Symmetry, Chirality, and Plane-polarized light: SME Winter Quarter Follow-up

Designing the SME winter chirality unit/project was quite an experience! As a curriculum designer, I learned a lot. We certainly accomplished the pedagogical goals and more in symmetry. I'm less sure about the chirality in molecules or plane polarized light aspects; the experience of actually teaching these in SME gave me a lot of ideas about how it could be better done in the future. Most of my redesign ideas for the unit involve making the inter-topic connections clearer. In my mind as I designed the unit, symmetry, polarized light, and chirality were inseparable, but I think that many of the connections that were so clear to me were, in the end, not clear to the students. This was partly because of my ordering of the topics.

As a whole the unit was successful, largely because the students became extremely involved in and motivated by their projects. However, symmetry, chirality, and plane polarized light were interpreted as three very separate entities, and we never brought students to the point where they could understand real-world systems like doubly refractive crystals or vitamin E-as we saw on the final, most could not even locate that molecule's three chiral centers. So for many of the students, symmetry was a digression, and chirality and polarized light were abstractions with little or no application to real life. I think the students found all three topics fairly interesting, but unconnected and intangible.

I loved putting together the lab activities and project and seeing the cool things that students came up with. Overall I was amazed by their creativity and by the amount of work that went into their webpages and presentations. Having the project happen online was critical to its success as it allowed students to access each others' work throughout the process, to reflect on each other's projects (as required), and to study each others' problems for the final. The web-based nature of the project did have the drawback that a lot of lab time had to be devoted to web interface issues rather than science issues. I don't know how to get around this; I suspect it's not very get-aroundable with current web-authoring technology. One thing that might be worth looking into next year is buying some high-level web-authoring tools like FrontPage. Though I've never used it myself, I've heard that it makes generating webpages, dealing with images and links, etc. much easier than in Composer.

For the Future

Following are some recommendations for the redesign of this unit for next year.

Lecture Curriculum

  1. Do symmetry first, then chirality, then polarized light. This quarter, we did polarized light, then symmetry, then chirality. In the polarized light lecture, Marty showed them a crystal that had a three-fold rotation axis when viewed along one direction and not in the other. He showed them that light was split into two beams-a highly cool demo-when it entered this crystal and noted that this was due to the different symmetries of the molecules in the two directions. (This fit in well with the concurrent pseudoscience lab unit; crystals are popular topics on many pseudoscience websites, and the double images they create are often cited as basis for their 'magical' properties.) The students thought this was cool, but they would have been able to understand what was going on much better if they had already had the lectures on symmetry and chirality. My initial rational for putting polarized light first was: 'Marty (physics lecturer) shows them that light is spiral, Brad (math lecturer) shows them that spirals are chiral, and Jim (chemistry lecturer) shows them that the chirality of molecules causes the molecules to recognize the chirality of the spiral light.' After seeing how the students responded to the unit, I would use a different rationale in the redesign: 'Brad shows them that spirals are symmetrically unique, Jim shows them that chiral molecules are symmetrically unique, and Marty shows them how the two interact.

    Feedback from Sharon corroborating this viewpoint: "It seems to me that chirality in molecules is hard to understand unless you are just coming off of symmetry. I think our students really understood the 2-D symmetries, but didn't retain a good sense of what 3-D symmetry is and what it looks like. I think chirality would be a good next step from their solid knowledge of 2D into the 3D world. Also, I'm not sure I'd do polarity before chirality because there are 2 curiosities piqued when they see the crystal demo. They naturally ask 'Why' and then the next question is 'what's doing this, the light or the crystal' and the answer is, of course 'YES'. So if they already know one part (crystal) they have fewer concepts to learn. Even if they just have a sense of "molecules can be chiral, so maybe that has something to do with it" They can be semi-satisfied with that answer (for the time being) and focus more on the polarized light issue."

  2. Do the math in class. A common complaint of the students was that in class we covered the easy-to-understand, high-level ideas, but on the problem sets and tests they were expected to do a lot of non-trivially difficult mathematical and chemical problems. During this unit, I think it is especially important liberally to pepper class time with break-out sessions and worked problems that either anticipate or mirror (pun intended) the homework and tests. They need to see some solved equations in symmetry groups in class before they encounter it on the homework-the very sight of the equations with their unfamiliar symbols and notation was scary for many. They also definitely needed some more examples of chiral molecules and chiral centers in class. Their performance on the final showed that they didn't really grok those concepts, which were supposedly (in this year's design) the punchline of the unit. Showing them the enantiomers of thalidomide and carvone really helped (I hope) develop an appreciation of the importance of chirality in biological systems like smell receptors and in the history of the pharmaceutical industry, but as we've seen, it didn't help them to identify the chiral parts of a molecule or to tell which molecules were chiral.

  3. Do diastereomers. This was a topic in my lecture notes draft that we never made it to in class. The rationale for making this a priority is that with an understanding of diastereomers the students would be able to think about real-world molecules like vitamin E. The word 'diastereomer' need never be said, but they should be able to reason that with n chiral centers, a molecule can have 2n possible configurations, all of which turn up in the mixture when the molecule is made synthetically and only one of which is biologically active. (The 2n rule anticipates the lectures on bits in the spring quarter as well-that connection might be good to make here.) It's only an added paragraph in the notes, maybe 5 minutes in lecture, and an extra problem on a problem set, but the real-world connection needs to be made more explicit if students are to come away with an appreciation for the importance of this concept in their daily lives. They should be able to explain to their friends afterwards, for example, why the more expensive vitamin E really is more effective.

  4. Make the connections between topics clearer. Marty foreshadowed a lot of stuff that never had its connection to the rest of the unit solidified, so students came away thinking polarized light was only tangentially connected to chirality (and that only because they had to use polarizing filters in the polarimeter lab). It might help if either: a. one faculty member lectured for the entire unit or b. the lecturing faculty shared their lecture notes with each other beforehand so that they can better anticipate / build on each other's topics. It would require a high level of organization to have lecture notes ready far enough in advance, but I am convinced it would be worth the extra effort.

Lab Project Redesign Suggestions

  1. Redesign the polarimeter lab. The students didn't understand the lab this quarter without a lot of brow-beating. I think it is an important lab to keep because the connections between molecular chirality and polarized light are most evident in using polarized light to detect chiral molecules. However, in order to really get the concept across I think the following would be helpful: a. Spend an entire lab period on the polarimeter instead of half on the mirror image activity and half on the polarimeter lab as we did this year. b. Do some introductory activities with just two polarizing filters and no solution between them. For example, an activity could be designed so that one student rotates the bottom polarizer without the other knowing and the other has to figure out how much. (This might also be a good break-out session.) Then, when they have the solution between the polarizers, they will be able to tell that the light was rotated, and this can lead into a class discussion of why that might be happening. c. The lab should happen after the lectures on chirality so that the students will have been introduced to the concept of polarimetry before coming to lab. Note that this necessitates covering polarimetry in lecture. This is important because lab topics that are never reiterated in lecture are interpreted as unimportant by the students and augment the perceived disconnect between lecture and lab in SME. d. Don't make the polarimeters so fancy-too many construction skills are required and these distract from the concept of the lab. Just throwing a filter, then a tube w/ toilet paper role, then another filter down on top of the light is plenty.

  2. Prevent students from all doing symmetry and beauty. It's definitely an interesting topic, but with such a large fraction of the class doing it, the other project topics got short-shifted. For next year, it might be worth setting up a system where at least one group per section has to do a project centered around plane polarized light and at least one group per section does one centered around chirality in molecules. This would help both because students would have a wider range of topics to reflect on / make connections between and because they would have more student-generated examples of problem topics to study for the test. I think the lack of good plane polarized light/molecular chirality study problems hurt them on the final this quarter, and I wish I had given some thought in advance to making sure all the topics got equal treatment instead of letting the students all gravitate to the project choice that had a quote from Glamour magazine in its description.

  3. Get the technology to make the projects really work. As noted at the beginning, it might be worth investing in some more high-end web authoring software. The web was really a sticking point for some students-I think that next year it is absolutely necessary to designate and devote some group lab time to orienting themselves to how to put their project on the SME page. Also, the 3-D movie was a very cool project, but with so much home-made equipment it was bound not to achieve the desired effect. The group did a good job of analyzing the scientific reasons that the result didn't come out looking as 3-D as they wanted and I know they learned a lot in the process. However, for next year, I'd be in favor of buying a real 3-D camera (one with two lens/aperture systems a couple of centimeters apart), and having them do a slideshow instead. This might be a more feasible project for amateurs.

  4. Coordinate the project requirements / meetings well in advance. This year, we tacked on the meet-with-faculty requirement and the meet-with-Doree-Allen requirement a little way into the project at the request of the faculty. These are both great ideas, but the last minute nature of the requirements resulted in poor coordination and organization of both. Perhaps next year this can be set up in advance so that there is no ambiguity about who has met with whom and when the appointments are scheduled. I think it is absolutely crucial that if the project is run similarly next year, Doree Allen needs to be at a faculty meeting prior to the setting of the project due dates. It might also be good to have the faculty and Doree Allen provide a copy of their notes from the student meeting to the TA's so that everyone's on the same page as far as the projects go.

  5. Do a group brainstorm. After the students have chosen their topics and started working, it might be helpful to have a group brainstorm in lab the next week. During this time, each group could present their topic and the class could spend 10 minutes asking questions about it and brainstorming ideas for how to make that group's project especially creative and rewarding. This would further involve the students in each other's projects and hopefully generate more interest in the many diverse topic areas covered by the projects.
Other Ideas

Following are random thoughts for additional examples, topics, and lab activities to try next year.

  1. Canceling One application of symmetry in math that we can all relate to is canceling. If you have the same thing on both sides of an equation, you can cancel. Very simple, but it brings the theme home. Other examples of how the symmetry of simple math problems makes solving them quicker are abundant (e.g. if there are 5 black marbles and 5 white marbles in an urn, then there must be an equal probability of drawing black and white because the problem is symmetric: white and black are interchangeable, etc.) One homework problem might be finding an example of a simple math problem in which a shortcut can be found using symmetry. I think this would help students get it that symmetry really is everywhere-not just in pretty pictures.

  2. Symmetric viruses A chemistry friend was recently telling me about some newly discovered viruses that are extremely symmetric because they have very little DNA. Apparently the small amount of DNA makes for a lot of the same proteins, which makes for a highly symmetric organism. I thought it was cool.

  3. Do Experiment 2-8 from Zare's Laser Experiments for Beginners as a very cool demo on chirality in molecules and how they interact with light. In this demo, you can apparently actually see the laser light spiraling through a test tube of chiral substance. I found it when I was looking through the book for laser labs for spring quarter-very very cool!! Some of the laser diffraction demos in that book would also be appropriate for symmetry or for polarized light-we mentioned diffraction only briefly because it is so complex, but Zare's book has a few basic concepts that students can use to understand the results of the demos/experiments. Be sure to provide ample break-out sessions during which the students can grapple with these concepts!

  4. Make your own kaleidoscope in lab Shortly after the unit, I was at the Exploratorium and noticed quite a few videos on Escher and a Make-Your-Own-Kaleidoscope kit in the gift shop. When I glanced through the kaleidoscope kit manual, I noticed a symmetry tutorial that echoed a lot of what we covered in class. It looked like a really great lab activity, and one that students would enjoy taking home.

  5. Circularly Polarized Beetles?! A few months after the unit, I met an astrophysics professor from BU who is thinking about designing a unit for nonscientists based on light. He had with him some beetles that were coated with a chiral fat; viewed through circularly polarized filters, they were black with one and colored through the other. This is the only animal known to do this in nature.