The End

Due to schedule constraints next week, it looks like this will be the last time I was able to be at Ypsilanti High School for the partnership program, so this will be my last post about it. This was also the last day for seniors, and unexpectedly a half-day - teachers are given the other half of the day to work on taking stuff off of the walls, and packing up, since there will be a lot of renovations going on over the summer.

Unfortunately, I didn't get to see the first-hour physics students, since the half-day was the later classes (although in the morning). I did get to visit with one of Mr. Ambrose's afternoon chemistry classes, and I was in Ms. Colwell's algebra class. Her students were working on factoring polynomials, and they were actually pretty diligent for a half-day/last day for seniors/day before a holiday weekend. Some of them were having trouble, so I showed them how I handle difficult polynomials - set up a table of the factors of the constant term and go through them to see which one works. Given only a few possible factors for the kinds of numbers they're seeing, this isn't very time-consuming, and it helps when you can't see things right away. I wished them all good luck, as well as Ms. Colwell.

As I think back on the year - on what I expected, and what I experienced - a few things come to mind. First, I've got a much greater appreciation for high school teachers. It's a tough job. Second, I was surprised that there don't seem to be any books of "typical labs". There are books teachers can buy with worksheets that they can photocopy and use in their classes, but if there are books of labs - instructions and lab sheets for students - no one seems to have them. If I had known this up front, then before starting the program I might have tried to work on some ideas for labs. During the year, it's difficult sometimes to plan things "on the fly". Third, I was interested to see the ways that it's possible to connect with students. Sometimes, a chance comment about an experience of mine would tie in to something that they had dealt with - often when least expected. Fourth, it was great to see that the students really liked to see practical applications of what they learned, since that was something that we as Teaching Fellows are capable of bringing to the classroom.

It's been a really interesting year, and the partnership program is a great one. Although I won't be able to participate next year, I look forward to reading the posts by the students at Michigan who will be participating, and I wish them the best of luck.

Cedar Point!

The field trip to Cedar Point was very tiring, but a lot of fun. Mr. Ambrose and I carpooled, while his students who were going rode the bus with Ms. Jones' physics students. When we got there, the students started out by getting the work done so they could concentrate on having fun after lunch. For their first activity, they had to try to find the height of the Space Spiral using their sextent - looking at its top, getting an angular measurement, then pacing off a particular distance and taking another measurement. We discovered that the sectant was difficult to use to get accurate results - while they did get a pretty good result, it took a number of different tries, and was very touchy. Small errors in the angular measurement could result in large errors in the result, which was an important point. The photos below show Mr. Ambrose and the students using the sextant, pacing off distances (and calibrating their pacing with a tape measure), and doing the data recording and calculations.

The students analyzed several other rides as well - the carousel (circular motion measurements and calculations), the Demon Drop (free-fall), the Wicked Twister, and their choice of one of the park's roller coasters (energy and kinematic equations). Of course, once the analysis was done, it was time for fun, and they went on quite a few rides just to enjoy them - including some that were a little much for me, though I did go with them on the Demon Drop, a few of the roller coasters, the carousel, and one of those rides that spins you around really fast.

I've got a lot of pictures, more than I can reasonably post here. I'll put the rest of them on CTOOLS for anyone else in the program who wants them, and I've already burned a set of CD's for Mr. Ambrose and for the students - I'm sure they'll want to have them as a memento of their trip.

Upcoming Field Trip

In Mr. Ambrose's physics class, they're now covering electric potential, preparing to do a little bit with circuits. They're also preparing for a field trip which some of them are taking - a trip to Cedar Point on Monday. I've been invited me to join them, so Mr. Ambrose and I will be carpooling down there, and the students will be on the bus with physics students from the other physics classes (taught by a different teacher). It should be a lot of fun - I've just put new batteries in my camera, so I should be able to get one or two pictures of students using homemade accelerometers on amusement park rides. Watch this blog for a few good photos... if all goes well with the camera, I'll post pictures and a summary of the trip sometime next week.

In Ms. Colwell's class, they were working on a review sheet for an upcoming test - they're having a test on trigonometry next Tuesday. Ms. Colwell mentioned that she'd like to take a field trip, if there was something that would be both fun for the students and relevant, and I thought that perhaps a planetarium trip would be suitable, if someone could explain how trigonometry has been used for celestial navigation. I'm going to investigate the possibility and see if there's anything suitable at U of M - even if it doesn't work out for this year (time is rapidly running out), it might make a great trip for her classes next year. I'm sure there are lots of great things at U of M that would make good field trips for students - maybe someone could make a list of them, and supply that to our partner teachers. Not only would it make it easier for them to plan field trips to the university, it might spark some ideas on their part for programs or trips.

Starting to wind down...

The school year is winding down for Ypsilanti High, and the teachers are planning on what material they need to finish up for the year. In Mr. Ambrose's physics class, they're going to be doing electric potential, capacitance, and circuits next - they had a test today over electric charge and electric fields. I've got an idea for an interesting lab - I talked to Mr. Ambrose about it, and he likes the idea, so I'll make sure it'll work and then we can look at getting the necessary supplies. If it does work, I'll describe it in a blog entry, and post the handout sheet on CTOOLS.

In Ms. Colwell's class, they've gotten to the Law of Sines and the Law of Cosines. Most of them seem to be doing pretty well with trigonometry, despite the fact that they're distracted and anxious for the end of the school year. Most of the seniors I've talked to have a countdown calendar, and they're really anxious for their graduation - understandable!

I'm starting to give some thought to what I'll do on the last day I'm in the classroom. I'd like to leave them with some kind of memory of that last day - not sure what yet. But I have a few weeks yet to think about it.

Bridge Pictures!

Here are the pictures from the bridge-testing day... I'll let the photos speak for themselves.

Just a few weeks to go...

There are only a few weeks left for seniors - about five weeks, as I recall, though if you ask them, they can tell exactly how many days they have left! Some of them are getting restless and it seems harder for them to settle down and pay attention. I can certainly sympathize - I remember what it was like when I was a senior - the weather was warm, an exciting future beckoned, and it was difficult to keep in mind that high school wasn't quite over yet.

In physics, Mr. Ambrose is teaching them electricity. Some of the material is difficult, but he's giving them a variety of harder and easier problems, so they can work their way into the hard stuff. Even though some of them grumbled a bit at first about the bridge project, they were asking for a new design project, so we're going to see what kind of an electric design project we can come up with - perhaps something where they make resistors, or capacitors, and put them into a simple circuit. It has to be complex enough to be challenging, but simple enough to get done in the remaining class time.

In Ms. Colwell's class, they're starting to get into trigonometry. Some of them seem to be picking up on it easily, but others aren't quite comfortable yet with our friends sine, cosine, and tangent. As usual, they wanted to know what this stuff is good for. One use, naturally, is in physics, with vectors. I also mentioned that you can use it anytime you're looking at angles - for example, if you want to know if you can get a piece of furniture through a doorway and perhaps around a corner. I'll give some thought to it, and see if I can come up with a few other good examples of trig that would be interesting and connect it to their lives.

Bridge testing

Well, today was bridge-testing day in Mr. Ambrose's class. All of the students' bridges passed - all held at least the specified two pounds! Most held more. First, we tested Mr. Ambrose's bridge; it started to crack with about 1.5 kg on it (which is a between 3 and 4 pounds). Then, we went through the students' bridges. Some just wanted the test weight on it; others wanted to keep putting on more to see how much it would hold. They seemed to be having fun, even those who hadn't been too enthusiasitic in the beginning. One bridge COULDN'T be destroyed with the weights available - we ran out of weights, and the stack was getting unstable, but the bridge didn't even visibly bend.

After testing the bridges, I put most of them onto the balance to see what their mass was. The heaviest was still under 20 grams in mass. We gathered back together as a class, and I pointed out that by using physics knowledge, they were able to make bridges that would hold many times their own weight, and contrasted that to early bridges, which were made large and massive since the people building them didn't know how to design them to be lighter. It seems like they learned something, and they had fun, so I'd call the project a success.

I did take my camera with, but the batteries died. Fortunately, Mr. Ambrose had his camera and took pictures; as soon as I get them from him, I'll post them on CTOOLS and perhaps put one or two on the blog. I should have them next week.

Back from Spring Break

Today, everyone was back from Spring Break, and a lot of people looked very tired - it's difficult to get back to waking up in the morning. Students have heard back from most of the colleges, it seems, and are making their decisions. One young man in Mr. Ambrose's physics class is going to Hampton, in Virginia. A young lady in the same class is trying to decide among Harvard, Yale, and Princeton. It sounds like the choice will come down to either Yale or Princeton for her - all are well-respected schools, of course. Of course, quite a few are going to Eastern. In that class, no one has selected the University of Michigan, but in Ms. Colwell's advanced algebra class, there are several juniors who have said they might consider Michigan.

In both classes, they were reviewing. Mr. Ambrose is giving a physics test, on light, tomorrow; Ms. Colwell is giving a quiz tomorrow on logarithms. The students all needed the review - many people forgot a lot over the break.

On Friday, we'll be testing the bridges in physics. If I remember my camera, I'll get some pictures of them, and post them, either as part of the blog post or on CTOOLS.

Day Before Spring Break

Next week, Ypsilanti High will be on spring break. A lot of students are already gone, and most were having trouble concentrating. It looked like about half of Mr. Ambrose's physics class was there. They worked a bit on a review worksheet on light, and had time to work on their bridges. Most are coming along pretty well; during the week after break, we'll put the two-pound weight on them, and see if they hold. Mr. Ambrose built a bridge himself, and it holds a full kilogram (2.2 pounds) without breaking. A few of them were surprised to see that, but the point I want them to get is that it isn't how much material but how well it's used.

In Ms. Colwell's class, I gave the presentation I'd prepared on logarithms. I tried to keep their attention by asking questions - when talking about decibels of sound, I asked them how many have iPods (most). And, when talking about pH, I asked how many of them are taking chemistry. Most of them at least listened politely - they seem to like it when I give little presentations, especially since the short worksheet I put together to go with it takes the place of their normal warm-up assignment. And, since some of the questions are conceptual, there are no right or wrong answers to worry about.

I also spoke to Ms. Colwell about an idea I had for an activity - have them make up their own number system, similar to the imaginary numbers. Make a few definitions, then figure out what they lead to. I have to think a bit about how to make it structured enough to give them some direction, but unstructured enough to allow room for creativity and fun. And, she wants to think about where best to place it in the schedule. One of the things I'd like them to see is that math isn't a robotic enterprise, it's a creative one. This will take a little bit of time to figure out, and maybe the best time for it would be in early May - maybe when they're between units towards the end of the semester.

Continuing the Construction

In Mr. Ambrose's physics class, he taught for a while - about light - and then gave the class time to work on their bridges. Some of them are having trouble, but others are coming along quite well. He built one himself, and we tested it with a 1-kg weight (2.2 pounds) - it held. The weight specified is 2 pounds, so if someone wants to see an example of a bridge that will withstand the weight, we have one. The due date for the assignment will be the Monday after spring break - that way, if they can't finish in class, they can make arrangements to meet their teammates to work over the break. Some of them work very well, but others need to learn how to use time wisely - it's a skill that will serve them well throughout their lives.

In Ms. Colwell's advanced algebra class, there was a substitute teacher. She's expected back Monday, so she just left a worksheet for the students to work on, and I spent my time there helping them when they got stuck. As I talked to the students, it became clear that some of them are still confused about what my purpose in the classroom is - they can't quite understand the difference between a U of M teaching fellow/graduate student and a student teacher. I wonder if there's some way we could build up a clear identity for the program in the students' minds... the obvious first thought is something like polo shirts with the OE^2 logo on them. There may be a better idea, but it's definitely something to think about, because part of the impact of giving them a role model could be lost if they aren't sure what the model's role is in the first place.

Starting to build

Today in Mr. Ambrose's physics class, the students started building their bridges. They all seemed to be having fun with it, even the young lady who wasn't paying attention on Friday. Some of them got farther than others; gluing toothpicks together takes a bit of practice, to avoid disturbing other toothpicks while placing new ones. Some students did try to get the project changed - asking if we could use tape, or straws, or Popsicle sticks, or some other modification that would make it easier. Of course, if the bridges were easier to build, we'd require them to hold more than 2 pounds - after all, 2 pounds isn't all that much.

Having a project like this also makes it easy to walk around and talk to the students, and see how they're doing in general. One very bright, ambitious young lady is planning to visit the colleges that have admitted her, so she can figure out which one to attend. She's got quite a tour planned, including both Yale and Harvard. She's also begun to consider graduate school. I'm encouraging that - she's smart enough that she'd be able to get funding from any kind of graduate program, particularly with a degree from a well-known university. She's the type of student who will take advantage of every opportunity that's available to her, work hard, and make the most of it.

In Ms. Colwell's advanced algebra class, they were working on a review worksheet for an upcoming test. Some of the students were stuck on particular problems; for some of them, radical equations were a massive headache, so we worked through a few of them together. They also got a quiz back. One young woman was really frustrated with herself - she got a B on the quiz, and quite a solid one, but she saw that all of her mistakes were avoidable. For example, the square root of five, squared, is five; she had written down 25 in that step of the problem. She's determined NOT to do that on the test. At least, since her handwriting is nice and neat, she'd get partial credit because it's possible to see where the error is.

Some of the students still don't want to use their class time productively, to get actual work done. Some of them say that they're tired. I always sympathize with that, because I'm often tired, too. I've gone in to YHS sometimes when I've had only four hours' sleep, and if I wasn't so busy, I could have easily fallen asleep. Once some of them found out how often I'm up half the night, they knew that I understand what it's like to be tired. When I try to get them to work through something, they'll usually at least make an effort, even if they were up half the night themselves.

Their Spring Break will be coming up in a few weeks, but in the immediate future, they get a long weekend - they have both Friday and Monday off for Easter weekend. It seems to me that, second semester, they get a lot more long weekends than they did during the first semester.

Beginning on Bridges

Today, in Mr. Ambrose's physics class, we introduced the bridges project. I went through the handout, and then showed them how you could work through a bridge truss, with the knowledge they already have, to find the forces present in each link. The point I wanted them to take away, and I think most of them got it, is that it's really just an application of what they already know. Then, they were instructed to form groups of up to three, and on Monday we'll start building. When the project is done, we'll test them to make sure they hold the required 2 pounds of weight, and then the lightest one that meets specifications gets extra credit points. Some of the students seem very enthusiastic, but there are a few who aren't. One young woman was not only not paying attention as the project was described, she was actively ignoring me and working on something else. That's a little bit discouraging - not only does it show a lack of interest, but I feel it shows a lack of respect. On the other hand, some of them were jumping in enthusiastically. They were a bit unruly - jumping in and interrupting at times - but at least it was obvious they were paying attention to what was going on, and they cared. I just wish I had a good way to handle people who are very obvious about their disinterest - a sarcastic remark isn't very adult or very professional, and a request to pay attention gets ignored.

In Ms. Colwell's advanced algebra class, they learned about radical equations, and how to solve them. She also pointed out that in these equations it's possible to find false solutions - things that fall out of totally valid math when you solve them, but are not themselves correct solutions when you plug them back in to check. She also gave a quiz, and while the students took the quiz, we talked about logs. They're going to be getting into logarithms, and she'd like me to give them some perspective on what logs are used for. I can certainly do that - starting with the log scale, which is used so often to plot things, and then logs fall naturally out of so many other things. On Monday, I'll have to talk to her about when would be the best time for that.

Next week, I'll be in on Monday, but not on Friday - it's Good Friday, and like University of Michigan, the Ypsilanti Public Schools are closed.

Bridges of Ypsilanti High

We were planning, originally, to start on a design project today in Mr. Ambrose's physics class, but that's been put off till next week - Ypsilanti High School had a snow day on Wednesday, and that pushed back other things, including a test. While I'm sure many students would prefer to work on a design project, the test really had to be given before the end of the marking period. Everything is ready to go, though, so next week we can start on the project. The students will be learning about trusses, using the physics they've learned to understand how a truss works, and then designing and building truss bridges out of toothpicks. The handout that they're going to be given will be posed on the CTOOLS site, in case any of the other Teaching Fellows want to look at it.

I did, unexpectedly, end up helping briefly in another physics class. The other physics teacher is out for a while, so her class has a substitute. The substitute doesn't have any background in physics, so during Mr. Ambrose's preparation period, we both went over there for a few minutes to help those students get started on their worksheets. I also put in a plug for the U of M tutoring - I told them that if they're having trouble, they should go to the tutoring and get help. With their regular teacher out, it would be especially useful. I can remember when I was in high school (back in the ages of stone tablets and quill pens), and we had substitutes, sometimes it was hard to learn the material. It could be very frustrating.

In Ms. Colwell's class, they're going to be having a test next week sometime. Today, they were working with radical notation. Some of them were having a little trouble figuring out problems like the square root of the square root of the square root of the square root of a variable to the power 256 - it really isn't hard once someone catches on that the square root sign is the same thing as the 1/2 exponent, which they've worked with before. Sometimes it seems notation trips up a lot of people - they take some time to really catch on to the fact that sometimes, two seemingly different things are just the same concept dressed up a little differently.

Physics and Future Plans

Today was a fairly quiet day... Mr. Ambrose gave his physics student a quiz. There was, as usual, some grumbling about that - no one really likes quizzes that much. They seem to be almost done with the wave material they're covering, so they'll be moving on to a new unit soon.

After going to a teacher's event at U of M, Mr. Ambrose has decided that he'd like to get some design experiences into the class, so we talked about that today. We're going to start with designing and building toothpick bridges - they're easy and simple - and then move on to do some other things. Fridays and Mondays, when I'm there, will be the designated day for those projects. I think the students will like it - we'll see how long they take before deciding how many there will be. This should be a really good way for me to have more of an impact, beyond helping with labs and things, and really let them see for themselves what engineers do.

Doing the Wave

Mr. Ambrose has started a new topic in physics - wave motion. Today, after a brief lecture, he had the students experimenting with long extension coil springs - and by long, I mean about 6 or 7 feet in their relaxed state. They worked in pairs and created both transverse and longitudinal waves, generated standing waves, and saw that waves would bounce off of the other end and return, and that two waves would pass through each other. There was no formal lab report, but they were required to participate, and most of them seemed to be having fun with it.

In Ms. Colwell's algebra class, they're getting ready for a quiz on Monday. They really don't want it then, but the snow day earlier this semester did disrupt the schedule a bit. I can sympathize with them - a day off at the time is nice, but it does have repercussions later. I talked with one of the young women in the class who had trouble grasping the whole purpose of imaginary numbers, and she's happier with some of what they've done more recently - their warm-up today included a problem on compound interest. She could not only understand that problem, but also see how it impacts her life. Imaginary numbers seemed very abstract to some of them. They're also working with powers, and most of them seem to understand that fairly well. Ms. Colwell always tries to tell them about applications for the math they're learning, so she mentioned that a lot of equations in science have a variable to some power.

So, what is all this stuff good for, anyway?

There was a special event going on today, and only five students were in Mr. Ambrose’s physics class. Instead of covering something that the majority would have to make up, he had a class activity with an air track – demonstrating elastic and inelastic collisions. The velocities of the cars on the track were measured with photogates, and we checked to see if momentum was conserved. We expected to see that a little bit of momentum would be lost, but that it would be close. Unfortunately, that wasn’t the case – the cars gained momentum. So, either we broke a law of physics, or else there was a large source of experimental error. We did find one big source – the air track wasn’t level. The cars were being accelerated by gravity, which messed up the results. Despite not being level, one set of results was within 25%, which isn’t bad for an ad-hoc setup.

In Ms. Colwell’s class, I gave a short presentation on the uses for imaginary numbers. They’re really not that hard to work with, given a little bit of practice, but conceptually they seem a bit remote from ordinary experience. Some of the students seem to be very “concrete” thinkers, and couldn’t quite grasp the meaning of imaginary numbers last week when they were learning about them. This is a common problem, I’d expect. I don’t remember what I thought when I first encountered them – I graduated from high school back in 1989, so it has been a little while – but several very prominent mathematicians had trouble with them. One girl’s comments last week echoed a quote from Leibniz - “I did not understand how… a quantity could be real, when imaginary or impossible numbers were used to express it.” She was having trouble with the idea that you could multiply a complex number by its complex conjugate and end up with something purely real. On the worksheet I gave them, I included a few quotes like this, and asked them for their views on complex numbers. There are no right or wrong answers – but I wanted to see them think about what the numbers mean.

In some contexts, they do have a real physical meaning, and that’s what the presentation was meant to show them. I chose two examples of places where imaginaries have real uses – electronic circuits, and control systems. In electrical engineering, use of imaginary numbers allows inductors and capacitors to be treated like resistors, and circuits to be described by algebraic equations rather than differential equations, which is a major simplification. In control systems, a particular system has a characteristic equation, and the real and imaginary parts of the roots tell different things about the system; the imaginary part tells how oscillatory it is – or as I described it to them, how “bouncy” it is. Obviously, in just a short time, I couldn’t go into any depth, but the goal was to let them know that these things do have uses and even physical meaning.

Next, they move on to powers. They’ve long been familiar with the very basics – squaring, cubing, etc. – but now they get to move on to negative and fractional powers. It’ll be interesting to see what kinds of conceptual difficulties this presents; again, it takes a simple concept that they can picture and extends it into a realm where it isn’t as easy to grasp.

I won’t be in on either Friday or next Monday, since they have a break – the students get a five-day weekend, and the teachers get four days, with a professional development day next Tuesday. So, my next post will most likely be a week from this Friday, when I’m back.

Back from a Surprise Three-Day Weekend

Friday morning, I checked the website for the local school closings, and discovered that the Ypsilanti Schools were closed due to snow. So, today when I went in, I hadn't seen the kids since last Monday, and they'd just had a three-day weekend.

In physics, they started off with a quiz on momentum. Some of the students said they'd forgotten too much over the weekend, but Mr. Ambrose lets them use their notes, books, and worksheets - everything but their neighbors - so if they've kept up with the work, then they've got plenty of material to draw on. Most of them seemed to finish up without problems, though two need to come in to finish later. (Makes me wish I could do that with tests - it would make them a lot easier!) After the quiz, they went over elastic and inelastic collisions. They should be finishing up momentum soon, and then they'll be moving on to other topics like electricity.

In Ms. Colwell's advanced algebra class, they're working with complex numbers. One girl couldn't quite understand how a number that "isn't there" could mean anything - she asked, how could you have "i" apples? Her math skills are good, but she seems to need to tie everything to physical objects. Another girl mentioned that her older brother is studying electrical engineering - I'm sure he uses plenty of complex numbers. Since I use them a lot - they're ubiquitous in controls work - I offered to put together a brief presentation for the class. Ms. Colwell and I agreed that next Monday would be a good time for it, since they have a test scheduled for Friday. I can also make up a brief worksheet to go with it that can be used as a warm-up - the assignment that gets them to settle down and work, and which keeps them busy while she takes attendance. Maybe, if they see areas where complex numbers are used, they'll seem a little more "real" to them. I can't blame them for having some conceptual difficulty - after all, for a long time mathematicians had trouble figuring out complex numbers. Descartes, who certainly was a talented mathematician, dismissed them as being meaningless. I've told some of them about things like that, and that it's OK to have trouble visualizing these things. They're easy enough to work with but they can be hard to understand. The fact that we don't even blink at them doesn't mean they're easy - it means they're familiar.

Starting the Second Semester

Today, students at Ypsilanti High started their second semester. There were a few changes in who was in various classes; one of the physics students in Mr. Ambrose's class is gone (part of the Early College program), and there's a new student in that class. In Ms. Colwell's advanced algebra class, there was at least one new face and a few students were either absent or in another class.

In physics, one of the students was excited to tell us that she had gotten into Yale. She isn't sure if that's where she'll go or not, until she hears from other schools, so a few people were teasing her about Yale being her "safety school". In terms of material, they had a simple introduction (via a worksheet) to the concept of momentum. After class, Mr. Ambrose and I talked about what kind of a lab would be useful for momentum. There are a lot of cool things that could be done, but many of them take expensive equipment that he just doesn't have.

In advanced algebra, they learned how to find the equation of a quadratic equation that fits data. Ms. Colwell showed them how to do it by hand with three data points, and also how to enter it into the graphing calculator and let it do the work. She does that a lot - shows them both how to do it on paper, and also how to use the tools they have. Personally, I think that's a good approach; sometimes, doing it by hand is actually faster, or it gives more insight into the process - but it's also important to be able to use the available tools to be more efficient when using it as a means to an end.

Review time

The semester is almost over at Ypsilanti High School. They have regular classes this week, then next week Monday's a holiday (King Day) and then they have exams on Tuesday, Wednesday, and Thursday. Some classes also have a test coming up this week, so the students have a lot of review to do. In Mr. Ambrose's physics class, he gave answers to one worksheet, answered questions, and gave out a quiz review worksheet. While they worked on it, I helped some of the students who were having trouble. I think most of them are going to do well, but there are a few who still need some work to get up to speed. In Ms. Colwell's advanced algebra class, they were working with quadratic equations and completing the square - taking a standard-form parabola and using the completing the square technique to put it into the form y - h = a(x - k)^2. Then, after their lesson, they had a quiz. During the lesson, Ms. Colwell gave them one or two problems to work out, and I helped a few students. Some of them don't even try when a problem is put up on the overhead for them to work, unless someone comes over and works with them - it isn't that they don't know how, because they do the problem correctly, but they just don't seem to want to bother.

Friday I'll be there, helping students as they review in class for their final exams, then next week I'll be off - as I said, Monday's a holiday, then they have three days of exams, then Friday is a day off for them. Since the new matches haven't been made yet, after the exams I'll return to the same classes, and keep working with them until the new TA/teacher matches are made. After that, I don't know if I'll be working with the same teachers or with different ones - we'll see how that works out.

Starting a new year

Today was the first day for the students after their winter break, and I was back at Ypsilanti High. The students were having a hard time settling down to work, for the most part. Most of them wanted to catch up with friends, and a lot of them were tired - like me, when they don't have to get up at 6 a.m., they generally don't, so getting up early again will take some getting used to.

In Mr. Ambrose's physics class, he started out with a worksheet that they did together, to get their memories refreshed. They're currently working with the concepts of work and energy, and tomorrow they'll be doing a lab - it's a pity I'll be missing that, labs are fun.

In Ms. Colwell's class, they're getting into quadratic equations. They've seen parabolas before, and have had some exposure to quadratics, but now they're getting into them in more depth, including the ubiquitous quadratic formula we all know and love. They had a short lesson, then time for homework. Some of them needed to be kind of coaxed into at least doing a few problems, since they just didn't feel like working. I helped out several of them get started - once the work gets started, it doesn't look quite so intimidating.