Today in Financial Math we were talking about approximate versus exact time, and ordinary versus exact interest. I was telling the class about my observations on the topic, and our textbook's handling on the matter. I don't think our textbook does a particularly good job. After this became clear in class, one student commented how it made him excited to try learning independently from it (this is my goal for the course, I've rambled about it recently). We all had a little chuckle. I think it was at this point that one student opened up a discussion on thoughts about the course structure. Mostly I don't remember exactly too much what was said. Students could not believe that I was expecting them to read the text, do problems on the reading before I had talked about the content, and then still come to class. At least one student made a comment about the price of the education I was apparently not giving the class.
I was a little bit entertained, to be perfectly honest. It seemed a pretty strong reaction to have after a single assignment. But ok, the course is different, it'll take getting used to. It helps (me, if nobody else) that I really do believe it's a good way to structure class.
On one hand, I seem to have students who were shocked that I am asking them try to figure things out for themselves. On the other, I apparently have students who feel that they can do this well enough to make class discussion worthless. My guess is that many of the students alternately believe both of these things. I just can't win :)
So anyway, after several minutes in class of many of the students sharing their thoughts, things calmed back down a bit, and we got back to the topic at hand. I heard some mumblings about how the course was "ridiculous". It might have been "absolutely ridiculous", I don't recall.
I want my students to embrace this course. I really think it can work. I decided that I should share more of my thoughts on the matter with them. I probably should have done more of this earlier. I did tell them how the course was set up on the first day. And I remember asking if I needed to try to convince anybody that learning independently was a valuable thing. At the time, nobody claimed to need convincing.
But anyway, I wrote a little response for my students, and have posted it on our course discussion board. I hope to continue the discussion with the students there. For whatever reason I also thought I'd share my letter here. So without further ado:
Dear Students,
I would like to take some time to tell you about my thoughts on why I have set up our course the way I have, as well as to give you some better insight into how I anticipate this course working and what I expect from you.
Here is how I envision this class working. Every Tuesday you will have an assignment due at the beginning of class. The assignment will say to read some sections of the textbook, and will require you to write solutions to exercises. The content will be things I have not talked about in class. I expect that in addition to reading the contents of each section, you will look at all of the exercises, not just those that are assigned. You should look at all of the odd problems, and all of the preliminary short answer questions, and try enough of them to test your understanding. When you can answer odd problems correctly without looking at the back of the book, you should feel like you are in good shape.
Your write-ups should be clear and well-written. Explain, in your write-up, where your formulas, and the numbers in them, come from. You might model your write-ups on the solutions in the back of the text, or the solution to example problems worked in the section. I anticipate choosing even-numbered problems from the text that are noticeably similar to nearby odd-numbered problems.
I have designated several hours on Monday for office hours. If you are stuck on homework problems, please feel free to come to any of the scheduled office hours. If you are working on things over the weekend and have a question, feel free to email me. Also, if you would like me to look at your work before you turn it in, Monday's office hours are a good time for that. As indicated on the syllabus, I am also happy to meet with you at other times throughout the week, by appointment.
There are some difficult problems in our text. I do not anticipate assigning particularly difficult problems on written homework. I would rather talk about these problems during class time, after giving you a chance to ask questions.
I expect you to come to class Tuesday with questions from the reading - things you didn't understand, or examples that didn't work out as you expected. If you work a problem in a manner different from that in the text, you should share it with us. As you are reading each section, keep notes on your thoughts and questions, they will make good discussion material. I will do the same.
Thursday's class will likely begin with a spill-over of any discussion from Tuesday. Also, I expect Thursday will be a good time to work on the trickier problems that were not assigned. Finally, as I intend to have homework graded for Thursday's class, we can spend time talking about any mistakes you (or I) made in our solutions.
I hope the above begins to address some of the concerns mentioned in class today about how coming to class would not be beneficial. I have a very hard time believing that you cannot benefit from discussion with 45 other individuals all thinking about the same content that you are. Had you really thought about all of the issues mentioned today about exact versus approximate time?
There remains the issue that I have designed this course to make you learn the material by reading the book. I expect that this is not the way many of your other courses are, or have ever been, structured. It's a good thing I got to you before you graduated.
I absolutely believe that reading a textbook is a good way to acquire an understanding of any new material. I believe that being able to learn independently will make you more attractive to employers. I believe, moreover, that this independence will help you in your personal life. It should inspire you to dream bigger, knowing that you can figure out the steps necessary to attain larger goals. As corny as that sounds, I stand by it.
I also believe that this sets up class time to be more beneficial than a traditional lecture. Why would you bother sitting through a class where an instructor will be delivering a lecture, the content of which is sitting in a book you could read when it best fits your schedule? How many of the lecture notes you have taken have been things that were written in your textbook? How is that an efficient use of in-class time? Doesn't it make more sense to have thought about material on your own, developed your own understanding and questions, and then use class time to address that?
Yes, this course is structured differently. Yes, it does require you to do work. I believe you can do it. And I will be there to help you when you need it. All I ask is that you try it by yourself first.
Tuesday, January 26, 2010
Sunday, January 24, 2010
Step Stool
I have a memory of, as a child, having my own little step stool. If memory serves it was yellow, and made of fairly sturdy plastic. My sister had one too. The stools probably had our names on them. Mostly I seem to remember using mine to reach the sink, when brushing my teeth or washing my hands. I'm sure I wasn't conscious of it at the time, but that step stool had plenty to offer.
A step stool is sturdy and dependable. If my step stool had ever slipped out from under me, or broken while I was using it, I would have been nervous to try using it again (if, indeed, it was still usable). I would not have used my step stool if I had not been confident in it.
A step stool is easy to use. I probably didn't need much instruction in how to use my step stool. There should be nothing complicated about using a step stool. If my step stool had some sort of policies I needed to be aware of (e.g., ``Do Not Use the Top Step''), they were ideally clearly marked, easy to adhere to, and did not artificially limit the use of my step stool.
A step stool is easy to take with you. My childhood step stool was probably relegated to the bathroom, but had I needed it, I could have easily picked it up and used it anywhere I had in mind. Knowing that I had a step stool, one I was confident in using, I could explore further.
A step stool is easy to move aside. When I was ready to use the sink without it, my step stool wasn't in the way. If I wasn't as ready as I thought, my step stool would be there to give me the boost I needed.
A step stool is an appropriate height. A step stool that is already as high as I want to go only necessitates another step stool. A step stool that barely reaches above the floor doesn't offer much.
A step stool doesn't reach the whole way. Making me go the last step will increase my self confidence. Making me do work along the way will make attaining the goal something I can be proud of.
A step stool gives one a higher viewpoint. With it, I might be able to see my way from where I am to where I want to be. Indeed, with another viewpoint, I might begin to make new goals, more ambitious than those before, or in another direction. My step stool would let me look in any direction.
A step stool never stops being useful. My childhood step stool could still help me occasionally. Any time I wasn't using my step stool, it would work just as well for my sister.
A good teacher is a step stool. One that adapts and grows. That challenges itself as it offers and inspires challenges for those who use it. That delights in the success of those it helps, and offers encouragement and patience when things don't go well.
-------------
How's that for a teaching statement? Better than last year?
A step stool is sturdy and dependable. If my step stool had ever slipped out from under me, or broken while I was using it, I would have been nervous to try using it again (if, indeed, it was still usable). I would not have used my step stool if I had not been confident in it.
A step stool is easy to use. I probably didn't need much instruction in how to use my step stool. There should be nothing complicated about using a step stool. If my step stool had some sort of policies I needed to be aware of (e.g., ``Do Not Use the Top Step''), they were ideally clearly marked, easy to adhere to, and did not artificially limit the use of my step stool.
A step stool is easy to take with you. My childhood step stool was probably relegated to the bathroom, but had I needed it, I could have easily picked it up and used it anywhere I had in mind. Knowing that I had a step stool, one I was confident in using, I could explore further.
A step stool is easy to move aside. When I was ready to use the sink without it, my step stool wasn't in the way. If I wasn't as ready as I thought, my step stool would be there to give me the boost I needed.
A step stool is an appropriate height. A step stool that is already as high as I want to go only necessitates another step stool. A step stool that barely reaches above the floor doesn't offer much.
A step stool doesn't reach the whole way. Making me go the last step will increase my self confidence. Making me do work along the way will make attaining the goal something I can be proud of.
A step stool gives one a higher viewpoint. With it, I might be able to see my way from where I am to where I want to be. Indeed, with another viewpoint, I might begin to make new goals, more ambitious than those before, or in another direction. My step stool would let me look in any direction.
A step stool never stops being useful. My childhood step stool could still help me occasionally. Any time I wasn't using my step stool, it would work just as well for my sister.
A good teacher is a step stool. One that adapts and grows. That challenges itself as it offers and inspires challenges for those who use it. That delights in the success of those it helps, and offers encouragement and patience when things don't go well.
-------------
How's that for a teaching statement? Better than last year?
Thursday, January 21, 2010
First Day
Well, my Financial Math class started today. I am not convinced it went particularly well. I'm trying to remind myself that the real test will come Tuesday (our next class meeting), after they've done some reading and their first assignment. Today I just wanted to talk about my goals for the course, and how it was structured.
I guess that's not all I wanted. I wanted to start the class off with lots of discussion, since that's what I want the class to look like for the rest of the semester. Not just me talking. I remember this happening last semester, and thinking it was a great thing. Perhaps it helps that I started with content on the first day last semester.
Today, besides people saying "Here" or so as I read their names from the roster, I think approximately 3 people said something during class. That might include me, I can't quite remember. Not quite all I'd hoped.
When I wrote my last post about this class, just two days ago, I was, for whatever reason, working under the assumption that a majority of the class would be first year students or so. It is, after all, a 100 level course. It turns out that nearly my entire class consists of seniors. I'm trying to remind myself not to expect them to be lazy before giving them the opportunity to prove otherwise. I'm having a hard time of it, to be honest.
I wanted students to to tell me why they were taking this class, and what they'd heard about it (since I knew little about it). One student said it filled a general math/science credit. Another said that he had heard it was a good intro to finance and things. I should have pressed the issue... I'm starting to think this course is looked at as any easy way to fill one last graduation requirement. And I sort of hate that.
On my run after class, trying to clear my head a bit, I realized that perhaps I was being too idealistic about this (I thought that's what ivory towers were for!). Looking back, I know that as an undergrad I cared very little about anything besides my math and computer science classes. I took whatever else I had to, but have no memory of enjoying learning any of it.
Since starting grad school, I seem to have really grown into loving learning. I basically cannot stop reading things online. And they aren't all math and computers and teaching. Well, mostly they are. But I also feel like I would actually be excited to maybe learn some history (which I always hated), more science, more literature... anything. My friend got my a gift card for a book store, and I wondered at some point if there was a convenient way to pick a "nice" random collection of books from scattered topics to read (feel free to leave a comment!). Broaden my horizons and all that.
Even learning financial math has been not bad. I've always shied away from applications. Today I went to the library and got a few popular-level books on finance. I felt a little dirty, honestly. But I was also excited to learn about things I know nothing about.
Surely my students will share this enthusiasm, right? I'm reminding myself who I was years ago, and realizing that probably many wont. But I'm also trying to remind myself that if I go to class thinking that, things will turn bad (worse?) quickly.
I did, in class today, get a nice chuckle out of the class when I told them I know nothing about finance. I expect many were a bit shocked when I told them that while I'd read the first chapter a few times, and skimmed the next two, I had no idea about the other three we'll be covering. I'm hoping they appreciate my honesty, and don't lose respect for the course. I'm wondering if a pop quiz is in order for Tuesday, to make sure they know I'm taking this class seriously.
I'll keep you posted.
I guess that's not all I wanted. I wanted to start the class off with lots of discussion, since that's what I want the class to look like for the rest of the semester. Not just me talking. I remember this happening last semester, and thinking it was a great thing. Perhaps it helps that I started with content on the first day last semester.
Today, besides people saying "Here" or so as I read their names from the roster, I think approximately 3 people said something during class. That might include me, I can't quite remember. Not quite all I'd hoped.
When I wrote my last post about this class, just two days ago, I was, for whatever reason, working under the assumption that a majority of the class would be first year students or so. It is, after all, a 100 level course. It turns out that nearly my entire class consists of seniors. I'm trying to remind myself not to expect them to be lazy before giving them the opportunity to prove otherwise. I'm having a hard time of it, to be honest.
I wanted students to to tell me why they were taking this class, and what they'd heard about it (since I knew little about it). One student said it filled a general math/science credit. Another said that he had heard it was a good intro to finance and things. I should have pressed the issue... I'm starting to think this course is looked at as any easy way to fill one last graduation requirement. And I sort of hate that.
On my run after class, trying to clear my head a bit, I realized that perhaps I was being too idealistic about this (I thought that's what ivory towers were for!). Looking back, I know that as an undergrad I cared very little about anything besides my math and computer science classes. I took whatever else I had to, but have no memory of enjoying learning any of it.
Since starting grad school, I seem to have really grown into loving learning. I basically cannot stop reading things online. And they aren't all math and computers and teaching. Well, mostly they are. But I also feel like I would actually be excited to maybe learn some history (which I always hated), more science, more literature... anything. My friend got my a gift card for a book store, and I wondered at some point if there was a convenient way to pick a "nice" random collection of books from scattered topics to read (feel free to leave a comment!). Broaden my horizons and all that.
Even learning financial math has been not bad. I've always shied away from applications. Today I went to the library and got a few popular-level books on finance. I felt a little dirty, honestly. But I was also excited to learn about things I know nothing about.
Surely my students will share this enthusiasm, right? I'm reminding myself who I was years ago, and realizing that probably many wont. But I'm also trying to remind myself that if I go to class thinking that, things will turn bad (worse?) quickly.
I did, in class today, get a nice chuckle out of the class when I told them I know nothing about finance. I expect many were a bit shocked when I told them that while I'd read the first chapter a few times, and skimmed the next two, I had no idea about the other three we'll be covering. I'm hoping they appreciate my honesty, and don't lose respect for the course. I'm wondering if a pop quiz is in order for Tuesday, to make sure they know I'm taking this class seriously.
I'll keep you posted.
Tuesday, January 19, 2010
A Confused Teacher
This semester I'll be teaching a course in financial math (a first-year-level course offered by the math department). This is a bit of a change from what I've been teaching (calculus, for 5 years). Moreover, I basically know nothing about the subject.
Ok, sure... you put money in a savings account, it earns interest at some rate, compounding sometimes, and you end up with more money than you started with. Conversely, you use a credit card to buy stuff, and it costs more, due to interest. I've got some grasp of those concepts (though not much... I mean... why would a bank give me money for having money?), and the equations involved. However, some of the chapters in the book that I'm supposed to cover are titled: "Discount Interest", "Ordinary Annuities", "Other Annuities Certain", "Debt Retirement Methods", and possibly also a chapter on "Investing in Stocks and Bonds". Well, I think I can claim to have heard those words before (not necessarily together), but that's as much as I can honestly own up to.
So I'm supposed to go teach a class (45 students) on a topic I basically know nothing about. This has put me in a bit of a philosophical mood. Or, since I also won't claim to know what philosophy is, let's just say: I've been thinking about how I should set up a course like this, and why I think that.
[Just a heads up. This post has parenthetical comments within parenthetical comments. And it isn't about LISP. If that gives you some indication about how rambly this post is, and you don't have time for it... perhaps I'll do better next time. See you then.]
My thoughts are: I'll be learning this stuff essentially as my students do. I will be no more an expert on the subject than they would be after reading each section. It believe it's quite possible that some students will come in knowing more about the subject than I do. So why should I lecture on it (nevermind if I should be lecturing when I do have an understanding (calculus))? Shouldn't they be able to teach themselves, just like I'll be doing? And then we can all get together and see if we came to the same understanding?
I asked basically these questions on twitter, where @michiexile was kind enough to offer up some thoughts. He stated that I've got some advantage, having spent more time learning how to learn, and also that I'm there to be "a bad conscience", "a voice of authority", and to "give context".
I can certainly see the bad conscience part. That's the point of making assignments with due dates. I'm not sure how much context I can give, though perhaps I'll do more reading in places besides the text, so I'll have more to share (but, again, they can do this). I'm not a particularly authoritative person, but perhaps that's something I should work on in my role as an instructor (or perhaps not?).
Clearly his point about having more experience learning is valid. If you kept count that high, I think I'd be in 22nd grade (only taking 21 of them though :)). With my students who I'm expecting to mostly be in 13th grade, that's approaching twice as many years in school (ouch). Surely I've picked up something in all that time. How can I best impart this knowledge (which I don't have a ready grasp on) to my students as efficiently as possible? I have no idea. My consolation is a guess that I'm not alone in not knowing.
It seems fairly clear to me that knowing a bunch of things is useful. Surely (though I have no experience to base this off of) employers like to hire people who already know many things, and know how to do many things. However, there is absolutely no way an employer can expect a future employee to know everything about pertinent subjects. There's quite simply too much out there. And this holds true especially for students fresh out of college, who almost certainly have significantly less experience than individuals who have been working for some time.
So it seems to me that what employers should be hoping to find is individuals who have a strong ability to learn. I'm guessing this isn't much of a revelation to anybody. I think I'd like to claim something stronger though. I believe that an individual who has a strong ability to learn independently makes for a stronger job candidate.
(Please don't think that my whole outlook is helping kids land jobs. I don't even want a job :), though of course money is nice. I have little idea how to get one anyway - that's a portion of the reason I'm still in school. Also, I don't have much in the way of an idea how an employer would determine if one individual is a stronger independent learner than another. I do believe the internet can help, by giving people a place to show what they do. But I'm getting off track (seems to be what I do).)
I've been trying, at least a little bit, to think about why I believe that an ability to learn independently is an admirable quality. Possibly I'm behind, and people have decided that it's simply true, sort of intrinsically or something. Perhaps not. Part of my concern is that I like to think that I have at least some ability to learn fairly independently (I'm quite possibly fooling myself), and so perhaps I just want to believe that this is an admirable quality. Or, more drastically, perhaps I've got some psychological issues about relying on other people. I like to think this isn't the case, but what do I know?
Having not much in the way of "other opinions" on the subject, I'm pretty much going on the assumption that I'll be doing well if I can get my students to be better independent learners. I'm not saying total independence. I'm not going to cancel all the class meetings and just have a final exam, and expect everybody to be fine at the end of the semester (man, think of all the free time though...). I know that I am not that independent myself (and I'm sure my thesis advisor would be quick to agree), and I don't think it's even a reasonable goal.
So here's what I think I'm going to do with my class. We have 75 minutes class periods, one on Tuesday and one on Thursday. Each Tuesday there will be an assignment due, presumably consisting of exercises from the text (I'm still working on this part), on sections that I have not talked about in class at all. This will require the students to read the appropriate sections, carefully, so that they actually gain an understanding of the material. I'm going to have office hours on Monday, to help students who got stuck on the assignment.
This is the way my undergraduate math courses were structured, by the way. I'm excited about diving in on this policy. I've made attempts in the past, with my calc classes, but went too easy with it, I feel.
So, great, my course is set up. Except, there's one small issue. I've got 150 minutes in front my students each week. If I'm not talking about new material, and they just turned in an assignment showing that they understand old material... what do I do with this time? This part has me seriously nervous (so I'm writing about it out here, good use of time :)).
My guess is that students (including me!) won't understand all of the material from the section. I'm planning on spending as much class time as possible and necessary having a discussion with my students (hopefully with them doing most of the talking) about any questions we have from the reading. Hopefully some will be confused about examples in the text. Hopefully some will still have questions about how to work problems. Hopefully some will have questions about how to interpret answers to questions.
I'm trying to think about what to do if they don't have anything to say. Or if they pretend they don't. I'm guessing if I say "So, since none of you have any questions, maybe I should just give you a quiz on this for you to earn lots of points on, and then we can all go home", some hands will go up (and some people will think going home is a great idea).
One thing I think I'll do is to try to keep track of my own thoughts and observations and questions as I read, so that I can share that with the class if they don't have their own things to talk about. I may also come with some extra examples, to give them time in class to work on them (possibly in groups, or as part of a game or something) and get better at problems simply by doing more of them. Possibly I'll be inspired to look at other materials online or in other books, and can come in with something to share from that reading.
I think talking about the material the students (and I) have just read, after we have worked some problems on our own, will help with our understanding of the material. Surely that's a good goal for the course.
But I was rambling on just a few paragraphs ago about getting my students to be more independent learners. I do think that setting up the course as described above will give them experience trying to develop this skill. I also think, however, that this goal can be addressed slightly more explicitly during class time. I hope that by keeping track of my own "how I read this section" process, I will be able to share that with the class. I touch on this a little above. But I could take it further, I think. I could perhaps scan a section of the text, and keep my notes on the paper as I go. Then during class I could walk through how I read the section with my class. Perhaps they'll pick up on things. Things like... what questions do I ask while reading? How can I tell if I'm actually understanding this material? Where can I go to answer questions I have? Perhaps the exercise will make me more aware of the process myself, and I'll be able to point something out. Perhaps students will point out their own methods of gaining understanding.
At this point I've probably rambled on far too much. Clearly this semester will be (or, at least, could be) an interesting one. I believe that I will learn quite a bit. I hope that my students also do.
Ok, sure... you put money in a savings account, it earns interest at some rate, compounding sometimes, and you end up with more money than you started with. Conversely, you use a credit card to buy stuff, and it costs more, due to interest. I've got some grasp of those concepts (though not much... I mean... why would a bank give me money for having money?), and the equations involved. However, some of the chapters in the book that I'm supposed to cover are titled: "Discount Interest", "Ordinary Annuities", "Other Annuities Certain", "Debt Retirement Methods", and possibly also a chapter on "Investing in Stocks and Bonds". Well, I think I can claim to have heard those words before (not necessarily together), but that's as much as I can honestly own up to.
So I'm supposed to go teach a class (45 students) on a topic I basically know nothing about. This has put me in a bit of a philosophical mood. Or, since I also won't claim to know what philosophy is, let's just say: I've been thinking about how I should set up a course like this, and why I think that.
[Just a heads up. This post has parenthetical comments within parenthetical comments. And it isn't about LISP. If that gives you some indication about how rambly this post is, and you don't have time for it... perhaps I'll do better next time. See you then.]
My thoughts are: I'll be learning this stuff essentially as my students do. I will be no more an expert on the subject than they would be after reading each section. It believe it's quite possible that some students will come in knowing more about the subject than I do. So why should I lecture on it (nevermind if I should be lecturing when I do have an understanding (calculus))? Shouldn't they be able to teach themselves, just like I'll be doing? And then we can all get together and see if we came to the same understanding?
I asked basically these questions on twitter, where @michiexile was kind enough to offer up some thoughts. He stated that I've got some advantage, having spent more time learning how to learn, and also that I'm there to be "a bad conscience", "a voice of authority", and to "give context".
I can certainly see the bad conscience part. That's the point of making assignments with due dates. I'm not sure how much context I can give, though perhaps I'll do more reading in places besides the text, so I'll have more to share (but, again, they can do this). I'm not a particularly authoritative person, but perhaps that's something I should work on in my role as an instructor (or perhaps not?).
Clearly his point about having more experience learning is valid. If you kept count that high, I think I'd be in 22nd grade (only taking 21 of them though :)). With my students who I'm expecting to mostly be in 13th grade, that's approaching twice as many years in school (ouch). Surely I've picked up something in all that time. How can I best impart this knowledge (which I don't have a ready grasp on) to my students as efficiently as possible? I have no idea. My consolation is a guess that I'm not alone in not knowing.
It seems fairly clear to me that knowing a bunch of things is useful. Surely (though I have no experience to base this off of) employers like to hire people who already know many things, and know how to do many things. However, there is absolutely no way an employer can expect a future employee to know everything about pertinent subjects. There's quite simply too much out there. And this holds true especially for students fresh out of college, who almost certainly have significantly less experience than individuals who have been working for some time.
So it seems to me that what employers should be hoping to find is individuals who have a strong ability to learn. I'm guessing this isn't much of a revelation to anybody. I think I'd like to claim something stronger though. I believe that an individual who has a strong ability to learn independently makes for a stronger job candidate.
(Please don't think that my whole outlook is helping kids land jobs. I don't even want a job :), though of course money is nice. I have little idea how to get one anyway - that's a portion of the reason I'm still in school. Also, I don't have much in the way of an idea how an employer would determine if one individual is a stronger independent learner than another. I do believe the internet can help, by giving people a place to show what they do. But I'm getting off track (seems to be what I do).)
I've been trying, at least a little bit, to think about why I believe that an ability to learn independently is an admirable quality. Possibly I'm behind, and people have decided that it's simply true, sort of intrinsically or something. Perhaps not. Part of my concern is that I like to think that I have at least some ability to learn fairly independently (I'm quite possibly fooling myself), and so perhaps I just want to believe that this is an admirable quality. Or, more drastically, perhaps I've got some psychological issues about relying on other people. I like to think this isn't the case, but what do I know?
Having not much in the way of "other opinions" on the subject, I'm pretty much going on the assumption that I'll be doing well if I can get my students to be better independent learners. I'm not saying total independence. I'm not going to cancel all the class meetings and just have a final exam, and expect everybody to be fine at the end of the semester (man, think of all the free time though...). I know that I am not that independent myself (and I'm sure my thesis advisor would be quick to agree), and I don't think it's even a reasonable goal.
So here's what I think I'm going to do with my class. We have 75 minutes class periods, one on Tuesday and one on Thursday. Each Tuesday there will be an assignment due, presumably consisting of exercises from the text (I'm still working on this part), on sections that I have not talked about in class at all. This will require the students to read the appropriate sections, carefully, so that they actually gain an understanding of the material. I'm going to have office hours on Monday, to help students who got stuck on the assignment.
This is the way my undergraduate math courses were structured, by the way. I'm excited about diving in on this policy. I've made attempts in the past, with my calc classes, but went too easy with it, I feel.
So, great, my course is set up. Except, there's one small issue. I've got 150 minutes in front my students each week. If I'm not talking about new material, and they just turned in an assignment showing that they understand old material... what do I do with this time? This part has me seriously nervous (so I'm writing about it out here, good use of time :)).
My guess is that students (including me!) won't understand all of the material from the section. I'm planning on spending as much class time as possible and necessary having a discussion with my students (hopefully with them doing most of the talking) about any questions we have from the reading. Hopefully some will be confused about examples in the text. Hopefully some will still have questions about how to work problems. Hopefully some will have questions about how to interpret answers to questions.
I'm trying to think about what to do if they don't have anything to say. Or if they pretend they don't. I'm guessing if I say "So, since none of you have any questions, maybe I should just give you a quiz on this for you to earn lots of points on, and then we can all go home", some hands will go up (and some people will think going home is a great idea).
One thing I think I'll do is to try to keep track of my own thoughts and observations and questions as I read, so that I can share that with the class if they don't have their own things to talk about. I may also come with some extra examples, to give them time in class to work on them (possibly in groups, or as part of a game or something) and get better at problems simply by doing more of them. Possibly I'll be inspired to look at other materials online or in other books, and can come in with something to share from that reading.
I think talking about the material the students (and I) have just read, after we have worked some problems on our own, will help with our understanding of the material. Surely that's a good goal for the course.
But I was rambling on just a few paragraphs ago about getting my students to be more independent learners. I do think that setting up the course as described above will give them experience trying to develop this skill. I also think, however, that this goal can be addressed slightly more explicitly during class time. I hope that by keeping track of my own "how I read this section" process, I will be able to share that with the class. I touch on this a little above. But I could take it further, I think. I could perhaps scan a section of the text, and keep my notes on the paper as I go. Then during class I could walk through how I read the section with my class. Perhaps they'll pick up on things. Things like... what questions do I ask while reading? How can I tell if I'm actually understanding this material? Where can I go to answer questions I have? Perhaps the exercise will make me more aware of the process myself, and I'll be able to point something out. Perhaps students will point out their own methods of gaining understanding.
At this point I've probably rambled on far too much. Clearly this semester will be (or, at least, could be) an interesting one. I believe that I will learn quite a bit. I hope that my students also do.
Thursday, January 7, 2010
Forgive Me, Gnu
Forgive me, Gnu, for the sins I am about to commit.
I have a plain old text file, whose contents are valid xml. It is my task to convert it into some sort of PowerPoint monstrosity.
Forgive me for embarking on this path. Forgive also those who have asked for said monstrosity, as they may know no better. Give me the strength to show them the light you have given the world. Indeed, thank you for showing me the way, that I decided initially to put my data into plain text, knowing that it could later be converted to anything.
I do not know if it is a larger sin, or some sort of compensation, that my current plan of attack is to first convert my file into an odp file. Or that I will be doing as much of the conversion as I can on a Linux system.
In the name of Stallman, Raymond, and Torvalds (and the many eyes I know not), amen.
I have a plain old text file, whose contents are valid xml. It is my task to convert it into some sort of PowerPoint monstrosity.
Forgive me for embarking on this path. Forgive also those who have asked for said monstrosity, as they may know no better. Give me the strength to show them the light you have given the world. Indeed, thank you for showing me the way, that I decided initially to put my data into plain text, knowing that it could later be converted to anything.
I do not know if it is a larger sin, or some sort of compensation, that my current plan of attack is to first convert my file into an odp file. Or that I will be doing as much of the conversion as I can on a Linux system.
In the name of Stallman, Raymond, and Torvalds (and the many eyes I know not), amen.
Wednesday, December 23, 2009
Desktop OAuth/Python Question
This post is slightly more tech-heavy than most of my recent posts. If that's not your thing, feel free to move on now.
[Update 20091223: NEVERMIND. I got it sorted. The url you re-direct a user to with OAuth doesn't need extra OAuth headers. So you really could just use webbrowser.open(). My bad.]
Suppose I want to interact with the twitter API via some python code running on my personal computer. Suppose, for grins, that instead of using the Basic Authentication I'd rather try OAuth (even though it's all running locally...). Part of the flow of OAuth authentication is that my script is supposed to direct the user to an address at twitter (oauth/authorize), with some OAuth specification headers in the HTTP request for that address (I hope I'm saying things within a few shades of correctly). Well, python provides the webbrowser module which should open up a url in the users browser of choice. And it does, pretty easily (based on my 1-test sample). The problem is that for the OAuth dealings, I'm supposed to pass additional HTTP headers, and I can't figure out how to do that with the webbrowser module. I tried creating a Request object, from the urllib2 module. If I were just making a url request using this library, I could make the Request object, with the extra headers, and things would go fine. But the webbrowser.open() method seems to want its url parameter to be a string, not a Request object.
So... how am I supposed to do this? Or am I not supposed to do this?
Am I supposed to use some other existing python based browser? How is the user supposed to feel like I'm not still in the middle of the authentication process? I mean, if my script displays a webpage using some graphical widget, and waits for the user's input, then I could just be grabbing their username and password while they log in to twitter, no? The point of having the user go to twitter and get a pin is that the user then tells me that pin. I don't put myself in the middle and grab the pin (or their username/password) somehow.
Does any of this make sense? Can somebody point me at a solution? Existing code that solves this problem?
[Update 20091223: NEVERMIND. I got it sorted. The url you re-direct a user to with OAuth doesn't need extra OAuth headers. So you really could just use webbrowser.open(). My bad.]
Suppose I want to interact with the twitter API via some python code running on my personal computer. Suppose, for grins, that instead of using the Basic Authentication I'd rather try OAuth (even though it's all running locally...). Part of the flow of OAuth authentication is that my script is supposed to direct the user to an address at twitter (oauth/authorize), with some OAuth specification headers in the HTTP request for that address (I hope I'm saying things within a few shades of correctly). Well, python provides the webbrowser module which should open up a url in the users browser of choice. And it does, pretty easily (based on my 1-test sample). The problem is that for the OAuth dealings, I'm supposed to pass additional HTTP headers, and I can't figure out how to do that with the webbrowser module. I tried creating a Request object, from the urllib2 module. If I were just making a url request using this library, I could make the Request object, with the extra headers, and things would go fine. But the webbrowser.open() method seems to want its url parameter to be a string, not a Request object.
So... how am I supposed to do this? Or am I not supposed to do this?
Am I supposed to use some other existing python based browser? How is the user supposed to feel like I'm not still in the middle of the authentication process? I mean, if my script displays a webpage using some graphical widget, and waits for the user's input, then I could just be grabbing their username and password while they log in to twitter, no? The point of having the user go to twitter and get a pin is that the user then tells me that pin. I don't put myself in the middle and grab the pin (or their username/password) somehow.
Does any of this make sense? Can somebody point me at a solution? Existing code that solves this problem?
Friday, December 11, 2009
Changing Calculus
Apparently toward the end of every semester I decide to write a post about changing calculus. At least, this is my second go at it. But today's attempt is more a follow-up to my most recent post, about the role of higher education.
My initial motivation in asking the questions in my last post was to provide some structure for what a calculus class should look like. Is the role of calculus really to make sure that all freshman know how to compute integrals by hand, and can use this to find the volume and surface area of a solid of revolution? That rising second years can go through mindless algebraic manipulations to arrive at an answer to a question that was asked without any context or applicability? Moreover, that they need to be able to do so by hand? Quick, find the antiderivative of $\sqrt{3-2x-x^2}$, no computers. Who gives a crap? How many times will that function, or one like it, actually show up in the lifetime of my student? I get paid to do math, and the only time I've ever cared about the answers to these algebraic questions was when I was taking or teaching a calculus course.
Looking back, I'm a little ashamed that the problem above was actually one I assigned as homework for my students this semester. What good does it do to have them work this integral by hand? Surely the answer depends on the students, right? My students going away from the sciences have gotten nothing out of this assignment. My students staying in the sciences have spent another... 5 minutes? 30?... practicing their algebra skills. Hurray‽
Look, I'm not saying algebra isn't useful. But I really do think it is over-emphasized in calculus courses (the ones I've encountered). My calc II course covered: techniques of integration, improper integrals, arc length and surface area of revolution, parametric curves, polar curves, multiple integrals, and infinite sequences and series. Lots of these are wonderfully fascinating and fun topics. Parametric and polar curves force students to start thinking about curves differently, to start re-interpreting functions and points in the plane. Infinite sequences and series are so unlike anything that's ever come before that they can't help but be interesting. Add up infinitely many things that get infinitely small, and produce an infinite value? Or a finite one? How the hell does that work? What does it even mean?
If not a single one of my students can do the integral mentioned above, I'm not sure that I'd feel bad about my semester. If not a significant portion of my students could tell me what was new about a parametric or polar curve, I think I'd be fairly upset (admittedly, now I'm a little afraid to ask).
My problem with my course is that algebraic manipulations are essentially given precedence over conceptual understanding. This is done by making exams that test algebraic nonsense, forcing instructors to make sure their students can do the algebraic nonsense, taking up valuable time that could be better used in other ways. With less time spent on algebra, more time could be spend on concepts, and more time could be spent on improving student's writing. The time spent on concepts makes it a more mathematically interesting and, I'd argue, worthwhile course. Whatever negative impact on my students is brought on by slightly less algebra practice will be more than compensated for by having them spend time thinking about ideas. More time spent teaching students how to write mathematics will force them to think more precisely about what they are saying and how to say it. How could this not be advantageous to students, whether they will be taking more math or not? Unless, of course, thinking about these ideas and how to write them is not aligned with the goals of my university. If the role of higher education isn't something that thinks this would be better, then I'm getting off this boat before it sinks.
So why not go for it? Spend drastically less time on techniques of integration and series convergence tests. Force students to turn in well-written assignments. Spend class time talking about what well-written math is. Spend time letting students play with computers to get a feel for parametric and polar curves. Computers will be faster and more accurate in plotting curves than any student ever will be. Give students time to plot lots of curves, changing parameters to see the effect on the graph. Make students look up resources online to learn how to find arc lengths or surface areas, instead of just telling them the formula (or even deriving it) and having them memorize it. Spend class time talking about how to read the resources they find, and how to evaluate them for quality.
My advisor pointed out, during our conversation mention in my last post, that there are some issues with trying new things. At the lowest level: who gets to teach such a course, and where does their funding come from? But I think better concerns that he mentioned are two that bring me back to some of my earlier questions.
These questions brought me back, full circle, to my initial desire for some formal guidelines for courses. I think it would be hasty to change all of our calculus courses around right away. I think a better solution involves some experimenting. Make a new course, make grad students apply to teach it, arguing for what they want to do differently, and require the instructor to report back on how it went. I think having formal guidelines for courses would aid the experimentation, because it gives an objective measure for comparing a newly designed course with a more traditional one.
I know that much of what I'm saying is oriented toward the way things are set up in my department. How is your department set up differently, and what does that mean about how calculus courses are structured?
Thoughts? Objections? (non-spammy) Links?
My initial motivation in asking the questions in my last post was to provide some structure for what a calculus class should look like. Is the role of calculus really to make sure that all freshman know how to compute integrals by hand, and can use this to find the volume and surface area of a solid of revolution? That rising second years can go through mindless algebraic manipulations to arrive at an answer to a question that was asked without any context or applicability? Moreover, that they need to be able to do so by hand? Quick, find the antiderivative of $\sqrt{3-2x-x^2}$, no computers. Who gives a crap? How many times will that function, or one like it, actually show up in the lifetime of my student? I get paid to do math, and the only time I've ever cared about the answers to these algebraic questions was when I was taking or teaching a calculus course.
Looking back, I'm a little ashamed that the problem above was actually one I assigned as homework for my students this semester. What good does it do to have them work this integral by hand? Surely the answer depends on the students, right? My students going away from the sciences have gotten nothing out of this assignment. My students staying in the sciences have spent another... 5 minutes? 30?... practicing their algebra skills. Hurray‽
Look, I'm not saying algebra isn't useful. But I really do think it is over-emphasized in calculus courses (the ones I've encountered). My calc II course covered: techniques of integration, improper integrals, arc length and surface area of revolution, parametric curves, polar curves, multiple integrals, and infinite sequences and series. Lots of these are wonderfully fascinating and fun topics. Parametric and polar curves force students to start thinking about curves differently, to start re-interpreting functions and points in the plane. Infinite sequences and series are so unlike anything that's ever come before that they can't help but be interesting. Add up infinitely many things that get infinitely small, and produce an infinite value? Or a finite one? How the hell does that work? What does it even mean?
If not a single one of my students can do the integral mentioned above, I'm not sure that I'd feel bad about my semester. If not a significant portion of my students could tell me what was new about a parametric or polar curve, I think I'd be fairly upset (admittedly, now I'm a little afraid to ask).
My problem with my course is that algebraic manipulations are essentially given precedence over conceptual understanding. This is done by making exams that test algebraic nonsense, forcing instructors to make sure their students can do the algebraic nonsense, taking up valuable time that could be better used in other ways. With less time spent on algebra, more time could be spend on concepts, and more time could be spent on improving student's writing. The time spent on concepts makes it a more mathematically interesting and, I'd argue, worthwhile course. Whatever negative impact on my students is brought on by slightly less algebra practice will be more than compensated for by having them spend time thinking about ideas. More time spent teaching students how to write mathematics will force them to think more precisely about what they are saying and how to say it. How could this not be advantageous to students, whether they will be taking more math or not? Unless, of course, thinking about these ideas and how to write them is not aligned with the goals of my university. If the role of higher education isn't something that thinks this would be better, then I'm getting off this boat before it sinks.
So why not go for it? Spend drastically less time on techniques of integration and series convergence tests. Force students to turn in well-written assignments. Spend class time talking about what well-written math is. Spend time letting students play with computers to get a feel for parametric and polar curves. Computers will be faster and more accurate in plotting curves than any student ever will be. Give students time to plot lots of curves, changing parameters to see the effect on the graph. Make students look up resources online to learn how to find arc lengths or surface areas, instead of just telling them the formula (or even deriving it) and having them memorize it. Spend class time talking about how to read the resources they find, and how to evaluate them for quality.
My advisor pointed out, during our conversation mention in my last post, that there are some issues with trying new things. At the lowest level: who gets to teach such a course, and where does their funding come from? But I think better concerns that he mentioned are two that bring me back to some of my earlier questions.
- It is hard to test conceptual understanding. It is much easier to test if a student can do some algebra. With several hundred students going through calculus every semester, this is a practical concern. How does a university handle scale?
- Institutional inertia would have to be overcome. Change is hard. We do this because this is how we've done this for a while now,
and it is clearly the best way to do thingsand it's going okand nobody has complained.
These questions brought me back, full circle, to my initial desire for some formal guidelines for courses. I think it would be hasty to change all of our calculus courses around right away. I think a better solution involves some experimenting. Make a new course, make grad students apply to teach it, arguing for what they want to do differently, and require the instructor to report back on how it went. I think having formal guidelines for courses would aid the experimentation, because it gives an objective measure for comparing a newly designed course with a more traditional one.
I know that much of what I'm saying is oriented toward the way things are set up in my department. How is your department set up differently, and what does that mean about how calculus courses are structured?
Thoughts? Objections? (non-spammy) Links?
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