Monday, August 30, 2010

Day 9

Perhaps the most frustrating day yet, although it wasn't necessarily due to the lesson. The openers (pdf) - which I thought they should be able to do fairly quickly and easily - stumped them. Completely. Even #1, which they seemed to think was simple on Friday, was a problem for many of them.

Opener #2, which I thought was an "easy" dimensional analysis problem (because I realized that they were getting lost in the really long ones I had been giving them), wasn't. It appears as though speed (miles per hour, kilometers per hour) is not as straightforward for them as I thought it was (they don't get that distance should go in the numerator, time in the denominator). I need to do a better job of checking my assumptions at the door.

Then opener #3, which were the same problems they were supposed to do for homework over the weekend, except I specifically asked them to find k today, were a mystery to many of them as well. I think that after going over all the openers, as well as today's lesson, they understand them much better, but today felt like I was starting over at square one.

Then the lesson (pdf) was looking at direct and indirect variation via the gear ratios on a bike. Following Friday's lead (which I'm still not sure I want to do), I structured it out the wazoo. (Interesting - Firefox recognizes "wazoo" as spelled correctly, but not "pdf.") I brought in my bike, borrowed a stand from another teacher at school, and stepped them through how far the wheel turned for one turn of the pedals when in different gears. I pre-counted the teeth on the gears I was going to use and pre-filled in that part of the table, so the students could just concentrate on how far the wheel went each time. I had students volunteer to come up and turn the pedals, catch the tire, and write the number of wheel revolutions in the table, but other than that I led them through it. Again, I think there was value in doing this today, but I was still doing too much of the thinking.

For homework for Wednesday I gave them what I was anticipating would be a fun, but not too tough, problem involving Lance Armstrong and the Tour de France (although now I wonder), and had them finish the last two steps of the bike variation activity.

Sunday, August 29, 2010

Day 8

Today went better, but I'm not sure I like why it went better. It went better because I did more. I structured it more, I scaffolded it more, I led them through it more. It seemed to go better, but at what cost? It's going against what I'm trying to get them to do, going against be less helpful.

So I'm torn. It's not that I mind structuring and scaffolding if I think it helps them become curious learners, helps them get to the place where they can inquire and explore more on their own. But I don't think that's what I accomplished today. I think I structured and scaffolded and therefore they didn't have to think much.

We explored inverse variation today by looking at distance, rate and time. The opener (pdf) was review, and I thought pretty basic, but they are still struggling mightily with dimensional analysis. Then we moved on to the lesson (pdf). We first looked at a digital picture of a falling tennis ball and then tried to figure out how fast it was going, how long it had been falling, and what height it had been dropped from. This was a hopefully fun way to look at inverse variation and solving one-step equations.We then used this video (downloaded and edited so they couldn't see the calculated mph) to look at d = rt again (thanks again Dan), and talk about inverse variation and solving one-step equations some more.

Overall, they seemed engaged, it seemed to go well, except I don't think it really did. Frustrated I am (in my best Yoda voice).

Thursday, August 26, 2010

Day 7

I think I may actually be getting worse at this. While not horrible, today didn't go at all how I wanted it to. It started with us getting a late start primarily because they forget to reset the bells after Back to School Night last night (and partially because our Link Crew brought doughnuts for the freshmen and they met in the cafeteria, but mostly the bells). So we started a few minutes late and, well, you know how I'm doing on my timing, so that didn't help.

We started with an opener (pdf), as usual, and I really liked the problems on this one (my age in seconds, but without the units; converting Deepwater Horizon daily oil spill into number of 2 liter bottles per second). Unfortunately, they didn't really know how to approach problems 1 and 2, which are the ones I liked. That's partially because we ran out of time yesterday, but it's also partially because they seem hesitant to dive into anything they don't already know how to do. I wrote on the whiteboards next to the smart board where the problems were projected some hints to get them started, but they didn't even seem to be interested in writing that down. I think I'm not doing a very good job of communicating with them about how I want them to approach mathematics, or perhaps it's not so much communicating but I'm not convincing/encouraging/selling them.

We then moved on to the lesson (pdf), where I pulled data from The Biggest Loser to explore direct variation. The wheels really fell off here because it took them an inordinate amount of time to graph four points on graph paper. (Obviously, inordinate is in the eye of the beholder, in this case me.) Not only did it take a long time, but many of them didn't graph the points correctly. I had made the assumption, obviously a bad one, that graphing was something they had done enough of that asking them to graph four points, with a decent amount of scaffolding in terms of the how to construct and label the axes, would not be a difficult task. So, again, I'm left wondering if my expectations are too high, if my assumptions about their background knowledge are incorrect, or if I'm close to being right on and just haven't managed to get them to buy in. (And I think I showed some frustration for the first time today. I'm chalking that up at least partially to being tired from Back to School Night last night, but that's still not a very good excuse. I need to be more patient.)

I again had to cut my lesson short of where I had anticipated getting, but at least this time I cut it at the right point so that I didn't talk through the bell (perhaps 15 seconds to spare). So I asked them to finish parts a-f on the second page for homework (we did part a, and started on part b). In addition, their homework includes watching the video on solving one-step equations. This is the second instructional video I've asked them to watch, but I'm still unsure about how many of them are actually watching it. (As an aside, I've debated with myself about how much to "check up on them," and I'm still in the stage of letting them learn the ropes. I'm thinking we're at about the end of that stage, though.)

So, tomorrow is another day, but I'm pretty sure I have too much planned again. This weekend will give me a chance to redo my plans yet again, and perhaps I'll get closer to the sweet spot next week.

Wednesday, August 25, 2010

Day 6

Today was our first assessment (pdf) over something I've taught (the Math Skills Assessment was over stuff they've theoretically already learned) - Proportions and Percents. Overall, the students did very well, although I was still surprised by how long it took a few students to complete it.

We then talked about different measurements systems and the process of dimensional analysis (including calculating how much Steven Spielberg makes per second), but again it took much longer than I anticipated (lesson, pdf). We didn't get to the last set of examples, including figuring out today's price of gas in Australia - I still hope to share that sometime with them. (I did ask them to do the two problems above that for homework - we'll see how they do on that.)

For homework, they need to check to see how they did on the assessment and, if they need to re-assess, to start studying and then schedule an appointment to re-assess. On our online portal system they can see their grade on the assessment, and in the comments I included which problems they missed (if any) and sometimes some additional notes. With the key (pdf) posted as well, they should have a good start toward figuring out what they need to work on and then re-assessing.

They also have those two problems we didn't get to that I mentioned above, and a short survey on graphing calculators so that I can get a better feel for how many students have - or soon will have - those. I then reminded them that Back to School Night was tonight (I only had about 8 or 9 families show up out of 30 students) and they should invite their parents, and that they'll need graph paper tomorrow.

So, I'm still struggling with how long activities are going to take, but I'm pleased with the results of the assessment. Now if I could just get them to be a little more lively at 7:21 in the morning . . .

Monday, August 23, 2010

Day 5

Well, I did better on the timing today, but still not good enough. I had one extra example built-in that I had to skip, and I had wanted to give the students a few minutes to work on five quick review problems in class but we didn't get to those either. On the positive side, I think they were reasonably engaged in what we did do (although it's awfully hard to tell with teenagers in a first period Algebra class that starts at 7:21 am).

We started with an opener (pdf) like usual. I really liked the first problem and I shared my thinking with them when we went over it. I'm struggling a bit, though, with my expectations on the other ones. At this point my assumption is that they should be able to do the third and fourth one fairly quickly and easily, as we've spent several days on this. And some students are definitely there, but just not as many as I had hoped. That's at least partially because they are (so far) choosing not to do some of the things I've asked them to outside of class. We're still in the stage where I'm giving them some leeway to figure this all out, but pretty soon they are going to need to step up if they're going to be successful with the variable schedule that our high school runs. Is it unrealistic to expect high school Algebra students to do problems 3 and 4, with a calculator, fairly quickly after several days of practice?

We then went through several applications of proportion and percent (lesson, pdf). Borrowing from Dan Meyer (I'm going to be writing that a lot), I started with a clip from The Bone Collector. The character played by Angelina Jolie needs to take a picture of a footprint before it gets washed away by the rain, but places a dollar bill in the picture first. I showed the clip and asked, "Why did Angelina do that?" We then talked about needing a reference for scale and how to use proportions to figure out the length of the footprint (see the lesson for a still from the movie clip). Tip: It's always helpful to get a $20 bill out and put it on the document camera - gets their attention. We then figured out the length of the footprint, which I think is kind of cool. (Figuring out the length of a footprint created on a stage somewhere in California eleven years ago just from a still picture? Yeah, I think that's cool.)

We then looked at similar triangles and the fact that the lengths of corresponding sides are proportional (didn't derive that or anything, just asked what they noticed). We then used that to try to figure out the height of our gym from a picture I had taken a week ago. I think some of the students really got this, but some of them just thought it was more noise. Not sure what to do about that.

The third example was some basic sampling, following up on our capture-recapture work from Friday. We talked about whether our class was a good sample for the question (yes for lunch, no for driver's license), and then I actually went across the hall to Mr. Swomley's class to get the actual number for the dog question. (Aside: not sure if the student are appreciating my humor or quirkiness yet.)

Due to time, I skipped the fourth example about the chemical formula for TNT. I thought that was a nice, quick connection to Chemistry, but my inability to plan for time correctly is killing me.

We then finished with the stock market example. I really thought this was a good one when I was planning it, and I think it worked okay just in terms of practicing percents, but I think perhaps the stock market isn't quite something most of them relate to right now.

The last page of the lesson includes the problems I was hoping to get them started on, but instead suggested they work on as part of their review for the assessment on Wednesday. Visit the post on the class blog for the description I gave them of the day and their full homework (more on the upcoming Skype session in a future post).

Sunday, August 22, 2010

Day 4

Yep, three for three. I over-planned again for Friday. I got closer to timing it right, but was still rushed at the end. I'm hoping that if my progress over the last three days is linear, then by about Thursday of next week I'll have nailed it.

We did an opener (pdf) and the students seem to be getting that down pretty well. For our lesson (pdf), we did a capture-recapture simulation. First I showed an edited version of a Discovery Education Streaming video (if you have Discovery, it's the one titled Estimating and Proportions: Counting Sheep). I edited it because I wanted to emphasize how they setup the proportions, and I wanted to step through how to solve them with the students, so I added a couple of still shots in the middle, and also cut out some for length.

The capture-recapture simulation was pretty standard. I gave them paper bags with an unknown quantity of red beans in them and a baggie of white beans. They then reached in and pulled out a handful of red beans, removed them, and replaced them with an equal number of white beans. We then took samples and tried to predict how many beans. It seemed to go okay, but their predictions were all over the place (despite having a similar number of beans in each bag) and it was hard to tell if they completely understood what we did. I'm not sure if I didn't explain things well enough/we didn't talk about it enough, or if it's just too early in the morning and they got it fine, they just don't express it at that time of day.

You can see their homework over on the blog (as well as a couple of photos). They have an online pre-assessment to begin preparing for an assessment over proportions and percents next Wednesday, they need to submit their expectations for the class via a Google Form, and they need to watch The Math of Rock Climbing video (more on why we're watching that next week).

On Saturday I also emailed each student (to their new Google Apps account, although they may not be checking it regularly yet) to see if they had any questions about the class, and also to encourage them to get caught up if they were missing any of the homework assignments. I also urged them to re-assess over the Math Skills Assessment if they needed to - that's proving to be a tough sell so far (not unexpected given that most of them are freshmen and still getting used to the idea that they're supposed to come in on their unscheduled hours, but still frustrating).

So, overall the week was okay, but not stellar. I'm hopeful that I'll improve my planning so that the timing works out better, and that the students and I will continue to get to know each other better which should help facilitate the learning. We'll see.

Thursday, August 19, 2010

Day 3

Yep, over-planned today, too. After not having enough time yesterday, I removed one of the examples I had planned to use today, but still ran a little short of time. I guess that's progress, but I hope that either I get better at estimating how long things are going to take, or my students settle into the system a little bit and perhaps things will move a little more quickly (or, ideally, both of those things will happen).

Today we once again started with an opener (pdf). I was impressed that all the students were in their seats and had started the opener by the time the bell rang. When we did our first one yesterday, I said that was the expectation. If they want a little extra time, then they can start a couple of minutes early if they want (or even more than a couple of minutes since it's a first period class). If they don't want any extra time, then they just need to be ready and begin right when the bell rings. The students did a great job with it today.

I particularly liked opener #4 today, as it was a little non-standard. I knew it would throw some (most?) of the students a little bit, but Grant was willing to stick his neck out and try answering it. (I didn't make him write out his answer, so you can't see it on the linked pdf, but he explained it.) Interestingly, he solved it the way I would've solved it, which was estimating ceiling tile width, counting the tiles, and multiplying. He estimated 3 feet per tile instead of 4, but I still thought that was great thinking as well as a willingess to take a risk and share. I was disappointed, though, that when I asked for any other approached students took no one volunteered one, but I realize it's still the first week. Hopefully we'll get there.

We then talked about their Math Skills Assessment and how important it was for them to get help on any areas they weren't proficient in, then come in and re-assess. I can tell this is a tough sell for many of them, which is pretty typical since most of them are ninth graders, but I was still hoping more of them would jump on the chance to improve.

We then moved into our first real lesson, learning about ratios and proportions (lesson, pdf). I thought it went well except for running out of time and leaving one really nice example off (which I'm hoping to come back to next week). I definitely need to work on spacing of my Smart Notebook files so that I leave enough room to write. I think it's okay when I'm talking with them in the room, but if they go back to review the file online it can get confusing.

Today was also the first day they were in groups. When they walked in I already had the desks in groups. I had them work on their openers individually (and quietly) for about four minutes or so (many had more time, of course, since they started before the bell). Then they had a few minutes to discuss it with their group before we went over them as a class. Before they discussed as a group, I had each group do a quick whip-around, introducing themselves and telling what kind of pet they had (or, if they didn't have a pet, what kind of pet they'd like to have).

The lesson was also primarily group work, although I directed it a lot in the beginning and then tapered off some throughout the class. Again, because I misjudged on time, I think I ended up rushing them a little faster than I should've and didn't let the groups struggle for as long as I wanted them to. Again, I'll hopefully get better with this.

We then briefly talked about their homework, including a too-quick discussion of how they should use the video. I'm hopeful they read the blog post carefully to really understand the three main sections of the video and how to use them, but I suspect I'll have to revisit this several times over the next couple of weeks before it really makes sense to them.

Wednesday, August 18, 2010

Day 2

I over-planned for today. We were only able to complete two of the three things I had hoped for today. I'm trying to tell myself that it's good to over-plan, but now I'm worried about my expectations for how much I can get done in a given class period.

Today we started with an opener (pdf) that was designed to both introduce the class to how we're going to do openers, and to give them a quick review before they took the Math Skills Assessment. When they walked into class I gave them a sample notebook page to show them how I wanted them to organize their notebooks, but I also said that if they wanted to use a different organization system they could, but they had to talk to me first and explain why they think it would work better.

After they worked the openers, we then went over them as a class. I worked out the first one (conveniently the most difficult one), let Vic (my special services cooperating teacher) work out the second one, then invited students up to work out the third and fourth before I finished the fifth one. Lots of silence when I asked for volunteers, but eventually someone did both times. This took about twice as long as I had planned for (probably 16-18 minutes).

Then they took the Math Department Skills Assessment, which all of the Algebra teachers at my school give in the first couple of days. They worked on that for about 20-25 minutes (I had anticipated more like 15-18), I collected them and then, because we were short on time, I worked out the key (pdf). I had intended on alternating on the key just like the opener, I'd do one, then a student, and so on, but I could tell I was going to run out of time so I just did them all.

At the end of class I quickly told them their homework for the night (as always, posted to the class blog):
  1. Check our online portal to see their grades on today's assessment. I broke the assessment down into the four skill areas (Adding & Subtracting Fractions, Multiplying & Dividing Fractions, Integer Operations, and Order of Operations), and they are responsible for getting help and then re-assessing on any one they scored less than a 4.5 on (on my 5-point scale).

  2. While they're on the portal, they should look up their Google Apps account info. This just got turned on, so I gave them instructions for how to look it up, and then they need to login, get to their email, and reply with a "got it" to a message that's there waiting for them.
Overall, the day was okay, but not what I was hoping for. Hopefully tomorrow, when we actually get to do some mathematics, will be better.

Monday, August 16, 2010

Day One

Today was the first day of school and it was kind of anticlimactic. On the first day of school each class has a class meeting during one period, and the freshmen class met during first period. Since the majority of my class is freshmen, I only got to see them for about twelve minutes before taking them to the class meeting.

I knew that going in, so I didn't plan a lesson, we just went over a few things about the class. When they walked in they found Algebra textbooks on their desks, each one with a slip of paper on it that had their name so they could find their desk (mostly alphabetical to start, helps me learn their names, but a few students were out of order because they need to be in the front). The paper also had the URL for the class blog on it and a message that that's where they could find the homework for tonight.

I greeted them at the door and said hi, then as they found their desks I had on the projector what they should do (find their desk, write their name and my name in the textbook, and that the freshmen would be leaving for their class meeting in about 10 minutes). After the bell rang I welcomed them and asked them to put their names in the textbook if they hadn't already as I went around and made sure I was pronouncing their names correctly.

Then we talked briefly about the weird schedule today and then I showed them the class blog and talked about each piece of their homework for Wednesday (our class meets four days a week, MWRF, so they don't have Algebra tomorrow). As you can see from today's post on the class blog, their homework was the following:
  1. Bookmark the class blog on the computer they'll be using at home. I talked about how they'll be visiting it pretty much every day, so they're probably going to want to make it easily accessible.
  2. Then they needed to review for the Math Skills Assessment. This is something the math department at my school does in the first couple of days of school for Algebra classes, to assess where they're at in terms of the basic computation skills they need to be successful in Algebra. As you can see from the Math Skills Assessment website, this year we asked students to work on it over the summer. As of this writing, we have 338 students who self-reported that they completed it (out of a freshmen class of about 580). That number probably includes a few who didn't and a few who filled it out twice, but there are also probably students who completed it and forgot to fill out the form.
  3. Then I asked them to read through our Class Expectations and then fill out the form to indicate they've read them. I also encouraged them to have their class supplies with them by Wednesday. Some of the students had already completed this, as it was part of the email to their parents I sent out about a week ago, but most have not.
  4. Then I asked them to write their About Me and get it to me as soon as they could. Again, several students had already completed this ahead of time, which was nice because I was able to refer to a piece of info about them in class when I was talking about the assignment. "I know so-and-so can probably dance just a little bit better than me. Of course, when I grew up Disco was popular, so all of you can probably dance better than me . . ."
  5. Then the last part of their homework was to take their textbook home and place it wherever they study, take a digital picture of it, and then email it to me. We won't be using the textbook in class, so I want it safely home where they can use it as a resource when they need it.
Then we had a little time left so I took them on a "field trip" of sorts. We walked by the Math Office so they could see where they could go to get help if I'm not available, then we walked by my office (I'm not in the Math Office because of the rest of my responsibilities) and talked briefly about how they can get help from me (schedule it in advance if they know in advance and I'll put it on my calendar and make every effort to be there, but if they don't know in advance they can always drop by and see if I'm there - they just can't count on it because I'm so often out and about in the building). We also talked about our Study Center as another place they could get help, but I couldn't show them that both because we were out of time and that's where students who hadn't picked up their schedules yet were getting them.

It's hard to do much in 12 minutes, and I always hate the first few weeks before we get to know each other and they're so quiet, but the day went fine given the circumstances. Wednesday we'll start with an opener and then the Math Skills Assessment, and then we'll develop some expectations for each other. That last part will be the first chance to really start talking/working with each other.

Friday, August 13, 2010

Welcome to the Blog

I've documented my partial return to the classroom over on The Fischbowl, but this is the place where I plan (hope?) to regularly reflect on my practice this year. I'm not promising anything, as the demands on my time have significantly increased (and they weren't too shabby before), but I'm going to give it a shot. If I do manage to blog semi-regularly here, I'd love for you to come along for the ride.

Students start on Monday.