"We tend to forget that happiness doesn't come as a result of getting something we don't have, but rather of recognizing and appreciating what we do have."
-Frederick Koenig
Monday, February 1, 2010
Sunday, January 17, 2010
Case Study: Multiple Choice
I'm taking a class on game theory this semester, and I thought this was an interesting passage from one of the books we're reading (called The Art of Strategy):
We think almost everything in life is a game, even things that might not seem that way at first. Consider the following question from the GMAT (the test given to MBA applicants).
Unfortunately, issues of copyright clearance have prevented us from reproducing the question, but that shouldn't stop us. Which of the following is the correct answer?
a. 4π sq. inches
b. 8π sq. inches
c. 16 sq. inches
d. 16π sq. inches
e. 32π sq. inches
Okay, we recognize that you're at a bit of a disadvantage not having the question. Still, we think that by putting on your game-theory hat you can still figure it out.
Case Discussion
"The odd answer in the series is c. Since it is so different from the other answers, it is probably not right. The fact that the units are in square inches suggests an answer that has a perfect square in it, such as 4π or 16π.
"This is a fine start and demonstrates good test-taking skills, but we haven't really started to use game theory. Think of the game being played by the person writing the question. What is that person's objective?
"He or she wants people who understand the problem to get the answer right and those who don't to get it wrong. Thus wrong answers have to be chosen carefully so as to be appealing to folks who don't quite know the answer. For example, in response to the question: How many feet are in a mile, an answer of 'Giraffe,' or even 16π, is unlikely to attract any takers.
"Turning this around, imagine that 16 square inches really is the right answer. What kind of question might have 16 square inches as the answer but would lead someone to think 32π is right? Not many. People don't often go around adding π to answers for the fun of it. 'Did you see my new car--it gets 10π miles to the gallon.' We think not. Hence we can truly rule out 16 as being the correct solution.
"Let's now turn to the two perfect squares, 4π and 16π. Assume for a moment that 16π square inches is the correct solution. The problem might have been what is the area of a circle with a radius of 4? The correct formula for the area of a circle is πr^2. However, the person who didn't quite remember the formula might have mixed it up with the formula for the circumference of a circle, 2πr. (Yes, we know that the circumference is in inches, not square inches, but the person making this mistake would be unlikely to recognize this issue.)
"Note that if r = 4, then 2πr is 8π, and that would lead the person to the wrong answer of b. The person could also mix and match and use the formula 2πr^2 and hence believe that 32π or e was the right answer. The person could leave off the π and come up with 16 or c, or the person could forget to square the radius and simply use πr as the area, leading to 4π or a. In summary, if 16π is the correct answer, then we can tell a plausible story about how each of the other answers might be chosen. They are all good wrong answers for the test maker.
"What if 4π is the correct solution 9 (so that r = 2)? Think now about the most common mistake, mixing up circumference with area. If the student used the wrong formula, 2πr, he or she would still get 4π, albeit with incorrect units. There is nothing worse, from a test maker's perspective, than allowing the person to get the right answer for the wrong reason. Hence 4π would be a terrible right answer, as it would allow too many people who didn't know what they were doing to get full credit.
"At this point, we are done. We are confident that the right answer is 16π. And we are right. By thinking about the objective of the person writing the test, we can suss out the right answer, often without even seeing the question.
"Now, we don't recommend that you go about taking the GMAT and other tests without bothering to even look at the questions. We appreciate that if you are smart enough to go through this logic, you most likely know the formula for the area of a circle. But you never know. There will be cases where you don't know the meaning of one of the answers or the material for the question wasn't covered in your course. In those cases, thinking about the testing game may lead you to the right answer."
We think almost everything in life is a game, even things that might not seem that way at first. Consider the following question from the GMAT (the test given to MBA applicants).
Unfortunately, issues of copyright clearance have prevented us from reproducing the question, but that shouldn't stop us. Which of the following is the correct answer?
a. 4π sq. inches
b. 8π sq. inches
c. 16 sq. inches
d. 16π sq. inches
e. 32π sq. inches
Okay, we recognize that you're at a bit of a disadvantage not having the question. Still, we think that by putting on your game-theory hat you can still figure it out.
Case Discussion
"The odd answer in the series is c. Since it is so different from the other answers, it is probably not right. The fact that the units are in square inches suggests an answer that has a perfect square in it, such as 4π or 16π.
"This is a fine start and demonstrates good test-taking skills, but we haven't really started to use game theory. Think of the game being played by the person writing the question. What is that person's objective?
"He or she wants people who understand the problem to get the answer right and those who don't to get it wrong. Thus wrong answers have to be chosen carefully so as to be appealing to folks who don't quite know the answer. For example, in response to the question: How many feet are in a mile, an answer of 'Giraffe,' or even 16π, is unlikely to attract any takers.
"Turning this around, imagine that 16 square inches really is the right answer. What kind of question might have 16 square inches as the answer but would lead someone to think 32π is right? Not many. People don't often go around adding π to answers for the fun of it. 'Did you see my new car--it gets 10π miles to the gallon.' We think not. Hence we can truly rule out 16 as being the correct solution.
"Let's now turn to the two perfect squares, 4π and 16π. Assume for a moment that 16π square inches is the correct solution. The problem might have been what is the area of a circle with a radius of 4? The correct formula for the area of a circle is πr^2. However, the person who didn't quite remember the formula might have mixed it up with the formula for the circumference of a circle, 2πr. (Yes, we know that the circumference is in inches, not square inches, but the person making this mistake would be unlikely to recognize this issue.)
"Note that if r = 4, then 2πr is 8π, and that would lead the person to the wrong answer of b. The person could also mix and match and use the formula 2πr^2 and hence believe that 32π or e was the right answer. The person could leave off the π and come up with 16 or c, or the person could forget to square the radius and simply use πr as the area, leading to 4π or a. In summary, if 16π is the correct answer, then we can tell a plausible story about how each of the other answers might be chosen. They are all good wrong answers for the test maker.
"What if 4π is the correct solution 9 (so that r = 2)? Think now about the most common mistake, mixing up circumference with area. If the student used the wrong formula, 2πr, he or she would still get 4π, albeit with incorrect units. There is nothing worse, from a test maker's perspective, than allowing the person to get the right answer for the wrong reason. Hence 4π would be a terrible right answer, as it would allow too many people who didn't know what they were doing to get full credit.
"At this point, we are done. We are confident that the right answer is 16π. And we are right. By thinking about the objective of the person writing the test, we can suss out the right answer, often without even seeing the question.
"Now, we don't recommend that you go about taking the GMAT and other tests without bothering to even look at the questions. We appreciate that if you are smart enough to go through this logic, you most likely know the formula for the area of a circle. But you never know. There will be cases where you don't know the meaning of one of the answers or the material for the question wasn't covered in your course. In those cases, thinking about the testing game may lead you to the right answer."
Monday, November 16, 2009
The weekend....
I went camping with two friends from work last night, and apart from the rain this morning which made packing up miserable, it was a wonderful time! We have decided to try and make it a monthly trip....it is such a stress-reliever for me to be out of St. Louis, and even better to be out in nature!
This is where we went, Mark Twain Lake, gorgeous!
I now have a very wet tent sitting in my bathtub just waiting for dry weather so it can be set up and aired out....
On a sad note, Matt left this weekend for CO...it's going to be hard to be far away from him...and hard not to be jealous of where he is!
This is where we went, Mark Twain Lake, gorgeous!
I now have a very wet tent sitting in my bathtub just waiting for dry weather so it can be set up and aired out....
On a sad note, Matt left this weekend for CO...it's going to be hard to be far away from him...and hard not to be jealous of where he is!
Wednesday, November 11, 2009
Some things....
Betsy and I have decided to start this up again.....I think its good, sometimes I think of things that should be shared with the world.
An update:
-I am in nursing school now and it is crazy stressful, but I am very happy with it thus far, as in I have not changed my mind and wanted to change my career path (yet again).
-I STILL work at The Fountain on Locust (which everyone should check out). It is a great place with great people (which is why I hold onto it even though I never want to go to work).
-I miss Betsy.
Something old: hilarious and wonderful
Something new: Well, its been on for awhile now, but GLEE is my new obsession....I don't normally keep up with TV shows but I will stop the world to watch this one.
Something borrowed: First linked from my roomie Claire's blog and thought it should be shared....maybe. Gaga is CRAZY. Very tempting to go to her show in January but it is probably sold out already and I don't really have $$ :(
Something blue: Love this.
An update:
-I am in nursing school now and it is crazy stressful, but I am very happy with it thus far, as in I have not changed my mind and wanted to change my career path (yet again).
-I STILL work at The Fountain on Locust (which everyone should check out). It is a great place with great people (which is why I hold onto it even though I never want to go to work).
-I miss Betsy.
Something old: hilarious and wonderful
Something new: Well, its been on for awhile now, but GLEE is my new obsession....I don't normally keep up with TV shows but I will stop the world to watch this one.
Something borrowed: First linked from my roomie Claire's blog and thought it should be shared....maybe. Gaga is CRAZY. Very tempting to go to her show in January but it is probably sold out already and I don't really have $$ :(
Something blue: Love this.
Monday, November 9, 2009
Hi, my name is Betsy, and I'm addicted to Marketplace.
Throughout the semester, my Economics professor has repeatedly encouraged my class to listen to Marketplace, a radio show put on by American Public Media that focuses on topics of economics and business. Before the occurrence of recent events, when Dr. Gillette mentioned the show, I would simply mentally roll my eyes and then forget about his advice as soon as a walked out of the classroom door; however, one day, in a fit of boredom and procrastination, I figure I would check it out. And now I can't stop.
There is a variety of shows to listen to (or watch!), ranging from sixty seconds to fifty minutes in length. The 10-minute morning report comes out daily at 6:30, so I listen to that while drinking my coffee and waking up. I usually try to catch the longer show sometime in the afternoon. One of my favorite tidbits is Marketplace Minute, a weekly video publication that sums up the week's business and economics news in a 60-second poem. Here is the most recent update:
I can't decide if it's a good or bad thing that Marketplace provides me with a guilt-free means of procrastinating; seeing as a teacher told me I should listen to it, I can do that instead of other homework, right?
There is a variety of shows to listen to (or watch!), ranging from sixty seconds to fifty minutes in length. The 10-minute morning report comes out daily at 6:30, so I listen to that while drinking my coffee and waking up. I usually try to catch the longer show sometime in the afternoon. One of my favorite tidbits is Marketplace Minute, a weekly video publication that sums up the week's business and economics news in a 60-second poem. Here is the most recent update:
Marketplace Minute With Bill Radke 11/06 from Marketplace on Vimeo.
I can't decide if it's a good or bad thing that Marketplace provides me with a guilt-free means of procrastinating; seeing as a teacher told me I should listen to it, I can do that instead of other homework, right?
Monday, November 17, 2008
Saturday, October 25, 2008
The people on the bus go...
Betsy and I are both using public transportation this semester to get to school, work, etc. I love it (most of the time) and I think Betsy does too. You do have some strange experiences though......
Abby's Bus Experiences:
1. A woman got on the bus, and since most of the seats were filled she stood near me and held onto the overhead bar. When she grabbed onto the bar all I heard was clink-clink-clink-clink-clink. When I looked up I expected to see a woman with a robotic hand...but no, it was her 4-inch (at least), all-natural fingernails. Unreal.
2. Some guy that I had never sat next to or spoken to but who was usually on my bus was getting off, but first he walked back to where I was sitting, looked me in the eye, and said "I like you because you're funny". Then he got off. It was really strange. The next time he was on my bus, we had a pretty awkward conversation in which he asked me a)if he was wearing too much cologne (apparently I was making a face), b) what my favorite cereal is, and c)if I liked gravy. I've been avoiding him since then...you know...wearing sunglasses, putting my hoodie on, pretending to sleep. Tricks of the trade...
Betsy's Bus Experiences:
1. A woman asked me if I was blind, I guess because I wear the same sunglasses every day and they're rather dark. (My dad mentioned that when she asked me "Are you blind" I should have answered "No, but I'm deaf." Too bad I didn't think of it at the time!)
2. The other day when I got on the bus, this kind of crazy looking woman with coke-bottle glasses stared at me for a while, but she stopped after a few minutes. She put on head phones and started singing to herself and dancing crazily in her seat. A woman she knew got on the bus a few stops later and sat next to her. Ms. Coke-Bottle Glasses opened up her bag and pulled out some M&M's, some hoho's, and a plastic case with four caramel apples. She gave her friend the first two items, then, displaying the apples, she whispered audibly to her companion that she was thinking of giving one to me because I "looked sweet." A little embarrassed, I pretended not to notice and just stared out the window; however, a few minutes later, the woman caught my attention and handed me one of the caramel apples, not giving me the chance to say no, so I simply said "thank you" and carried a caramel apple all the way home. . .
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