YPSD Math and Physics Classroom Experience

The End

2008-05-23T06:42:00.000-07:00

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!

2008-05-12T19:29:00.001-07:00

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

2008-05-09T10:35:00.000-07:00

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...

2008-05-02T09:38:00.000-07:00

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!

2008-04-25T09:27:00.000-07:00

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

Just a few weeks to go...

2008-04-21T13:38:00.000-07:00

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

2008-04-18T08:42:00.001-07:00

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

2008-04-14T09:30:00.000-07:00

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

2008-04-04T09:46:00.001-07:00

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

2008-03-28T10:24:00.000-07:00

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

2008-03-17T12:44:00.000-07:00

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

2008-03-14T10:23:00.000-07:00

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

2008-03-07T23:25:00.000-08:00

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

2008-02-29T08:41:00.000-08:00

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

2008-02-22T10:02:00.000-08:00

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?

2008-02-11T09:02:00.000-08:00

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

2008-02-04T09:39:00.000-08:00

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

2008-01-28T10:40:00.000-08:00

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

2008-01-14T09:31:00.000-08:00

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

2008-01-07T12:06:00.001-08:00

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.

Presentation to Algebra students

2007-12-14T10:28:00.000-08:00

Today, I presented to Ms. Colwell's algebra students - in two classes, actually. Normally I'm in her fourth hour, today I was in both her third and fourth hours. The presentation was on optimization, which ties into what they've done recently with linear programming. I showed what linear programming versus non-linear programming were by building a model with foamcore, hot-melt glue, and floral foam. The model is shown at the left - the blue and gold model is the linear programming model, and the blue and green model is the nonlinear one. (Unfortunately, they don't make floral foam in U of M colors!) I showed them that if you try to find the minimum, in the linear case, there's only one point - drop a marble in, and it always rolls to the same spot. If you drop a marble into the nonlinear one, it can go to different places, either internal or on the boundary.

The students had a worksheet that I'd made up, and the answers to the questions were all in the presentation that I gave. I explained how to set up an optimization problem - choose the system of interest, get an objective function, select variables, formulate constraints - and a little bit about how to solve them. Next, I gave them an example of a real optimization problem. Most problems I've done have been pretty technical, and a bit dry, so I got information from a lab-mate of mine. Tahira Reid and two other students in ME 555 last winter did a project that involved optimizing the hair of African-American women, involving length, styling, and damage from various sources. Tahira was generous enough to give me a copy of their slides and her permission to show them to the students, so I selected some of her slides and went over the goals of the project and some of the issues involved. Obviously, a lot of the math was too advanced for them, so I didn't dwell on it in any depth, just showed them how the problem was set up.

Next, they turned over their worksheet and there was an exercise we did together: make up a new optimization problem. I wasn't sure at first whether it would be better in small groups or as a class, but we ended up doing it as a class. In the third hour algebra class, they came up with several ideas - optimizing a guitar, for length of time between tuning; optimize life in general (that would be a rather complex objective function!); optimize a textbook, for minimum weight. We set up the optimization of the textbook. They selected quite a few possible design variables (I had asked for two) - thickness of the cover, thickness of paper, size of type used, size of margins. When we considered the constraints, they decided that making the textbook cover resistant to ripping was one constraint, and another big one was readability. In terms of margins, one of the constraints had to be that the margin couldn't be negative. Once the problem was formulated, I asked them whether they thought it would be hard or easy to solve. They decided - and I agree - that this would probably be a fairly easy problem, since a lot of things are linear.

In fourth hour, they decided to optimize popcorn quality. This was a little more difficult, since we had to talk about what makes quality popcorn, and what could be included. Some of the factors that could go into the "popcorn quality metric" were that it doesn't burn, it should all pop, big kernels, and taste. Variables could include the bag's dimensions, temperature, amount of popcorn in the bag, and amount of butter used. Some of the constraints were minimum and maximum temperature, that the bag should be pretty, and that it had to fit into the microwave. When the bag's attractiveness was brought up, I told them about some of the work being done on optimization and aesthetics, and how that could be expressed mathematically in terms of proportions, among other things. When I asked if the problem would be easy or hard to solve, they decided - and again, I agree - that it would probably be a hard problem. The size of the problem was one thing they mentioned. Another was that it was probably non-linear. One person also said that everything is kind of subjective, so how do you know you have the right function? Someone else might make a different function for the perfect popcorn. That brought up a really good point, which I hope they remember - that it's important to start with the right problem before you try to solve it.

Overall, they seemed to be interested. Some of the students really got into the exercise, but they all liked the change - and the fact that, aside from turning in the worksheet I gave them, Ms. Colwell didn't give any homework. The third hour said that if a presentation by me means no homework, could I come back again sometime?

Slippery roads today...

2007-12-10T11:04:00.000-08:00

There were quite a few students either absent or late today, due to weather - there isn't much snow, but the freezing rain made the roads a challenge. Many of the buses were late, so attendance in first hour physics was rather low. Today's physics work was reviewing for their test tomorrow. The test is going to cover circular motion and universal gravitation. I looked over the test that Mr. Ambrose is planning to give, after class was over, and I think that it's fair; the students who have been working hard and doing the homework should do just fine on it. After the test, they're going to move on to energy.

In Ms. Colwell's algebra class, they learned how to use matrices to solve systems of linear equations; then, while most students took a quiz, I took one of the students aside who had been absent and wasn't taking the quiz, and went over some of the material he had missed. He hadn't been there when they learned how to solve equations by linear combination, so we went through those problems. First I set up and solved one, then I gave him a problem with slightly different numbers for him to do; then I set up a slightly different problem, more complex, and did the same thing. By the end of the class period, he seemed to be catching on pretty well. He'll still need practice, of course, but that's true of everything.

The students in both classes have gotten to know me fairly well by now, and they're more comfortable just talking. I had mentioned to them, several times, the need to do a "sanity check" and gave an example of how it had helped me to catch an error that could have haunted me down the road in my own work. I had to re-do a fairly big bunch of derivations, but at least I knew where the algebra started going wrong. One of the algebra students said that sounded frustrating, and asked how I kept wanting to do it. It was a serious question, so I told him the truth; that I did occasionally have days when I DIDN'T want to. Everyone has days when nothing goes right and it would be easy to just quit trying. Sometimes work doesn't go right, and the world as a whole seems terribly dark and pointless. But if I do my work right, it will make a difference - if I can develop a better method of doing something, that matters. I told him about the pleasure, when I was working in industry, of seeing a machine that was just sketches on paper at one point turn into a real, physical thing - and that in a special way, it was MINE, regardless of who it was actually sold to. I told him about the special feeling of realizing something that quite likely no one had seen before, looking up at the stars in the quiet night sky, and thinking that at that moment, you know some small thing that no one else does. The rewards are more than worth the difficulties, in the end. I don't know if he totally understood what I was trying to describe, but if he gets a little bit of it, maybe he'll gain more of a joy in learning.

Circular motion and Inequalities

2007-12-03T10:45:00.000-08:00

On Friday in Mr. Ambrose’s physics class, the students did an experiment. They ran a string through a tube and connected one end to a weight; the other end was connected to a small rubber stopper. One person spun the stopper in a circle, and the other one timed it. The idea was to measure the period and the radius, calculate the speed and centripetal acceleration, and compare it with the force provided by the weight. Most of them had pretty good experimental data and relatively low errors, once they did the calculations properly. In the rush of doing the lab, there were quite a few careless errors, but they’re smart enough to see that if the results are THAT far off, something is wrong. I helped several of them find their mistakes, and many times it was a decimal point in the wrong place, or reading a number out of the wrong column. Running a “sanity check” on results is a good skill to get in any field, so I think making those errors actually had a use. Today, they moved on to doing problems on curves – things like how fast can a car go around a curve without skidding. They haven’t gotten through banked curves yet, but that will be the next topic, and then they’ll move on to universal gravitation.

In Ms. Colwell’s class, they’ve been working with inequalities, and graphing them on number lines. I’ve mentioned that inequalities are useful in linear programming, and it turns out they’re actually going to cover that. Since that falls into the area of optimization, Ms. Colwell is going to give me a class period next Friday to talk about optimization and non-linear programming. Obviously, I can’t teach them in one class what it takes multiple graduate classes to learn, but I can give them an idea of what you can do with this type of math and why it’s important.

Rotating and translating

2007-11-26T09:16:00.000-08:00

Today was an easier day for both classes. In Mr. Ambrose's class, they had a test just before the break, so they were starting a new unit. He gave them a brief introduction to the equations involved in uniform circular motion, and a worksheet. Most of the students were having a bit of a hard time settling down - I can sympathize, it was hard to get up this morning after a long weekend. They were also checking with him on what their grades are - the marking period ended right before Thanksgiving, so report cards are coming out soon. There are several students who have pulled their act together and really improved a lot, and they can be proud of that. Also, a few people are starting to get college acceptances, and one young lady just got notified that she's admitted to her first-choice college. Now, she says it's a matter of scholarships, since she can't afford them.

In Ms. Colwell's class, they're working on using matrices for translations. I helped a few students, but most of them seemed to have the idea pretty well. A few of them had some minor confusion, but it was easily resolved, and most of them got a good start on the homework during class. One student didn't feel like doing his homework - he said he'd take it home. I asked if he wouldn't rather get it done and free up that time, but he said no. I think it's a shortsighted decision, but he has to deal with the consequences. By that class period, most people had settled down and were better able to work than during first hour. They're just about done with Chapter 4, and will be taking a test pretty soon.

Oh, and the subject of birthdays came up somehow... I don't remember the conversation... but mine is coming up this week. One student asked how old I'd be, and I told her that "it's 25 in hexadecimal." If she's interested enough, she can figure it out. I doubt if she'll go through the math to figure it out, though.

Almost to the break...

2007-11-19T10:27:00.000-08:00

Most of the students seem really excited about Thanksgiving break. They don't have class Wednesday, Thursday, or Friday. I'm a little envious - when I was in high school, I only got Thursday/Friday off for Thanksgiving. A five-day weekend is pretty generous!

In Mr. Ambrose's class, they were reviewing for a test tomorrow. As usual, some of the students are getting the material really well, and others still need work. We'll see how they do on the test. There's one young man who's been doing a tremendous job - he's obviously been working hard, since he's pulled up his grade from the "OK/good" range to "great". He's doing all the stuff that he's been told he should to succeed - taking notes, at least trying problems even if he doesn't understand them, paying attention in class - and it's paying off. I'm really happy to see it, since it'll carry through to his future in college as well. What some of these kids need to learn is that putting in an effort is a big part of the battle - if they do that, they're ahead of a lot of people already. Anyway, their test is over Newton's Laws, including the good old familiar F = ma, and they also have friction in that unit. After the break, they'll be getting to the mathematics and force behind circular motion. They've already touched on it in lab - the fact that things won't go in a circle unless there's a force acting on them - and now they'll get the detailed treatment.

In Ms. Colwell's class, they're working on reflection and rotation using matrices. Some of the students still need practice with matrices, but they do have a fair amount of homework so they're getting the practice. On Friday, I gave a short presentation in the class, on how matrices are used in robotics. Those are rotation matrices, so they tied in quite well with what they're doing now. It also gave them a preview that the trigonometry they're going to learn later on will also be useful.

It's amazing to see how fast the year is going - it seems like just a short time ago, I was over at YHS for the first time, and now we're approaching the holidays. Before long, it'll be the end of the year - what an incredible thought.

Recognizing the points and the uses of things....

2007-11-12T12:49:00.000-08:00

Today in Mr. Ambrose's physics class, they were reviewing a worksheet from Friday, and started on a new one. Some of the students started out class not really being sure what they needed to do to solve some of the problems, but by the end of class they seemed much more sure of themselves. One point that was brought out in one of the problems, and which we discussed, was the existence of irrelevant information. One of the easiest problems given was something like, "What is the weight of a 50-kg object when it moves with a horizontal acceleration of 5 meters per second squared?". The answer is just mg - 50 times 9.8. The acceleration is irrelevant. Mr. Ambrose talked about how, in labs, you can measure any number of things - the question is which things you need. I pointed out that it's useful in other fields, too - including humanities. Some of the students in the class, while talented in the sciences, don't plan on science-based careers, so tying everything together could be useful to them. We discussed the fact that whether writing an essay or solving a problem, one of the key things to ask yourself is, "What is the point?" In science, what is the problem I'm trying to solve? In English, it might be "What am I trying to say?" Another useful point they learned was that the normal force and the weight are NOT the same, even though they often are the same magnitude. To demonstrate that, Mr. Ambrose showed that you can change your "weight" on a spring scale by pushing down on a nearby object. We also noted that the scale reads in pounds and in kilograms, which isn't strictly correct since the scale does NOT directly measure mass. It really should have a label indicating that it's only calibrated for Earth-based use.

In Ms. Colwell's class, they learned how to multiply matrices. She had mentioned last week that some teachers only taught how to multiply them by hand, others only taught how to do it on calculators, and she taught both. I think she's got the right approach - sometimes, for small matrices, it's quicker to just do it by hand, and it's always a good idea to understand the background instead of just having a "black box" - or gray, in the case of some calculators. But it's also useful to know how to use the tools to make it quicker, once someone understands it. I may know how to multiply a 100 x 100 matrix by a 100 x 80 matrix by hand, but that doesn't mean it's a good use of my time. Also today she told the students about some of the uses of matrices. Her list didn't have any good engineering examples, so I added one - robotics. Robotics is way cooler than business, at least to a lot of people (myself included), so she's asked me if I can put together a quick example of how matrices are used in robotics. I'm going to look in my notes from robotics classes - I took a couple of robotics courses in my masters' degree at UIC back in about 1999/2000 - and put together something they can understand that will show how you can use them to work with really cool stuff.

Going in Circles

2007-11-05T11:14:00.001-08:00

Today in physics, Mr. Ambrose had them doing a simple lab. Each group had a piepan with a section cut out of it, and they had to roll a golf ball around the edge. The important task was to predict what would happen when the ball came to the empty section, and then to see what really happened - would it continue on a curved path in the absence of anything to force it to do so, or would it go straight? Anyone who's had physics can tell what it did - it went straight. Some of the students predicted that, but others thought it would keep going in a curved path. I told them not to kick themselves over being wrong - Galileo had the idea that there was some form of "circular inertia", that the planets would naturally move in circular paths without any applied force. It wasn't until Newton that someone realized the truth, and formulated it as a law of nature - which is why this one is Newton's first law. It's instructive for some students to realize that this stuff which is so obvious once you learn it was once a new, shocking idea.

In Ms. Colwell's algebra class, they were working a practice test - they have the real thing on Wednesday. Many of the students are doing quite well, but there are some who still struggle. One of the challenges for me is to figure out who needs help, and who needs to be left alone for a few minutes to think. Some people catch on quickly; others catch on, but they need to be given a chance to do so. If someone jumps in to help too quickly, it short-circuits the process. One student in particular needed to be given a few minutes. He knew what he was doing, but needed a chance to think about it. The key, I think, is to know when someone is getting frustrated because they're stuck, and when they just need space to work through the idea at their own pace. I wish I knew the answer to that - I try to read it from their expression and the way they're acting. One thing that does seem to work sometimes is to look at how they're holding the pencil. Someone who's frustrated tends to clench it, whereas a person who's thinking holds it a little more loosely. I don't know if it always holds true, but it seems to be a good enough guide to start with. The truth is, everyone's different, so there won't be an answer that's true 100% of the time about 100% of the students. It's not like a problem in math or science that always has the same answer - people are far more complex than that. Of course, that's part of what makes them interesting.

Off-Schedule...

2007-10-30T10:33:00.000-07:00

Today isn't normally a day that I go to the high school, but my schedule's a bit off; I was out of town at a conference and re-arranged when I do what for this week. Friday I'll be back to the normal schedule. Today was also kind of an unusual day at Ypsilanti High School. They had MME testing going on, so there were no regular bells, no announcements, and a fair number of students weren't in class. Mr. Ambrose used the class time to review, let students work independently, and for students to complete make-up work like quizzes that they'd missed. Some of them used the time wisely, but others just sat and talked. I'm not sure whether they were caught up, or just didn't feel like concentrating on their work. As much as it's a good idea to use your school time to work, I know sometimes you just can't focus well. I did learn something interesting from one young woman; she mentioned that her mother had once studied engineering, but didn't complete her engineering degree. She said her mom has considered going back to school. I really hope she does give it serious thought - not only would it set a great example for her daughter (who is a very bright and ambitious young woman), but it would be a great thing to do for her own sake. I know a lot of people say you can't go back to school, but that's just not true. I worked for 13 years before quitting to start on my Ph.D., and while being an older student presents special challenges, I bring a different perspective which I think can be helpful. Diversity isn't just racial and ethnic, although that is important - it's everything that makes a person who they are and influences how they think. That includes race, ethnicity, gender, age, and life experiences - and such a long list of things that if I typed them all, this post would be HIDEOUSLY long and no one would ever finish reading it.

In Ms. Colwell's algebra class, they were working on linear regression and on sequences. She's really trying to get them to think - for instance, they had a set of points, figured out the slope and intercept of the equation for the best-fit line, and then she asked them, "Is a line a good fit for these points? Why or why not?" In this case, the correlation was around 0.18, and after they discussed it, most of the students understood that it really isn't a good fit. I explained how, when you work with data, it's important to look at whether the model you're trying to use (in this case, a line) really matches. You can find the "best fit", but it might still be pretty bad if the points are all over the map - or if you try to fit a line to a quadratic relationship. When they started working with sequences, I mentioned that I've had homework (in an optimization class) that involves sequences; often, when you're using an iterative method to find a solution, you start with some value and use a specified rule to find the next value in the sequence, then the next, until you're done. Obviously, the sequences they study are far simpler than what a graduate student has to use - simple ones like 3, 6, 9, 12, ... but I was able to let them know that this, too, actually has some real-world purpose beyond just filling a section of the algebra book.

More Projectiles, and Slope-Intercept Lines

2007-10-19T10:47:00.001-07:00

Today in Mr. Ambrose's physics class, the students were doing a lab. In this lab, they dealt with projectiles fired at an angle. In the first part of the lab, they fired a marble with the "cannon" at a horizontal position, and used the point where it landed to determine the muzzle velocity. Next, they chose an angle, predicted where it would land based on the muzzle velocity, and fired it to test the prediction. Generally they did pretty well with their predictions, though they were a little off. Most of them see to grasp projectile motion fairly well, although there are still a few who are confused. One thing that I see is that some of them instantly start putting things into equations without ever asking themselves, "Is this equation applicable?" As an example, they have an equation for the range in terms of initial velocity and angle - but it only applies if the projectile is launched from the same height where it lands, which isn't always the case at all, and certainly wasn't in the lab. I tried to explain that you always have to consider what your circumstances are, and when a certain equation is valid, and I hope that came across. Generalizing what they've learned to new problems can be a challenge for some of them, though it's a critical skill that they would find useful in other areas.

In Ms. Colwell's algebra class, they're working with lines in slope-intercept form and graphing them. Most of them seem to be getting it pretty well - I helped a few with questions, but for the most part, they were doing OK.

Fire one! Fire two!

2007-10-12T10:22:00.000-07:00

Today, Mr. Ambrose had his physics class doing a projectile motion experiment. They had a small launcher set up on a lab bench ready for them, suitable for marbles. There was a piece of paper on the floor with distance markings from the muzzle of the launcher. Each student fired a marble once to test range, and then to get data, they put a piece of carbon paper down in the proper area. The whole idea was to measure where the marble landed, and using the height of the launcher, landing point, and acceleration due to gravity, figure out what the speed was when it was launched. For extra credit, they were supposed to figure out where to place a hoop of a given height so that the marble would go through it. Unfortunately, time ran out before that could get done, though several teams did very nice calculations of where to put the hoop. Some of them have caught on very well to the concepts, though there are still a few who seem a little shaky on it, and one or two who are really struggling.

In Ms. Colwell's advanced algebra class, they're learning about joint variation, including combined variation - all those multi-variable equations we all know and love. Some students needed help, but many of them really just need practice. Several students who didn't seem to pay attention before are now taking notes and appear to be trying, which is a great sign. One student who was doing badly has improved tremendously - he raised his hand to answer a question (correctly) today, did well on the last quiz, and appeared to be doing fine on the worksheet they were given. He's one of the students who I suggested go to tutoring; if he did in fact go, it certainly helped. Obviously he's doing something differently. That's one of the best parts of this program - seeing that something has made a difference to one of the students.

Conic sections everywhere…

2007-10-05T14:13:00.000-07:00

The physics class is working on projectile motion now – one of the most basic applications of two-dimensional kinematics, and of course, that’s our familiar parabolic motion that we all love. Today, Mr. Ambrose was doing examples for them. Some of them seemed to understand, but there are a few who are having trouble with the concept that you can separate out the X and Y motions, and treat them separately. I’m trying to think of something that would help – a lab, or demonstration, or some particular example, or something that would make the concept more concrete to them. This is really a key point and if people don’t get it, they may be able to do problems, but they won’t truly understand the material.

In Ms. Colwell’s algebra class, they’re working with hyperbolas and inverse-square functions. As they were going through them, talking about the domain and range, I pointed out that they really do need to be aware of domain and range of functions. In my optimization class that I’m taking, and in the work I’m doing for my research, that is something that has to be considered. Some of them seem to think that once they’ve finished a particular section of the book, they’re done with it. I’m trying to help them see that it comes back – as I put it today, “like the night of the living dead” – a bit of a weird twist, but it seemed to get a few people’s attention. There are a few students who really don’t seem very motivated, and I’m wondering how to reach them. I don’t know if they’re distracted by outside issues, or whether they simply aren’t interested in the material. Right now, I don’t know what the answer is, except to work with them when they’re having trouble and not give up.

Vectors and Variation

2007-10-01T10:03:00.000-07:00

The physics class is working on vectors, in preparation for two-dimensional kinematics. Today they were going over some examples and doing a problem in class. One thing that hurts some of them is that they don't take notes. Some do, of course, but there are a few students who never write anything down. I'm not sure if it's because they don't see the point, or if they never learned how to take good notes, but it's definitely something they need to work on, especially since a lot of them intend to go to college. Perhaps the tutors can help make the point that note-taking is an important skill, and maybe a few hints on taking good notes would help.

In algebra, they spent the class on the Fundamental Theorem of Variation. It seems pretty obvious to someone who's been doing math in various contexts for years - if you double "x" in this equation, or multiply it by 3, what happens to "y"? They're all capable of doing the algebra, but it takes some time and practice to get confident with it, since to them it is a new concept. A few of them could use extra help and may go to tutoring.

Update on both classes

2007-09-24T10:06:00.000-07:00

In Mr. Ambrose's physics class, they just got back their first test today. Some of them were happy with how they did, but some of them would like to have done better. I've let them know that tutoring will be available from NSBE, and some of them do seem interested in it. A few of them may find it very helpful to get caught up.

So far, they've gone through one-dimensional kinematics. The next thing they're going to be doing is going over vectors, in preparation for two-dimensional kinematics. I was talking with Mr. Ambrose about how to get the concepts illustrated, possibly through some kind of lab or activity.

In Ms. Colwell's algebra class, they're getting ready for a test tomorrow. I was helping some of them work problems in class, and I noticed something interesting. Many of them really do have the right idea, and can do the problems if you ask them what each step is, but they seem to lack confidence. That may be something that practice would remedy. It's a big problem, though, since I can see it holding many of them back. They're given an equation to solve, and they know what to do, but they don't feel confident that they're doing it right.

Recently, they've been working on solving equations, on functions (also on recognizing what is and is not a function), and on word problems - taking a problem and formulating the equation, then solving it. It seems to me that they do need more practice on word problems, as well as solving equations, but most of them understand what a function is pretty well.

Uses for Math

2007-09-17T10:38:00.000-07:00

So far, I've mostly been observing in Ms. Colwell's Advanced Algebra class and occasionally helping a student with their individual work in class, but today I had a short presentation put together, which I gave to both her third hour and fourth hour classes. It was titled " What’s math good for, anyway? A true story of an engineer on vacation, a desperate customer, and a literal back-of-envelope calculation." It was about a drive-train calculation that I did on an envelope, in a parking garage in Milwaukee, on my cell phone with a customer. I'm not sure if the students followed all of the math, though it wasn't anything really beyond algebra, but at least they got to see that math has some actual uses in real life. I tried to engage them in the presentation by asking them questions and showing them that they already know at least some of the stuff that I was using as a practicing engineer. Ms. Colwell seemed to think that it was of some use to them - breaks up the usual routine and shows them something new. As an assignment, she asked them to take a few notes on what I had to say and include them with their homework when they turn it in tomorrow, so I know they were at least half listening. Some seemed more interested than others, of course - not everyone has the same level of interest in the same things.

I'm going to e-mail her a copy of the presentation so she can have it for her files - it might come in useful in the future as an example for an advanced math class.

Physics Experiment

2007-09-10T11:48:00.000-07:00

The physics class did an experiment on Friday & analyzed the data today. On Friday, we went outside and measured off how far we were from the wall of the school, and clapped two pieces of wood together. The idea was to synchronize the claps with the echo, time how long 20 claps took, and use that data to calculate the speed of sound. The class also calculated what it should be based on the air temperature for the day.

Everyone's value was a little high, but some people were closer than others. One set of lab partners got a value of 335 m/s, where we'd calculated 333 m/s - extremely close! The farthest value was the teacher's - he measured over 400 m/s for the speed of sound. One of the students asked about eliminating that piece of data from the set when calculating the average for the whole class, which started an interesting discussion of when you can or can't eliminate data points - and how do you know?

The whole class seems very bright and interested in the subject - it's a joy to help out with them. They'll be starting on kinematics next, and Friday when I'm there Mr. Ambrose is planning to do another lab.

Starting out the semester

2007-09-03T18:43:00.000-07:00

Well, it's the start of the semester and the beginning of a new experience working with the TA partnership program. I'm looking forward to it - I'll be working with one of the math classes (advanced algebra) and one of the physics classes, spending Monday and Friday mornings at the school.

Thus far, I've met with both teachers - Thomas Ambrose and Doriane Colwell - over at the high school, and have gotten a bit of an idea what they intend to cover in their classes.