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A New Look & Project Reports
February 27, 2004

If you've looked at this blog before, I'm sure you'll notice the new look. I realized that my old format was quickly becoming unwieldy. Hard to read and manage. I'm using a little piece of software called "Easy Blog Maker." It's not incredibly full featured, but I think it will make this blog a bit easier to read. The software is for MS Windows, and is very easy to learn. You can find it here.

We finished the project presentations in class today. Overall I was very pleased. One thing to note, I had scheduled Wed. for presentations, we only finished 4 out of 6. So, we're one day behind schedule now. I was really pleasantly surprised by the high level work in both sections of my class. In my 9AM class there were two teams that stood out. Both gave very well-designed presentations. One team had totally nailed the mathematical problem. The other came very close. Most surprising was that the best team overall was in my 10AM class! And, the team included the worried student who sent me a panicked email the second day of the semester! This team got the math right, brought in a lot of relevant external material, related the project to their individual engineering backgrounds and closed the presentation with an alternative to the spin-casting method that I had never thought of! Really great work. They also had a neat idea for getting their team members all involved in the presentation. Two members of the team spoke, the other two interjected with very pointed questions at just the right moment. Though staged, it worked very well and made the presentation much more lively than the others. During the presentations, I took copious notes. I also had them give me CD's with their presentations on them. I distributed my standard oral presentation rubric and had one member from each team evaluate the team who was speaking. I had them give these evaluations right to the teams without my ever seeing them. I encouraged them to be candid and constructive. I think this was a good idea. It kept the audience involved a bit. We did have the problem that all teams were talking about the same topic, this lead to a bit of boredom in the audience. In grading the presentations I assigned a max of 40 points for overall presentation, a max of 20 points for context and content outside of course material and a max of 40 points for mathematical correctness and content.

After we finished the presentations in class, I had the students evaluate each other. I used the team rubric from the ITUE. Again, I encouraged the students to be candid. I reminded them about the 25% of their grade fact. I had them hand me back the forms. I will distill comments for each individual student this weekend. This will take a considerable amount of time, but I think this level of feedback is necessary, at least at the start of the semester.

After the students finished their forms I had them reassemble into teams and come up with the best three things they saw and worst three things they saw during the presentations. This lead to a really lively useful discussion about what to do and what not to do during a talk. We also touched on the good and bad of MS PowerPoint. I was tempted to do this exercise before they spoke, but I'm very glad we did it immediately after their presentations. I think some of this will stick.

The two best presentations are available here and here.

Another Opportunity Lost
February 24, 2004

Missed another opportunity for a minute-write or mini-PBL exercise today. We're talking about the equations of lines and planes in 3-d. The first natural question is "What do you need to specify a line (or a plane) uniquely?" While I began the discussion with this question and tried to elicit the answer from the class, I think giving them 1-2 minutes to write out their ideas beforehand might have improved the discussion. Perhaps if they wrote it out individually and then came up with a group answer in 1-2 minutes? Reminder to self - every time I introduce a new definition - think PBL! I had one group come to me today in a panic about the presentation for tomorrow. One of their teammates decided to drop the course (last night). He was the person they sent to talk to me yesterday about their project. It was clear from his visit that he had no idea what the group had been doing, he left rather unsatisfied. I think it was a good decision for him to drop. But, the group itself had really not made much progress. Two of the team members came and spent an hour with me today (the third could not make it). We had a mini-group meeting concerning the project. I wanted to give them direction, but not give them answers. I made them think through and work out (in detail) what they were trying to question me about. The process really helped them clarify their thoughts and I think got them on the right track. I hope they also went away thinking about how they as a group should be functioning in the future. I did give them a bit of an admonishment about coming to me so late in the process. But, they did come to me which is a good sign. I'm still worried about the sleeper groups who I haven't seen... I'm curious as to whether or not others using PBL (in math or elsewhere) encounter this problem of teams coming to them late in the process with basic questions. What is the best way to handle this? On on hand, I'm tempted to not help at all and let them bomb completely one time. On the other hand, this is not a low stakes project. They have had some low stakes group work, in-class one day exercises. Some groups bombed. Curiously, not the same groups who are panicking today.

M&M
February 23, 2004

Team presentations are in two days! The panic is setting in! I had visitors today during office hours for the first time (at least concerning the project.) Thankfully, all of my visitors seemed to be roughly on the right track. There are various states of panic. Some groups are still at the "we've figured out there are forces in this problem, but don't know what to do next stage" while other groups have advanced to the "we've got it mostly nailed down but can't seem to get this constant correct" stage. Obviously, the later cases have me less worried. Well, at this point, I think I need to be philosophical. I've given them the tools they need, showed them how to use them, now we'll see if they do. I was noodling with my next PBL exercise for this class. There was a recent article in Science News about the packing of M&M's. I'm imagining building a narrative around a breakfast conversation started by this article. Some possible questions: Why would anyone study the packing of M&M's? What is the volume of an M&M? How do we draw a 3-d M&M (so we can do computer simulations of the packing)? If you wanted to compare the packing of M&M's with the packing of spheres, what size sphere do you need? If you were really crazy and took the intersection of an M&M and a Lifesaver, what would you see? With regards to learning issues: Why do scientist study things like this? How do you sketch ellipsoids? How accurate of an approximate description can you obtain from a few measurements? I'm thinking I should also bring in a container filled with M&M's and make guessing the correct number of M&M's part of the problem. To do that, they would need to read and understand the Science News article, come up with a good estimate for the volume of an M&M, and do some arithmetic. I'm curious to see how close they could get.

Feedback
February 20, 2004

In class today I handed back team evaluations from Wen's team updates. I used a rubric based on one from the ITUE workshop. It was a modified oral presentation rubric where I included more emphasis on mathematical content. I was very harsh in my evaluations and in the end decided not to record this grade. Rather I returned it (along with written comments) to each team and urged them to think of this as a preview of their grade next Wen. My intention, (of course), was to bump up the level of activity in the teams that have been slow to start. We'll see if it worked. I also took a first look today at the team exercise from Wen. I'm very impressed by some of the answers. One group even recalled information from Calculus II and used it to help solve this problem! It seems the key learning issue that came out of this exercise was the notion of approximation or model. The real intellectual leap required to do this problem is the one from the chain to an idealized chain where the mass is concentrated at a point. The other key learning issue was realizing that you can go out and get additional data when you need to solve a problem. That is, not every problem has all of the information you need to solve it built into the problem. This is how an exercise like this differs from a textbook problem. I've also been thinking about PBL in the context of the MEC Lab. One of my goals for the lab is to integrate the lab into mathematics courses at as many levels as possible. The hanging chain exercise from the other day is a good example. It doesn't really need a lab, you just need a chain, some magnets, and a ruler. The problem differs from other PBL scenarios that I've seen in that I'm not providing a context based on a real world story. Rather, we're taking a REAL real world object, putting it in front of the class, and studying that object. This, of course, is similar to a lab based exercise in the sciences. But, here the "lab part" is much much simpler and can be done in a traditional classroom. One final thought - in case you haven't realized this yet, many whiteboards in classrooms are magnetic! This makes it real easy to hand things like a chain, a mass on a spring, etc. You can then sketch and do measurements on the board surrounding the actual object. Very useful!

A Fun Day
February 18, 2004

Very fun and interesting classes today. We had group updates. The team presentations are next week. Today, each team was to imagine that they had been asked by their boss for a progress report. I asked them to address the question: "What is the shape of the free surface and why?" The question was intentionally vague. What I wanted was a convincing answer. We had quite a range. One team said "The shape is an elliptical parabaloid." Good start, but that the was also the end of their presentation. On the other end of the spectrum, several teams had made great progress and presented an almost complete derivation of the equation governing surface shape. One group even had the physical parameters correct and was able to make some predictions from their model! The 9AM class was once again better than the 10AM class. I only have one group that I am really worried about. It's the group in the 9AM class mentioned above. The idea that the shape was an elliptical parabaloid was mentioned in a previous class discussion. I could not tell if they had done any work at all on their project. I'm worried that they have not. This particular group is also very quiet during group-work time in class. They seem to lack any leader. We also did a mini-PBL exercise today in class. I hung a chain on the blackboard, told them the tension in the chain when it was hung by one end and asked them to find the tension in the chain when it was hung from two ends. I left the chain hanging on the board (from two ends) and left a ruler at the front of the classroom as well. All groups struggled. Eventually someone in the class would realize that they didn't (on the paper in front of them) have enough information to solve the problem and would ask me if they could look at the chain! Of course! Then students were running up to the front to make measurements. It was interesting to see different groups settle on measuring different things in order to get the data they needed. One other neat thing today. My 9AM class contained a team whose approach to team project was very different from what I had imagined, but correct nonetheless.

Timing
February 17, 2004

Slightly misjudged my timing today. Wanted to lecture on the dot product and do a team exercise with vectors. I finished introducing the dot product, but barely started the team exercise. I have tommorrow budgeted for group work. We're going to do two things. Each team is supposed to give an update of where they are with there team project. I asked them to address the question: "What is the shape of the free surface and why does the free surface take that shape?" I think I saw some suprised looks. I'm hoping they have been thinking about this, but am worried they have not. I'm so tempted to give away the story, but that would be counterproductive. Came across an interesting quote from Feynman today. Supposedly, on the day he died, the statement "What I cannot create, I do not understand" was found on his blackboard. Interesting perspective on learning.

Missed Opportunity
February 16, 2004

Missed an opportunity to do a PBL exercise today, but I think it worked out OK anyway. Our topic for the day was vectors. What are they, what are they good for, how do we think about them geometrically, how do we think about them algebraically? I'm always a little bit worried when presenting very basic material. This is a vector blah blah blah. And the students think "I know what a vector is" and promptly fall asleep. Today, I began the lecture with the question "What is a vector anyway?" and tried to develop through class discussion the notion of a vector and its properties. Reasonable success. Both sections of the class came up with the words "magnitude" and "direction." Neither section came up with the notion of a vector as an ordered n-tuple. This is OK, I'd rather they have some geometric intuition on which to build. On the other hand, it gave us a good opportunity to discuss the difference between a vector and its representation. I think it would have been a good minute-write exercise to have each student define vector on their own before we began the class discussion. While a good number of the students were engaged, about 1/3 were clearly not. Perhaps forcing them to write out their understanding would have been useful. There is also the subset of students with glassy eyes who perk up as soon as I write something on the board. They copy it down and then go back to glassy mode. Would a minute-write have snapped them out of their reverie? I'm going to work on developing a vector based exercise for Wednesday. Another interesting opportunity presented itself today. We were discussing vector addition. Surprisingly, both classes defined vector addition in terms of component-wise addition rather than a geometric head-to-tail definition. We talked a little bit about the notion of "definition." We were free to define vector addition in any way we liked, we choose the component-wise method because it is useful. This notion of useful led back to the geometric picture. We want our algebraic definition to align with our geometric intuition.This seems a good entry point to inject a little mathematical sophistication into the discussion. Why do we define things? How do we choose the objects with which we work? There must be an exercise to get this point across. Developing mathematical taste and sophistication is one of my learning objectives for this class (for any class!). I'm getting the feeling (already!) that I'll do a better job with this class as a PBL based class next time around! One other observation from today - my 9AM section is more alive than my 10AM. Is it me? The room? The students?

First Lecture
February 13, 2004

Had our first lecture today. We discussed coordinate systems in three dimensions. It was nice to be able to illustrate the utility of the coordinate systems in the context of their ongoing group project. Because the project motivated some of the material we talked about today, it was clear many of the students had actually been thinking a little along these lines already! A big plus was the questions during class. I usually encourage questions, but during the first few class meetings encounter silence. Both sections today answered and asked questions. In my subjective opinion, more than they would have had I started the semester with this lecture. Could it be that two days of class discussion and group work have helped the atmosphere in the class? Now can we sustain that…

A Day Off?
February 12, 2004

No class today, but I do need to figure out how to respond to the student email from yesterday. We have class tomorrow. Should I revise what I'm doing in light of things I learned or stick to the schedule? I'm worried about covering the syllabus. This is a new concern for me. In the past, the PBL type courses I've taught have all been upper division courses that weren't pre-reqs for something else. The courses were also very math modeling oriented and leant themselves naturally to PBL. I didn't realize how challenging it is to do PBL in a lower-division course, especially one that is a core-course and has a standard syllabus. Ok, time to stop avoiding my first panicked student. Upon reflection, perhaps the panic is not about PBL, but just about the course? Here's my email response:Dear X,Thanks for your email. I'm glad to see you are starting off the semester on the right foot by attending class, reading the chapters, and attempting the homework problems. To put your mind at ease a little bit, over the next few classes we will have lectures that cover sections 13.1, 13.2, 13.3, and 13.7. You've already begun a good strategy for understanding the material - you've read the sectionsbefore we discussed them in class. For Friday, I would focus on 13.1 and 13.7. We'll discuss these in class, I strongly urge you to raise questions during the discussion. Next week, we'll cover 13.2 and 13.3.But, I'm also slightly concerned. Lectures won't be magic in the sense that you'll instantly be able to solve all the homework problems once the lecture is over. Many times, the homework will be an extension or variation of what we do in class. This will require considerable thought and effort on your part, to not only be able to reproduce what we discuss, but to understand it and internalize it sufficiently to be able to extend it to new, unfamiliar situations. I know that sounds daunting, and it is, but I'm sure you will be able to do this. It will just take time and patience.Good luck and please feel free to email me or stop by with other questions and concerns.

Day Two
February 11, 2004

Second set of classes today. I wanted to introduce the first team project. This is a three week project. At the end I'm asking students to give an 8 minute presentation to the class. The problem revolves around the spin-casting method for making parabolic mirrors. The teams represent consulting groups who have been hired by NASA to evaluate the spin-casting method and report on whether or not it's a worthwhile investment. The mathematical content I want them to get is mainly the notion of writing a force balance using vectors. That will let them derive the shape of the free surface in the spin-casting method. I tried to begin the same way as yesterday, started with a simple handout, let them write answers individually, and then brainstorm as a team. The teams then reported out. I'm worried that my questions are too vague, that I'm asking them to figure out too much. I then distributed a second handout. This one set the scenario for their project. I asked them to come up with learning issues. I tried to explain what I meant by learning issues, but mainly got back a reiteration of the questions on the handout. We discussed this a bit, tried to break things down into smaller pieces. I don't know how much got through.Tonight I got my first email from a student panicked by the PBL format. An excerpt: "I was just wondering if you would be holding a lecture within the next few days on the upcoming chapters in the book. I noticed that there was a homework assignment from the text book, so I went ahead and read the chapters. The only problem is that I do not understand the way the book explains how to do the problems and I never have understood in previous classes. Even when I took math 241 and 242, I still had difficulty understanding until the material was taught."How do I respond to this one?

First Day of Class
February 10, 2004

This is the first day of our semester here at UD and the first day of this blog. I’m trying something new this semester, namely teaching Math 243 – Calculus III in a semi-PBL format. The class meets four days per week for “lecture” plus one day per week for recitation. I’ve decided to have at least one lecture day per week devoted entirely to team based learning and to intersperse team activities with “mini-lectures” during the rest of the week. The recitation section (run by a TA) will serve as a regular meeting time for project teams, plus a place for students to get help with their homework. I’ve asked my TA to be flexible in running the recitation section and to allow for group work as we proceed. If you’d like to see my syllabus, it’s here.

» March 2004