Geometry got me WAY off task today. They asked if we could have "Physics Friday" since they know I am certified to teach physics. We ended up talking about the scale of the universe and the new laser-based communications system that NASA is launching tomorrow. It was a good discussion and they were actively engaged, even the students who typically have their heads down.
Discussions like this leave me conflicted. On one hand, I know that they don't go to the math standards and I have a ton of stuff that I have to cover in not that much time. On the other hand, which is the hand that always wins this debate, I'm an educator first and a math educator second. If I can provide students with information that they are excited to receive, I'm going to do it.
Part of my job as an educator is, in my opinion, to expose to students to as many ideas and opportunities as possible, to show them the glory and beauty of the world. Dr. Neil DeGrasse Tyson says that astronomy is the gateway drug to academics. If you get interested in space, you have to learn math, chemistry, physics, biology, history, etc... We are always looking for a "hook" to get kids interested in what we have to talk about. What about the idea that we talk about what they are interested in? We don't have to do lessons on XBoX or Playstation to get them interested in school. They have varied interests and, more importantly, if they haven't been exposed to a myriad of topics, how do they even know what they are interested in? There is a major at UNLV where students design and build Las Vegas stage shows and roller coasters. THAT'S A JOB!!! The Ford Motor Company has someone on their payroll with the job title of "futurist" whose sole purpose at work is to think about the future of cars. That job might as well be "Science Fiction Writer in Residence!" If we don't tell our students about it, who will??
After our talk, we worked on line segments (yawn) and I started them on the locker problem.
We have 1000 lockers and 1000 students. The first student opens all of the lockers. The second student closes every other locker. The 3rd student changes the state of every 3rd locker. If they are open, he closes them. If they are closed, he opens them. The 4th student does the same to every 4th locker, and so on.
Typically, this problem is accompanied by a question like "Which doors are open after all of the students are done?" or "Is locker number 298 open or closed?"
Instead, I took a page from Max Ray and the Math Forum at Drexel and asked "What do you wonder?"
I got some great answers. Is there is a pattern? What happens when they are all done? How long would that take?
I got some not-so-great answers. Why would they do that? Don't they have anything better to do?
I have faith in Max that the more I do this, the more they will know the kinds of questions I'm looking for.
I liked the activity, but I don't think I gave them enough time. They were working well, but you really have to do almost 25 iterations before you really see the pattern. I told them to work on it over the weekend and I trust that 80% of them will obsess about it. It's a great problem!
During the previous two years of teaching Math 8, I found myself getting insanely frustrated at the lack of skills and numeracy of my students. I was infuriated that I had to teach subtraction to 8th graders. It has nothing to do with how smart they are, but all to do with practice and how they approach problems. I can't explain it but I found it depressing how low they were. This year, the skills are at about the same level, but with double periods, I feel as though I have enough time to show them the patience they need and deserve.
We spent much of the time today doing practice problems with absolute values although we only did about 10 total. After several conversations about formatting with other teachers, I decided that it was worth the time to slow down and emphasize the importance of having them write their steps on different lines. I willingly and happily answered whatever questions they had, even if I felt they were a little low for the class, or if they could have come up with the answer if they had taken a few minutes to think about it.
Even typing that sentence, I realize I should have, instead, asked directed questions to get them to answer it themselves. I'll keep it in mind for next week.
After that, we sliced pizza.
If I have a pizza with no cuts, how many slices do I have? If I cut it once, how many slices? If I cut it twice, how many can I have at most? What about three times?
After we drew these on the board, I asked them to work in groups and figure out how many slices could be formed out of 4 cuts, if you don't care about the size of the slice. What about 5 cuts?
It went well and they seemed to get into it, but I think it could be improved by maybe using a circular geoboard or some other physical manipulative. If I had planned it further in advance...
In any event, I'm looking forward to a nice relaxing weekend, other than the 12 miles I have to run. I'll be setting up the Mathalicious lessons that I plan to do next week. I'm very excited about them, but I've been putting it off because it's a little intimidating. I need to just jump in with both feet.
Also, I got AppleTV installed in my class, so now I need to come up with fun ways to use it. I plan to have the kids play Wuzzit Trouble sometime soon.
I'm beat. Time to go home, change into shorts, make some pizza and hugs my kids. I hope they don't pee on me.