I have been enjoying the last couple of days preparing for my Statistical Mechanics class. My new angle is to throw in a bit of differential geometry to expose students to its beauty as well as to give them a new and powerful tool to solve problems.
This morning, I was going over my notes on canonical transformations - a topic that I also covered in Classical Mechanics last semester. One concept that I still find a tad uncomfortable is in the manipulations of the quantities q, the coordinate, and q dot, its associated velocity. Central to the calculus of variations is the assumption that these two variables are independent. I can logically understand how this is the case, but my gut protests.
One of my colleagues, who shares an interest in the beauty of differential geometry, gave me the book Applied Differential Geometry, by William L. Burke. I noticed recently the most magnificent dedication on its inner cover, which reads, "To all those who, like me, have wondered how in the hell you can change q dot without changing q."
I can't wait to dive into this wonderful book; but, it will have to wait until I meet a looming proposal deadline and have prepared/delivered an invited talk in a few days. I must get back to preparing for my class, which meets in 45 minutes. Mornings before class are one of my favorite times...
Showing posts with label classical mechanics. Show all posts
Showing posts with label classical mechanics. Show all posts
Friday, January 21, 2011
Sunday, August 29, 2010
Preparing for class
I am spending large chunks of time preparing for a new class that I am teaching this fall. I never found classical mechanics particularly difficult; but, writing lectures and solving problems is still a challenge.
I devote each Saturday and Tuesday to course development. Though I took a couple of breaks to eat and surf the web, I remained true to my schedule. After grading last week's homework assignment and a quiz on Saturday, I continued to plow through the textbook and organize the material for my lectures.
My serious teaching career (excluding my work as a teaching assistant in grad school and an instructor at a community college) started 20 years ago at Washington State University. Those years have not jaded my enthusiasm for teaching. I continue to make adjustments based on my past successes failures.
But how are improvements possible when good teaching is difficult to define? While there is mounting research on pedagogy, in my mind, many of these studies are inherently flawed. For example, while courses that are based on peer instruction and conceptual problem solving certainly lead to better understanding, it makes it difficult to cover the same amount material. Admittedly, it is wasteful to teach lots of stuff that everyone forgets; but, coverage is also important - especially if a course is a prerequisite in a sequence courses. Such trade-offs must be carefully weighed in an undergraduate curriculum, especially for the student who will take one or two physics classes in a lifetime.
Graduate programs, on the other hand, are populated by motivated students who have both an interest in and an aptitude for physics. PhD programs like ours are based on coursework and research. All students take a set of core classes in their first two years. To become a PhD candidate, they must pass the PhD qualifying exam, which is given at the end of the forth semester.
The qualifier exam committee solicits two problems from each faculty member. A list of topic areas is used as the basis of the solicitation to ensure that the test is well-balanced. Thus, the qualifier exam reflects what the faculty as a whole believe is the core competency of a PhD in physics, and is not necessarily limited to the material covered in class. However, past exams are made available to the students as a study aid.
I find this system to be the ideal game-theoretic approach to ensure buy-in by all parties. It reflects poorly on me as a professor if the students were to do poorly on the part of the exam that is associated with my course. This makes me think very carefully about how to most effectively cover the material to get the optimal balance between breadth and depth. The looming qualifier exam motivates the students to learn the material for long-term understanding, not just for a particular test. Everyone works harder as a result.
My approach is to stress the fundamentals and give lots of examples. I gloss over topics that the students can learn on their own. When preparing a lecture, I first read the material, sometimes many times, until I feel I have a good understanding of the concepts. I then identify what I think are the important points, and use them as anchors in my lectures. I post readings and homework assignments on the web well ahead of the lecture dates so that the students are well prepared for class.
In crafting my lectures, I select problems from the end of the chapter on the basis of how well they complement my notes and whether or not they challenge the student to think more deeply. To select appropriate problems requires me to first suffer through the calculations. This time-consuming task give me ideas on how to fine tune my notes to address potential misunderstandings.
The night before my class, I go over my notes to make sure that I stress the important issues. The morning before my class, I copy my notes to scrap paper, going over in my mind the flow of my presentation. I pay particular attention to the anchor points.
Finally, I reproduce my lecture on scrap paper without looking at my notes. My preparation is complete when I am able to navigate from one anchor point to the next based on general principles of physics and logic.
So to finally get back to my diary entry after this long-winded diversion, I spent most of Saturday reading the textbook, writing notes, and working physics problems. This reminded me of how learning physics requires an intense and prolonged effort. I am thankful to my employer that my teaching responsibilities force me to spend time thinking very deeply about the subject that I love so dearly. And then, I get to share my enjoyment with a group acolytes who share my enthusiasm for learning.
I devote each Saturday and Tuesday to course development. Though I took a couple of breaks to eat and surf the web, I remained true to my schedule. After grading last week's homework assignment and a quiz on Saturday, I continued to plow through the textbook and organize the material for my lectures.
My serious teaching career (excluding my work as a teaching assistant in grad school and an instructor at a community college) started 20 years ago at Washington State University. Those years have not jaded my enthusiasm for teaching. I continue to make adjustments based on my past successes failures.
But how are improvements possible when good teaching is difficult to define? While there is mounting research on pedagogy, in my mind, many of these studies are inherently flawed. For example, while courses that are based on peer instruction and conceptual problem solving certainly lead to better understanding, it makes it difficult to cover the same amount material. Admittedly, it is wasteful to teach lots of stuff that everyone forgets; but, coverage is also important - especially if a course is a prerequisite in a sequence courses. Such trade-offs must be carefully weighed in an undergraduate curriculum, especially for the student who will take one or two physics classes in a lifetime.
Graduate programs, on the other hand, are populated by motivated students who have both an interest in and an aptitude for physics. PhD programs like ours are based on coursework and research. All students take a set of core classes in their first two years. To become a PhD candidate, they must pass the PhD qualifying exam, which is given at the end of the forth semester.
The qualifier exam committee solicits two problems from each faculty member. A list of topic areas is used as the basis of the solicitation to ensure that the test is well-balanced. Thus, the qualifier exam reflects what the faculty as a whole believe is the core competency of a PhD in physics, and is not necessarily limited to the material covered in class. However, past exams are made available to the students as a study aid.
I find this system to be the ideal game-theoretic approach to ensure buy-in by all parties. It reflects poorly on me as a professor if the students were to do poorly on the part of the exam that is associated with my course. This makes me think very carefully about how to most effectively cover the material to get the optimal balance between breadth and depth. The looming qualifier exam motivates the students to learn the material for long-term understanding, not just for a particular test. Everyone works harder as a result.
My approach is to stress the fundamentals and give lots of examples. I gloss over topics that the students can learn on their own. When preparing a lecture, I first read the material, sometimes many times, until I feel I have a good understanding of the concepts. I then identify what I think are the important points, and use them as anchors in my lectures. I post readings and homework assignments on the web well ahead of the lecture dates so that the students are well prepared for class.
In crafting my lectures, I select problems from the end of the chapter on the basis of how well they complement my notes and whether or not they challenge the student to think more deeply. To select appropriate problems requires me to first suffer through the calculations. This time-consuming task give me ideas on how to fine tune my notes to address potential misunderstandings.
The night before my class, I go over my notes to make sure that I stress the important issues. The morning before my class, I copy my notes to scrap paper, going over in my mind the flow of my presentation. I pay particular attention to the anchor points.
Finally, I reproduce my lecture on scrap paper without looking at my notes. My preparation is complete when I am able to navigate from one anchor point to the next based on general principles of physics and logic.
So to finally get back to my diary entry after this long-winded diversion, I spent most of Saturday reading the textbook, writing notes, and working physics problems. This reminded me of how learning physics requires an intense and prolonged effort. I am thankful to my employer that my teaching responsibilities force me to spend time thinking very deeply about the subject that I love so dearly. And then, I get to share my enjoyment with a group acolytes who share my enthusiasm for learning.
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