Math 580

This page will be used to post response to feedback. I will try to explain why I am or am not taking the suggested actions. Of course I will not post every feedback that I receive; reserving the right to not post positive ones that I do not think require a reply as well as negative ones that are inappropriate (though feel free to send positive ones as well, it is helpful for me to know what you think is working well in the class.)

January 29, 2006

Feedback: I just read your response to the feedback and it said that you are going to add an additional review session that will go from 8:00-9:00 am on Thursday, well, that is not going to help me because I have classes every Thursday that start at 8:30 until 10:30. So by adding the different time review session, will be of no benefit to me. Is there any possibility of putting on a different day at a different time? I would definately go to it, but I cannot afford to miss any of my other classes.

Response: This response pertains not to just this request, but all of them in general so far. The two things I want to address are the review sessions and homework sets. First off, the review sessions. Thursday morning is the only time that is convenient for me to conduct a review session. Since it seems the 8-9 am will not help people, we will go back to having them from 9-10:30 as we originally scheduled. If this does not work into your schedule I apologize, but this is the only time that is convenient for me. You are welcome to organize your own study sessions amongst your team members or other classmates. Each team has had a representative at each review session thus far, so you also might photocopy their notes and look them over. The review sessions are nothing magical. All we do at the review sessions is go over homework that has already been turned in. If you are unable to make it to a review session, there is no reason you can't attend office hours or make an appointment to meet with me to go over old homework questions you were not sure on. We will not have a review session this week as the midterm is on Monday and no homework will have been turned in this week to go over.
Next, the homework. From now on I will indicate which problems I am going to grade before you turn the assignments in. I will continue to post the problems I believe are important for you to know how to do, but this way if you choose not to do some of the homework you will know which ones will be graded. This does not mean that anything that is not graded is not important. This will allow you to decide how indepth you want to learn the material and have better control on how much time you spend on the homework sets.

January 27, 2006

Feedback: I want to say thank you for having the review sessions. They have been helpful. I understand with time constraints it is difficult to fit the schedule of everyone. I also agree the pace of the course has been fast. However, other courses in the math department that needed to cover a large amount of material simply did so at more of a surface level. That is, we would cover material quickly, but without getting into the more intricate/sophisticated problems. Would it be possible to do something along those lines? Right now, the work required for this class is about the same as the 2 other math classes combined (a total of 8 credit hours which are generally regarded as equally or more difficult than 580) that I am currently taking. Perhaps the reason that some students do not have the basics is because we skimmed over them so quickly or were expected to figure them out without ever seeing more correct solutions than the ones that you provided after we did the homework. I think you have a good point that as we move to higher mathematics we will need to figure more and more out on our own. But it seems to me that a teacher serves no purpose if not to teach and help students master the material. Why go to class if you can just read the book or find the proof somewhere else? For me the answer is to get the examples, because understanding the more concrete examples is how I learn. I think you understand AFTER you have solved a problem correctly. Until then, your understanding may not have been as clear. In other words, if I try to go from a theorem to a problem with no examples, chances are that I will be stuck for a bit. Many times the problems requires a "trick" for that type of problem that you do not realize until you have seen/done a number of problems. Examples make life (and math) much more rewarding because the expedite your solution. So thank you for the examples you have given. They have helped tremendously.

Response: I do try to do examples of many of the theorems and definitions, but for some it is not possible (for example, proving there are infinitely many primes, there really isn't a way to do an example for that one). I will try to make sure I am incorporating examples whenever possible to make things concrete and you should feel free to stop me in class and ask for some examples whenever you feel it is appropriate. As for the covering the material at a surface level, if we do not cover things such as integers and division fairly indepth, it will be exceedingly difficult to understand the more abstract concepts to be covered later. I will try to make sure that I am not assigning problems for individual homework that are too indepth and difficult. The only one this week that seemed very indepth or particularly difficult was problem 17. It IS important that you do examples on your own however. The material and examples always seems easy when watching someone else do it and is much more difficult when trying to do it on your own. Before you begin doing problems from a section you should go through each theorem and plug some numbers in to see what it really says and make sure you understand the theorem. The homework problems do sometimes require a trick to solve them, though by far the majority of homework problems to this point have been strictly applying the definition. It is not possible for an instructor to show you each trick so that you'll know them all before doing the homework. As you point out, you truly understand the material after you have solved a problem. The difficulty and beauty of this type of course is that there is no recipe for doing problems. In calculus, a professor could show you how to do a u-substitution and then you could do a bunch of them on your own using the exact same method. In this type of class that is not possible, it requires logic and mastery of the material at a deeper level to do the problems. That is a source of frustration when trying to do the problems, but also a source of joy when figuring a new problem out for the first time. Please keep in mind I am always available to help you out if you are stuck on material. You don't have to only ask about assigned homework problems in office hours.

Feedback: I have been spending many hours on your homework and yet I still do not understand all of the concepts that you are trying to teach. It feels like you are rushing through each section, without making sure that we understand it. It is important not to assign 2 homeworks, weather it is team homework or individual in the same week, I think it would be better to assing just a couple extra problem per homework than to load us down each week with as much as you have been. Also, I think that it is imperative that you ask all of the class when a good time for (everyone) would be for your review session. I have wanted to come to both of them, but since I have class right during the time that you set I could not attend. If you are going to review, please make sure that you put it in a time when everyone can attend.

Response: There seems to be three main issues here to address: the speed at which the course is moving, the amount of homework, and the review session time. It is true that this course is moving quite quickly, and I am sorry that it may seem that we are moving through the material with a lack of regard for making sure that everyone is understanding the material. This is definitely not my intention. However, we have a syllabus that we must adhere to so that people finishing this class are prepared for Math 581. Myself and the other instructor for Math 580 scheduled out before the term how much time we could spend on each section and still finish the material by the end of the semester. Right now we are just about right on target. In theory it would be wonderful to go slowly through each section and make sure every student completely understood each concept. In reality this is impratical not only because of the time constraints, but also because of the different levels of students in the class. You will most likely see that in future classes many instructors will spend less time making sure you understand the material. I have actually never been in a class where numerical examples of the theorems were worked out. For example, a professor usually states the Chinese Remainder Theorem, proves it, and then moves on without doing any examples. It is expected that at this point in your mathematical career you are getting to the point where you can work out examples for yourselves. I am trying to help bridge that gap by working out some examples for you.
The second issue is the amount of homework being assigned. This week was particularly difficult because you had team homework and individual homework due on the same day. This is an abnormality that arose because of the midterm on Monday. I wanted to make sure you were able to get feedback before the midterm and did not have homework due on the day of the midterm. In general team homework will be due only every 1.5 to 2 weeks. I could assign only a couple of homework problems per week. However, doing that few of homework problems would not help you learn the material and not adequately prepare you for the midterm or the next class. When there are students still unable to do induction or state what a function being surjective means, this indicates not that I am assigning too much homework, rather too little. For some students the assigned homework may be more then they need to be able to understand the material, for others it will be the perfect amount, while for others they will actually need to work additional examples to the homework I assign. If you struggle with the homework it may be wise to work out some examples of what the homework is asking as well as what the theorems are stating to get a better grasp of what is going on. One also needs to keep in mind that this is another area where different abilities come into play. While it may take one student several hours to solve a problem, many others in the class may only take 10-15 minutes to solve the same problem. It may speed up homework if you work together in your homework teams, or at least with some of the people from your homework team. That way you can brainstorm to come up with ideas quicker.
The final issue is the time of the review session. It is difficult, if not impossible, to find a time during the day that will be convenient for everyone in the class. Everyone has different class/work schedules, including people who live off campus and commute to school. To try and help so that everyone can attend at least some of the review sessions I will start alternating weeks between the Thursday 9-10:30 am time we have been having them to also include a Thursday 8 - 9 am time every other week. Therefore, after the midterm next week we will have the review session from 8-9 am in the normal room on Thursday. One should also keep in mind that these review sessions are extra sessions to class. It is not required you attend. I am having these review sessions, as well as passing out some homework solutions, as a courtesy to help you learn the material. With that in mind I am going to consider when is convenient for me as the primary factor determing when review sessions take place.