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.
Monday, November 26, 2007
Monday, November 19, 2007
Almost to the break...
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.
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.
Monday, November 12, 2007
Recognizing the points and the uses of things....
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.
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.
Monday, November 5, 2007
Going in Circles
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.
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.
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