Ah yes. Time flows differently through different parts of a schedule.
Three fifty-minute lectures spread over Monday, Wednesday, and Friday seem to fit a topic, and the mood of a section, completely differently from the "same" 150 minutes spread over a single 6 to 9 pm interval. The length of time a given topic takes, and the engagement of the students seems to be completely elastic, depending on the time of day. Although there are questions, discussion, and argument in both instances, in the evening version of 150 minutes I feel as though there are some for whom the details of complete induction are an irritating distraction from world 'o warcraft or urgent discussions with a neighbour.
Complete induction. This seems to be the flavour of induction where the character of base cases comes into focus. Since a valid proof by complete induction doesn't require any base cases, and doesn't really provide a template for the sort of values you should assume are base cases, you're forced to think about which natural numbers n can have P(n) established about them without referring to any smaller natural number (induction free!), and which require the helping hand of an induction hypothesis.
3 comments:
hmmm*ponders*....I would definitely agree with your comment on the different reaction speeds of students depending on the time of day, however i would disagree with the notion that only those students at night are subject to frustration regarding complete induction, or longing for their computer screen.
In my opinion i would think that the response time would vary DRASTICALLY as well as the level of understanding and absorption of information. But that is simply due to the length of the days as we approach winter and the decrease of peoples immune systems as December approaches....
On Complete Induction i would think that there would be three hurdles to over come in that sort of question:
1)figuring out if it is complete or simple, and this is fairly easy based on the position of information relative to n where P(n) is concerned
2)discovering the cases where n is not defined or where it does not exist
3)figuring out the algorithm or "trick" that's gonna help you get through the actual Induction step itself
the rest should flow like hair from Paul's head.....i hope that joke wasn't out of line...hahaha
DOM
i totally agree with the different speeds or reactions from 3 1 hour lectures, or just 1 3 hour lecture.
i know i can't sit still if i were to sit in this course for 3 hours straight!
The remark of World o' Warcraft was quite comical, mainly because of the truth behind the statement. I've found that during night classes, student carrying around laptops are a lot more distracted than students who use them during day classes. There is a higher level of alertness with day classes than night, on average. I only say that because personally, I'm a lot more alert during night classes than days. I also find that the two 10 minute breaks are a lot better for the students than the single 20 minute break. The chance to "wake up" during night classes is nice. Over all, of course you would see a difference between night classes and day classes, but they both come with equal pros and cons.
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