yell at them because yelling isn't effective. It only serves to show the anger, which isn't productive. I told them that if they had questions, to put their hands up and I would be around but that I didn't want to hear any conversation.
Three students came into my classroom with nothing. No book, no notes, no paper, no pencil. One of these then proceeded to ask me questions about an unrelated topic. I know that they are still children, but I can't figure out how they could see this as acceptable behavior.
After I told them to sit silently and work, they did! I have been very strict in past years and this year, I've been letting up a bit. I don't think that was a mistake, but I need to make sure to remind them of the expectations in my class.
Also, since we had a fire drill during the first section, which ate up 15 minutes of that class, and I promptly forgot about during the second section. I did not fill the time...
In geometry, we derived the formula for distance between two points on a coordinate plane from the Pythagorean theorem. It was not what I had planned to do and it was a bit haphazard, but as I said, my technology failed, so I improvised. I may have stated previously (in my post on preparation) that I think I am a master improvisor. (Ok, passable.)
I realized halfway through the explanation that I was going WAY too fast so I backtracked and did a better job the second time, doing a considerable amount of formative assessment to determine where questions were arising and addressing them before they got swept under.
The warm up was fascinating. When I wrote it down, I figured that it was a basic problem on algebra and line segment length, but when we started going over it, we discovered something interesting.
|A picture on a computer of a picture on a computer. Meta...|
It was (maybe) a very poorly written question. I say maybe because if my lesson goals had been different, it would have been AMAZING! We quickly found, through conversation, that since the order of the points was not given, there were three distinct configurations for the problem, one of which was impossible by the numbers given. I had the students explain to me why it was impossible and why the other two answers were valid.
It was a great teachable moment for them and for me. Especially in that class, I'm constantly being reminded that I have a ton to learn.
Speaking of my own learning:
I've decided to start working on switching over to Standards-Based Grading. It seems to align much better with my goals for my classroom and I'm becoming increasingly concerned that my current grading system is arbitrary and I can't justify it any more.
I have an insane amount of work to do and things to learn, but I have incredible resources through Twitter and the MTBoS who are willing to hold my hand as I make this journey. If you are an educator interested in improving your craft, and you are not on twitter, you are missing a huge opportunity. It has changed my life and it will change yours too.