Last semester I took ORIE 3500, Engineering Probability and Statistics II. On the first day of class, our professor told us that we would have weekly homework assignments that would count for a large portion of our grades. He also told us not to get discouraged if we found ourselves still having trouble with a problem after working on it for five or six hours, the problem sets were meant to be challenging. In order to deal with this somewhat absurd level of difficulty, I ended up forming a study group with several other students in the class. The weekly goal of our group was to complete (and understand) that week’s assignment.
As far as internal representations we used, we had our own individual knowledge of statistics, logic, calculus and math in general, and our memories of what we had learned in lecture and through reading the textbook. Our external representations included our lecture notes, the textbook itself, articles we found about statistics on the internet and our calculators. The transformation involved bringing together all these representations and using them to attempt to solve these 5 or 6 relatively impossible problems.
The transformation step generally occurred through a multi-step process. We would each start the assignment individually, drawing on our own unique representations. Then we would get together as a group and compare what answers we came up with, and then try and work together drawing upon one another’s knowledge to come up with solutions for the more difficult problems. Finally, when things got really bad, we would go to office hours and attempt to use the representation of a TA’s mind.
I would say that the task was loosely coupled for the most part. Although all of us were nice people and wanted to help each other, each member of the group had a main goal of his own success in the course. If one of the members understood the homework perfectly (or if he thought the task difficulty and uncertainty was low) then he might be less willing to go to our group sessions. For extremely difficult assignments, task uncertainty was high and we would end up spending more time together, and we would have to work on more of the problems in a group setting, thus coupling was tighter.
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I was in this group! I agree with all of the representations that you detailed in your blog. I think it's interesting that because of the difficulty of the task at hand, we used more representations to aid us. The collaboration involved multiple representations of material in order to promote understanding and come up with some concept of an answer, but also I like your emphasis on the intense process with which we transformed all of the representations in order to get to an answer. You can really see how the difficulty of the task influences the system of collaboration used.
ReplyDeleteYes, I always looked forward to seeing what seemingly impossible problems would consume my Sunday nights last semester. I followed a pattern similar to the one you described here in doing homework for this class. First I did as much as I could on my own, then collaborated with a friend. Often we still didn't get all the answers, so we would end up finishing the assignment at the drop boxes. This was an interesting experience because most of the people were there to ask others for help. Therefore no one was really sure of their answers, yet we worked out many problems successfully together. That made the last-minute drop box crowd feel like a surprisingly tightly coupled group.
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