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Friday, April 01, 2005
So, uh, I should probably say this in the comments for wed's post, but whatever: what is this CMS thing in Waterloo? What events are happening? I've found something: is this it? If it is, it shouldn't be too hard to come to Waterloo on the Sunday, as Jamsie's wedding is on the Saturday.
Learning Centre Fun
I've managed to be incredibly busy this week, while at the same time accomplishing very little. Not quite sure how that managed to happen. On Wed. evening in the learning centre I had two women come up and basically ask me to teach them calculus. I sighed inwardly, but in the end, it wasn't so bad, and they seemed to learn some things. As a friend at school mentioned the next day, it was a really good opportunity to put one's ability at teaching to the test. I certainly didn't look on it quite so positively at the time :)
There are two main things I think I've learned from this whole learning centre thing. One is that the vast majority of students that come to the learning centre are very eager and willing to learn. I suppose I got the impression somewhere that most would be very resistant to 1-on-1 learning, but that has not been the case in the slightest. I can only think of one real jackass in all my 6 months or so doing this.
The other is my belief that many, many of the problems students have is due to lazy teaching. What do I mean by lazy teaching? Skipping steps and/or doing things too quickly when a concept is first introduced, in addition to not fully explaining the ideas behind said concepts. There seems to be a strange dual mentality in this regard. The teacher assumes the students are quick enough to follow all of the steps they skip in their examples, but too stupid to understand the reasoning behind the concept. Many times students can't do problems because the way they have seen it done in class leaves out vital steps, while at the same time they are confused because they don't see the guiding principle behind the idea. In my experience, sometimes all I have to do is just expand a step or explain a concept a little bit more, and the student can easily do the problem.
What I'm referring to here is the first year calculus classes - this is where the majority of students come to me from. I think there is a general mentality in mathematics departments (and I have been prone to this as well) that most people at university can't really do or understand calculus. The trouble is, the professors believe this when they teach it, so the problems mentioned above crop up, and as a result, people don't do well at calculus.
¡ExPLOzErS!
So Ben mentioned he wanted to know how to play ¡ExPLOzErS! It's similar to Domineering. You play on an nxn board. One person plays up/down, the other left/right. In Domineering, your only move is to play two of your pieces in your (up/down or left/right) configuration somewhere on the board. By up/down or left/right I mean one person can play his two pieces at (x, y) and (x, y+1), and the other at (x, y) and (x+1, y). Last player to move wins. See the above link for some examples of Domineering.
In ¡ExPLOzErS! you can either play a domineering move, or blow up a single one of your pieces. When you blow up the piece, the square it is on is "destroyed", and unusable for the rest of the game. In addition, any pieces contiguous to it are removed from the board, and one can play on those squares again. In the example game at the above link, if one player destroyed at (5, 8), then the pieces at (6, 8), (7, 8), (7, 7), (8, 7), and (8, 6) would all be removed, and the square at (5, 8) would become unusable.
I'm not really sure this is quite the correct ruleset for it yet though. The trouble is that Domineering itself is essentially a "hot" game: whoever plays first has an advantage. So the "blowing up" move is not usually a good move - if you do it, you open up sections of the board, and give your opponent the chance to play first in those sections of the board, which is an advantage because of the hotness of Domineering. I'm pretty sure, though I haven't really thought about how to prove it, that a Domineering move, if one is available, is always better than an exploding move.
Moreover, the game values I've found for this game seem to indicate that is simply a hotter version of Domineering. For example, the game value of a certain configuration in Domineering is {3/2|-2}, the value in ¡ExPLOzErS! was {5/2|-3} - the ratio of left's value to right value remains the same, the temperature has simply increased (temperature is actually a real thing in game theory, measuring how much the two players want to play first in this game).
Anyways, the point is, I think it would be better if the exploding move is changed to: blow up a piece, then place somewhere. This increases the value of an exploding move - in fact, I've found a board position where an exploding move is better than a domineering move. However, it is not always a better move, so this ruleset might strike a nice balance between the two types of moves. I'll have to see what kind of game values this version gets.
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Geez, I wrote a lot. Oh well, haven't written much in a week.
Learning Centre Fun
I've managed to be incredibly busy this week, while at the same time accomplishing very little. Not quite sure how that managed to happen. On Wed. evening in the learning centre I had two women come up and basically ask me to teach them calculus. I sighed inwardly, but in the end, it wasn't so bad, and they seemed to learn some things. As a friend at school mentioned the next day, it was a really good opportunity to put one's ability at teaching to the test. I certainly didn't look on it quite so positively at the time :)
There are two main things I think I've learned from this whole learning centre thing. One is that the vast majority of students that come to the learning centre are very eager and willing to learn. I suppose I got the impression somewhere that most would be very resistant to 1-on-1 learning, but that has not been the case in the slightest. I can only think of one real jackass in all my 6 months or so doing this.
The other is my belief that many, many of the problems students have is due to lazy teaching. What do I mean by lazy teaching? Skipping steps and/or doing things too quickly when a concept is first introduced, in addition to not fully explaining the ideas behind said concepts. There seems to be a strange dual mentality in this regard. The teacher assumes the students are quick enough to follow all of the steps they skip in their examples, but too stupid to understand the reasoning behind the concept. Many times students can't do problems because the way they have seen it done in class leaves out vital steps, while at the same time they are confused because they don't see the guiding principle behind the idea. In my experience, sometimes all I have to do is just expand a step or explain a concept a little bit more, and the student can easily do the problem.
What I'm referring to here is the first year calculus classes - this is where the majority of students come to me from. I think there is a general mentality in mathematics departments (and I have been prone to this as well) that most people at university can't really do or understand calculus. The trouble is, the professors believe this when they teach it, so the problems mentioned above crop up, and as a result, people don't do well at calculus.
¡ExPLOzErS!
So Ben mentioned he wanted to know how to play ¡ExPLOzErS! It's similar to Domineering. You play on an nxn board. One person plays up/down, the other left/right. In Domineering, your only move is to play two of your pieces in your (up/down or left/right) configuration somewhere on the board. By up/down or left/right I mean one person can play his two pieces at (x, y) and (x, y+1), and the other at (x, y) and (x+1, y). Last player to move wins. See the above link for some examples of Domineering.
In ¡ExPLOzErS! you can either play a domineering move, or blow up a single one of your pieces. When you blow up the piece, the square it is on is "destroyed", and unusable for the rest of the game. In addition, any pieces contiguous to it are removed from the board, and one can play on those squares again. In the example game at the above link, if one player destroyed at (5, 8), then the pieces at (6, 8), (7, 8), (7, 7), (8, 7), and (8, 6) would all be removed, and the square at (5, 8) would become unusable.
I'm not really sure this is quite the correct ruleset for it yet though. The trouble is that Domineering itself is essentially a "hot" game: whoever plays first has an advantage. So the "blowing up" move is not usually a good move - if you do it, you open up sections of the board, and give your opponent the chance to play first in those sections of the board, which is an advantage because of the hotness of Domineering. I'm pretty sure, though I haven't really thought about how to prove it, that a Domineering move, if one is available, is always better than an exploding move.
Moreover, the game values I've found for this game seem to indicate that is simply a hotter version of Domineering. For example, the game value of a certain configuration in Domineering is {3/2|-2}, the value in ¡ExPLOzErS! was {5/2|-3} - the ratio of left's value to right value remains the same, the temperature has simply increased (temperature is actually a real thing in game theory, measuring how much the two players want to play first in this game).
Anyways, the point is, I think it would be better if the exploding move is changed to: blow up a piece, then place somewhere. This increases the value of an exploding move - in fact, I've found a board position where an exploding move is better than a domineering move. However, it is not always a better move, so this ruleset might strike a nice balance between the two types of moves. I'll have to see what kind of game values this version gets.
---------------------------
Geez, I wrote a lot. Oh well, haven't written much in a week.
