Off-Schedule...

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

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!

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…

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

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.