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Snow classes
March 4, 2005
We've been set back by about a week because of weather. It really interupts the flow of class. Oh well, it is not in my power to control the weather. Last night was the first time we met as a class in a week and a half. I lectured about recursion relations. I had asked them last class to read chapter one in their text which deals with recursions. I also sent them an email reminder of this fact when we missed our classes because of snow. I was happy to see that many people seemed to have done the reading. It was also clear that they had a hard time with the material. That's ok though, I'm thrilled if they read it before we discuss it, and then hopefully revisit it after we discuss it in class. I also graded and returned their homework assignments. These involved making estimates and making estimates understandable. Overall, they were very well done. A common mistake was a failure to cite sources for statements of fact that are not common knowledge. (The Great Lakes contain X gallons of water.) A second common mistake was a failure to write the answers in an intelligible manner. This is typical in math classes - you get a bunch of scribbled equations and then a boldly written answer. I'm trying to break them of this habit. The best part of the homework was the response to the so-called "grades." We've had many discussion about how they should interpret these numbers. My policy seems to be sinking in - no one came and asked for points back. Many came and asked me to explain where they went wrong. Even those I had misgraded simply came to me to understand if it was my mistake or theirs - but did not ask for "points." I think they are starting to see this grading process as a conversation, as constructive criticism, as an opportunity to find and fix the holes in their knowledge. Do I hope for too much?
All the information in the world
February 24, 2005
I mentioned a few weeks ago that in addition to teaching mathematical modeling in Math 518, I'm also teaching a graduate special topics class in nanoscience, Math 824. The goals of Math 824 are two-fold. First, I'm trying to give students a firm foundation in nanoscience. We're doing this by reading and discussing the primary literature in the field. At the end of the course, I hope they'll feel confident enough to be able to explore nanoscience further as they wish. The other goal of Math 824 is to improve their skills in reading scientific papers. So far this semester we've read 5 papers. Two were transcripts of talks by Richard P. Feynman. One was an article from Scientific American. The other two were journal articles. During our discussion of the fifth article, which was from an IEEE journal, it became clear that comprehension had dropped significantly compared to students reading of the other four articles. Yesterday, we spent the first 1/2 hour of class discussing reading again. The discussion was lively and interesting. It was clear that students were feeling a lot of anxiety over their failure to read this one article well. I had them identify precisley why they found it difficult. Most of the answers I expected. A lot of jargon, the article assumes a lot of background, explanations were terse, the context of the work was not well explained, etc. A few of the answers were unexpected. One student said he was fooled by the age of the article. (The paper was from 1967.) Since it was an older paper, he expected it to be easy! I'm not sure what to make of that comment, but I was amused. The other unexpected response had to do with how students used the internet. When I asked them if they had tried to find other sources of information about the topic of the article, many of them responed that they had. All of those who had had simply Googled keywords like "resonant gate transitor," or "tuning problem." They were then faced with the problem of finding relevant information from among millions of hits, or ending up with no hits at all. Since this topic is not like say "nanotweezers," where you can easily find relevant information, they met with little or no success. They did not take the next obvious step of going to the science citation index and tracking the papers that cited the paper we were reading. They didn't try any library databases. The certainly did not physically go to the library. I asked them what fraction of the information in the world they thought was available online. The answer was "most of it." My guess would be that that answer is wildly wrong. I would estimate less than 1% of all the information in the world in online. I would also contend that the information that is available is not really well organized. This is a calculation I need to do! Maybe I can give the problem to my Math 518 students!
How many bricks?
February 23, 2005
Last Thursday I gave my class a homework assignment. This was a follow up to the in-class assignment we did involving making basic estimates and understanding large numbers. One of the problems asked them to estimate the number of bricks on the UD campus. Last night in looking at their answers, I was very very pleased. These guys did excellent work. I think they really get this idea now. I think the last week and a half have taught me some important lessons as a teacher. First, its important to put aside my own emotional response to students work. In particular, I need to be sure to put aside any dissapointment I might feel when they don't measure up to my expectations. Instead, I need to focus on why they haven't measured up and what I can do to communicate what I haven't communicated. The other lesson is the importance of flexibility. Essentially one class period was devoted to this estimation topic. This was completley unplanned, but has turned out to be a wonderful entry point into so many topics in mathematical modeling. It's the type of thing I wish I had thought of doing when teaching this type of class before! If I had tried to adhere to my timeline, I would have missed a wonderful opportunity.
Last night we also resumed our discussion of the Great Lakes project. The discussion was richer than our first discussion. We've moved forward a bit. The next issue I must deal with is in getting them to see how we can focus our efforts on parts of a complex problem. That is, how it is useful to take small bites. We don't need to deal with both pollution and invasive species at once. We don't need to consider every aspect of pollution remediation. I need to get across the notion of higher order effects.