2009-10-27
John Travoltage
I'm in the process of putting together a presentation on sound and music. While searching for some good interactive examples of waves, I found this website hosted by the University of Colorado - Boulder. They host a large number of java simulations for common phenomena (including math, physics, chemistry, biology) and they're all free. The quality varies greatly between applets, but some of them are really clever and make for great visualization. Just try out the My Solar System and you'll see what I mean. I may try to work the sound wave one into my presentation, or take the students to the computer lab to use a few of the applets together.
2009-10-22
Of Milk and Men
Molly and I have established a routine in problem solving and how we deal with the week. Her classes usually have to complete a quiz on Fridays, and after that quiz l use the remaining time to either give a presentation or do a word problem. This week, following a quiz that emphasized fractions, I decided to regale the students with problem #1790. The problem emphasizes the use of fractions in determining volume and introduces the concept of a factorial.
Once again, I find that the first class is much less receptive than the second class. I'm not sure if this is a result of applying my learned lessons from my first lecture to the second, or if the students in the second class are simply more involved. In both instances, I was struck by the lack of suggestions when we asked about what the students wondered. In this case, I assign some of the blame on the fact that I had copied the question onto the problem statements. However, I find that most of the students don't care enough to wonder anything about the question in question. After prompting, several of the students were willing to accede the presence of a pattern in the problem statement. Though the problem already explicitly indicates the pattern, I counted this as a win.
Solution strategies were once again lacking, the students either had no idea how to approach the problem, or just didn't care. I really would like to give the students the opportunity to work for several minutes on their own, but past experience has suggested that they just become distracted within a minute or two. Instead, I did my best to illustrate the pattern evident in the problem. Following that, I helped them construct an equation that would show how much milk was ultimately left.
At this point, several students were dismayed that we had spent nearly ten minutes in introducing the concept of factorials. While I don't regret a minute of the process, they were more upset that they were not allowed to work on their homework during that time. In fact, I'm surprised that more than one student opted to write out the final answer to the question in question.
While I can appreciate the philosophy that props up the instruction techniques from the Math Forum, I'm concerned that the level of engagement from the students is insufficient. While most of the problems are interesting from a calculation perspective, they lack any lasting impact on the students themselves. Mrs. Porter and I are in the process of discussing what the best technique is to engage the students in the problems. In particular we're trying to find some way of adding an incentive to the equation.
Once again, I find that the first class is much less receptive than the second class. I'm not sure if this is a result of applying my learned lessons from my first lecture to the second, or if the students in the second class are simply more involved. In both instances, I was struck by the lack of suggestions when we asked about what the students wondered. In this case, I assign some of the blame on the fact that I had copied the question onto the problem statements. However, I find that most of the students don't care enough to wonder anything about the question in question. After prompting, several of the students were willing to accede the presence of a pattern in the problem statement. Though the problem already explicitly indicates the pattern, I counted this as a win.
Solution strategies were once again lacking, the students either had no idea how to approach the problem, or just didn't care. I really would like to give the students the opportunity to work for several minutes on their own, but past experience has suggested that they just become distracted within a minute or two. Instead, I did my best to illustrate the pattern evident in the problem. Following that, I helped them construct an equation that would show how much milk was ultimately left.
At this point, several students were dismayed that we had spent nearly ten minutes in introducing the concept of factorials. While I don't regret a minute of the process, they were more upset that they were not allowed to work on their homework during that time. In fact, I'm surprised that more than one student opted to write out the final answer to the question in question.
While I can appreciate the philosophy that props up the instruction techniques from the Math Forum, I'm concerned that the level of engagement from the students is insufficient. While most of the problems are interesting from a calculation perspective, they lack any lasting impact on the students themselves. Mrs. Porter and I are in the process of discussing what the best technique is to engage the students in the problems. In particular we're trying to find some way of adding an incentive to the equation.
2009-10-14
Animal Farm
References to the Russian revolution aside, a little over a week ago I did the Math Forum's Problem #5156 titled, Ostrich Llama Count. I've been remiss in my virtual live web blogging, so here is my belated account of how things went down.
As I described in Problems with Words, we began with Noticing and Wondering. I decided to continue my policy of writing everything down, with the sole exception of the student who wondered how large the ostriches' reproductive organs were. Sadly, that was one of the few suggestions for Wondering I got and we had to troop on (I'm all for suggestions on how to up the number of wonders). The students were more attentive through the beginning of the problem, and I felt like the stronger approach in teaching was producing results.
As we transitioned to solution strategies I had a last second realization that the algebra approach might be a bit of a reach as the concept of solving for a given variable hadn't been addressed in lecture yet. Several students successfully worked through the problem by using a table or by guessing and checking. For the remainder of the time I tried to explain how to substract the same number from both sides. As with last time, it was hard to tell how much the students actually understand. It also didn't help that I was using O as the variable for the number of ostriches.
2009-10-13
Destructive Tendencies
I have a few ideas that I've been throwing around about presentations for class. Any input on these ideas would be wonderful.
- Super Bouncy Balls - United Nuclear provides the necessary chemicals to make your own Super Bouncy Balls. While it's more of a chemistry demonstration, it would present the opportunity to go from a chemical equation and molecular masses to how much of each chemical is needed. There's also the downside of giving 50 high schoolers each their own superball. I suppose only one needs to be made, but I'd actually like to involve the students somehow.
- Something Small - When I was in high school I began the trek to my current profession after working in a biology lab. Being able to manipulate items too small to see and retrieve observable results was amazing. I'm not sure where this would go; while plasmas offer plenty of opportunities in this respect, most of the math is a bit too involved for class.
- Math Rap - I recently conducted a survey of the class on what topics they'd most like to learn about. Top of the list was football and rap, while football has plenty of opportunities to involve math, I've been tearing my hair out day and night about rap. Off the top of the head, a few topics come to mind. Rhythmic structures could be used to discuss how a consistent number of syllables in each line gives the impression of better flow. On the other hand, I have an oscilloscope that would allow me to talk about waveforms and superposition (in a pretty intuitive way). Similarly, using a computer and audio software to do FFTs would let us analyze an audio sample for its beat pattern.
The Uncertainty Principle
Over the last several weeks of classes, I've noticed that it's impossible to predict whether a given student be in class on any particular day. In fact, there are several students on the roster whom I haven't seen yet. Weirdest of all, in this menagerie of truancy, is the steady appearance of new students.
After speaking with Molly, it seems that there's a large variety of reasons for this. In some cases, the students were being shuffled to smaller classes where they'd get more attention, in others they needed to switch course times for scheduling reasons, so on and so forth. I can't help but find it strange and off-putting that students have not yet settled their schedules over a month into the school year. The needless distraction of having to learn a new teacher's protocol, getting used to the new schedule, familiarizing themselves with the new class, all work together to take away valuable time from actual education.
I find that our classes are usually struggling to make net progress on a day to day basis. This issue is particularly noticeable in the fourth hour class which has over thirty students. A typical class period is split into the following sections:
After speaking with Molly, it seems that there's a large variety of reasons for this. In some cases, the students were being shuffled to smaller classes where they'd get more attention, in others they needed to switch course times for scheduling reasons, so on and so forth. I can't help but find it strange and off-putting that students have not yet settled their schedules over a month into the school year. The needless distraction of having to learn a new teacher's protocol, getting used to the new schedule, familiarizing themselves with the new class, all work together to take away valuable time from actual education.
I find that our classes are usually struggling to make net progress on a day to day basis. This issue is particularly noticeable in the fourth hour class which has over thirty students. A typical class period is split into the following sections:
- The Starter - A short set of ~5 problems meant to emphasize important aspects of the previous lecture. During this period, Molly will generally walk around and check to see if the students have completed their homework.
- Checking - Time during which the students correct their starter, and correct their own homework.
- Lecture/Quiz - Meat of the class, often the time during which new topics are introduced. Quizzes are frequently held on Friday in order to cement the previous week of learning.
- Homework - If time permits, Molly will help the students get a head start on the homework.
2009-10-01
Problems with Words
Almost all Teaching Fellows have the same set of responsibilities; we all do presentations, a field trip, demonstrations, and several other things. As a math TF, I have the added fun of integrating new ways of teaching problem solving. Last week was my first attempt at using some of the methods provided by the Math Forum. Herein, you will find out how well that attempt went.
For those counting, I chose Problem #3520 to try. Simply put, it involves solving a system of five simple algebraic equations. I wanted to try this one because the development of the equations was simple, but the problem was long enough that it'd be difficult for the student to see the immediate conclusion. Each class began with a session of Noticing and Wondering. Here we all wrote down and discussed what we noticed and wondered about the problem (without yet knowing the question). This was followed by some attempts to prompt suggestions from the class on solution techniques. Finally, we ended with a discussion of the actual solution.
The Noticing and Wondering did not go entirely smoothly. Many of the students didn't see the importance to thinking about the problem statement, and instead tried wisecracking their way through the section with silly suggestions. In response, I decided the best thing to do was to write down their silly suggestions on my list. After this, I was glad to hear the students start chastising each other over meaningless statements. Unfortunately, this led to only two or three very forward students saying anything, and the rest quickly became detached from the lecture.
While I tried to get some discussion going on how to solve the problem, no one was willing to say anything, even after some hints on how to approach the problem. When I was teaching a college lab, this is the point at which I'd stand around saying nothing until someone volunteered a solution no matter how long it would take. With less than an hour to do practice problems, the starter, take attendance, hand back papers, and lecture, each minute not spent teaching feels like one lost. By the second class there was little more than a brief pause and comment between the noticing/wondering and the solution. Thankfully, I got some help from the students on writing out the equations.
At the end of the class, Mrs. Porter and I picked up the problems from each student. I've just finished grading them; you might ask,"Ben, how do you grade a problem that you solved for the students?" I would reply, "I treated them like notes, and the students who wrote down all major steps of the solution got full credit." This might seem like an easy grade for most students, but I counted a total of 29 papers when there are 48 students enrolled in these classes. How can I convince the students that there's a reason behind all that's going on? I wish I could have two hours with them to answer all the questions they have, but don't feel like asking.
As an epilogue, I'll be trying another word problem tomorrow. This one should be a bit shorter and I actually worked through this one with the instructors from Drexel. Counting ostriches and llamas, maybe I can come up with a slightly more interesting alternative...
For those counting, I chose Problem #3520 to try. Simply put, it involves solving a system of five simple algebraic equations. I wanted to try this one because the development of the equations was simple, but the problem was long enough that it'd be difficult for the student to see the immediate conclusion. Each class began with a session of Noticing and Wondering. Here we all wrote down and discussed what we noticed and wondered about the problem (without yet knowing the question). This was followed by some attempts to prompt suggestions from the class on solution techniques. Finally, we ended with a discussion of the actual solution.
The Noticing and Wondering did not go entirely smoothly. Many of the students didn't see the importance to thinking about the problem statement, and instead tried wisecracking their way through the section with silly suggestions. In response, I decided the best thing to do was to write down their silly suggestions on my list. After this, I was glad to hear the students start chastising each other over meaningless statements. Unfortunately, this led to only two or three very forward students saying anything, and the rest quickly became detached from the lecture.
While I tried to get some discussion going on how to solve the problem, no one was willing to say anything, even after some hints on how to approach the problem. When I was teaching a college lab, this is the point at which I'd stand around saying nothing until someone volunteered a solution no matter how long it would take. With less than an hour to do practice problems, the starter, take attendance, hand back papers, and lecture, each minute not spent teaching feels like one lost. By the second class there was little more than a brief pause and comment between the noticing/wondering and the solution. Thankfully, I got some help from the students on writing out the equations.
At the end of the class, Mrs. Porter and I picked up the problems from each student. I've just finished grading them; you might ask,"Ben, how do you grade a problem that you solved for the students?" I would reply, "I treated them like notes, and the students who wrote down all major steps of the solution got full credit." This might seem like an easy grade for most students, but I counted a total of 29 papers when there are 48 students enrolled in these classes. How can I convince the students that there's a reason behind all that's going on? I wish I could have two hours with them to answer all the questions they have, but don't feel like asking.
As an epilogue, I'll be trying another word problem tomorrow. This one should be a bit shorter and I actually worked through this one with the instructors from Drexel. Counting ostriches and llamas, maybe I can come up with a slightly more interesting alternative...
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