PHY 430 is a junior/senior level course in quantum mechanics for physics majors. The material covered in the course is pretty standard for this level (I use the Griffiths text, which is probably the most common one used for this course, and cover most of the first half of the book). I have struggled to incorporate active-learning into this course because quantum mechanics is so counter-intuitive. Because the class focuses on the mathematical formalism the material is highly technical. I do work in some discussion of the experimental basis of quantum mechanics, as well as some issues regarding the interpretation of the theory - but these come mostly in the form of writing assignments (PHY 430 is a writing-intensive course, part of Berry's Writing-Across-the-Curriculum program).
This past semester (Spring 2009) when I taught PHY 430 I finally decided to start working in some active learning. At that point PHY 430 was the only class I taught where I spent most of class time lecturing - and I didn't like the fact that I was still lecturing in that class. So during the semester I managed to create a series of group tutorials for the students to complete in class. We did these tutorials for a little over half of the class periods. One tutorial was based on some Open Source Physics simulations created by Wolfgang Christian and Mario Belloni of Davidson College. I created the rest of the tutorials by going through my lecture notes from the last time I taught Quantum Mechanics and deciding which steps in the derivations/examples the students could do on their own. So I still lectured a fair bit (just under half the class periods), and I gave them a lot in the tutorials - but they spent most of their class time DOING quantum mechanics rather than hearing me talk about it.
It went surprisingly well. The students were able to get through the material I wanted them to get through. We had a couple of delays when tutorials took longer than I had anticipated, but we were able to catch up later on. And overall I think the students learned the material very well. Their performance on tests was quite good. It was a small class (6 students) so it's hard to say if this would have worked with a larger class - but I was pretty happy with it on the whole.
The tutorials I created are not fantastic. I would say they are definitely not as good as the materials I have created for PHY 101 or AST 120. But I think the tutorials are more effective than lectures. Since, for the most part, the tutorials covered exactly the same material as my lecture notes would have I didn't really have to sacrifice any "coverage" in order to include more active learning. I'd like to continue improving the tutorials, so that they can lead the students to genuine insight instead of just a formal understanding of how quantum mechanics is done. Hopefully I can make tutorials (or some kind of active learning method) a bigger part of the course in the future. But I'm definitely not going back to all lecture.
Monday, June 22, 2009
AST 120: The Copernican Revolution
AST 120 is a course on the Copernican Revolution originally created by Paul Wallace. I took over teaching the course in Fall 2008 and taught it again in Spring 2009. During the Fall 2008 semester I developed a series of active-learning curricular materials for this course, which I will describe here.
The materials I developed consist of 25 activity worksheets designed to be completed by groups of 4 students during a 75 minute class period (with some time left over for lecture/discussion). The worksheets guide the students through an exploration of astronomical phenomena (mostly naked-eye observations of stars and planets) as well a variety of theories that have been proposed to explain these phenomena. Most of the activities require the use of computer simulations for making simulated observations or visualizing theories of planetary motion. I have created 53 open-source computer simulations for use with these activities. I have also adapted 10 laboratory exercises, originally developed by Paul Wallace and designed to be completed in a 120 minute lab period, to include more active-learning through the use of computer simulations. Finally, I have created two major project assignments that are designed to assess student understanding of the course material.
The first sequence of activities focuses on observing the motion of the sun, moon, stars, and planets. Most of this is done using Starry Night, a commercial planetarium program. (Some, but I don't think all, of the activities could be done using open-source software like Celestia and Stellarium.) Students observe the (apparent) daily motion of the sun and stars, the monthly motion of the moon, the annual motion of the sun, the synodic and zodiacal periods of the planets, and the precession of the equinoxes. They discover that "signs" of the zodiac are way off from their standard astrological definitions (which were correct when they were formulated about 200 BC, but precession has changed things). Students also complete labs in which they use a celestial globe, observe a simulated gnomon (sundial), study the phases of the moon and make their own moon observations, and learn about the constellations during a night lab.
The second sequence of activities deals with the astronomical theories of the Ancient Greeks (Eudoxus, Aristotle, Apollonius, Hipparchos, Ptolemy). Computer simulations are used to help students visualize the geometrical constructions used in these theories and also to show what these theories predict for the motions of the planets as seen from Earth. The simulations help students see the real power of the Ancient Greek theories (even though we now know these theories are incorrect). For example, the theory of Eudoxus could produce retrograde motion which is the most striking feature of the motion of the planets. The theory of Ptolemy could produce retrograde motion AND properly correlate that motion with changes in the brightness of the planet. Active engagement with these Ancient Greek theories shows how scientific theories evolve and are replaced by theories with greater explanatory power. A lab in this section allows students to recreate the observations and calculations used by Eratosthenes to determine the diameter of Earth.
The next sequence deals with the revolutionary heliostatic theory of Copernicus. Again simulations are used to help students visualize the theories and how the relate to observed motions of the planets. With the aid of the simulations students can determine the orbital periods of the planets and measure the size of the planetary orbits (relative to the size of Earth's orbit). They also discover the the Copernican theory predicts parallax effects that are not observed, and learn that this problem can be resolved if the stars are MUCH farther away from the sun than Earth is.
After Copernicus we briefly study the work of Tycho Brahe. Students learn how to use parallax measurements to determine the distance to astronomical objects. They use this method (along with simulated observations in Starry Night) to find the distance of the moon, sun, and Halley's comet from Earth. They also use a computer simulation to examine the relationship between the astronomical systems of Ptolemy, Copernicus, and Tycho.
Next is a sequence of activities on Kepler. Students use computer simulations to explore Kepler's idea that the planets were confined to spheres nested between Platonic solids. They also examine simulations that illustrate the development of Kepler's theories on planetary motion. They construct an orbit for Earth using a compass, straight edge, and three observations of Mars. Finally, they complete a lab exercise in which they apply Kepler's three laws of planetary motion to a variety of problems.
A sequence of activities on Galileo's telescope observations and physical theories is next. Students use computer simulations to reproduce Galileo's measurement of the height of mountains on the moon and see how Galileo's observation of the phases of Venus refuted the standard Ptolemaic theory. Students use a computer simulation of Galileo's sunspot observations to determine the rotational speed of the sun, and also apply Kepler's laws to the motion of Jupiter's moons to find the mass of Jupiter relative to that of the sun. Simulations and experiments are used to investigate medieval ideas about motion as well as Galileo's ideas about falling bodies and neutral motions (close to the modern concept of inertial motion).
The final sequence of activities deals with the theories in Newton's Principia. Students use simulations and mini-experiments to learn about Newton's laws of motion. More simulations illustrate how the right centripetal acceleration can produce a circular orbit, and how an inverse square centripetal force can reproduce all three of Kepler's laws. Finally, they examine Newton's argument that projectile motion on Earth is qualitatively the same as the motion of the moon, illustrating the universal nature of gravity.
For the first project students are given observational data for a fictional solar system. From this data they must construct both Ptolemaic and Copernican orbits for their home planet/star, as well as for two other planets (one inferior, one superior). After calculating the orbital parameters they must draw diagrams representing the orbits for each of the two systems. This project assesses student conceptual understanding of these two astronomical systems, as well as factual knowledge about astronomical terms and calculation methods. In the second project students must write a paper defending the Copernican system against an attack from a fictional Aristotelian (I wrote the attack myself, but it I used arguments derived from 17th century primary sources, mainly Galileo's Dialogo). This project assesses student understanding of Galilean/Newtonian physics and how these physical concepts led to the overthrow of the old Aristotelian/Ptolemaic system and justified the acceptance of the Copernican/Keplerian system.
Student response to this course has been very good. The students seem to enjoy the activities and they like working with the computer simulations (especially Starry Night, but they like the simulations I created as well). Overall I have been very pleased with the way this course has gone and I plan to continue teaching it this way indefinitely.
Paul Wallace has written a textbook for this course which I have modified. We plan to publish the textbook in a few years (it's not quite publication-ready at this point, although the students have been pretty happy with it).
Anyone interested in this course and the simulations and curricular materials I use should go to http://facultyweb.berry.edu/ttimberlake/copernican/ where the open-source simulations (but not Starry Night) and activity/lab worksheets can be downloaded for free.
The materials I developed consist of 25 activity worksheets designed to be completed by groups of 4 students during a 75 minute class period (with some time left over for lecture/discussion). The worksheets guide the students through an exploration of astronomical phenomena (mostly naked-eye observations of stars and planets) as well a variety of theories that have been proposed to explain these phenomena. Most of the activities require the use of computer simulations for making simulated observations or visualizing theories of planetary motion. I have created 53 open-source computer simulations for use with these activities. I have also adapted 10 laboratory exercises, originally developed by Paul Wallace and designed to be completed in a 120 minute lab period, to include more active-learning through the use of computer simulations. Finally, I have created two major project assignments that are designed to assess student understanding of the course material.
The first sequence of activities focuses on observing the motion of the sun, moon, stars, and planets. Most of this is done using Starry Night, a commercial planetarium program. (Some, but I don't think all, of the activities could be done using open-source software like Celestia and Stellarium.) Students observe the (apparent) daily motion of the sun and stars, the monthly motion of the moon, the annual motion of the sun, the synodic and zodiacal periods of the planets, and the precession of the equinoxes. They discover that "signs" of the zodiac are way off from their standard astrological definitions (which were correct when they were formulated about 200 BC, but precession has changed things). Students also complete labs in which they use a celestial globe, observe a simulated gnomon (sundial), study the phases of the moon and make their own moon observations, and learn about the constellations during a night lab.
The second sequence of activities deals with the astronomical theories of the Ancient Greeks (Eudoxus, Aristotle, Apollonius, Hipparchos, Ptolemy). Computer simulations are used to help students visualize the geometrical constructions used in these theories and also to show what these theories predict for the motions of the planets as seen from Earth. The simulations help students see the real power of the Ancient Greek theories (even though we now know these theories are incorrect). For example, the theory of Eudoxus could produce retrograde motion which is the most striking feature of the motion of the planets. The theory of Ptolemy could produce retrograde motion AND properly correlate that motion with changes in the brightness of the planet. Active engagement with these Ancient Greek theories shows how scientific theories evolve and are replaced by theories with greater explanatory power. A lab in this section allows students to recreate the observations and calculations used by Eratosthenes to determine the diameter of Earth.
The next sequence deals with the revolutionary heliostatic theory of Copernicus. Again simulations are used to help students visualize the theories and how the relate to observed motions of the planets. With the aid of the simulations students can determine the orbital periods of the planets and measure the size of the planetary orbits (relative to the size of Earth's orbit). They also discover the the Copernican theory predicts parallax effects that are not observed, and learn that this problem can be resolved if the stars are MUCH farther away from the sun than Earth is.
After Copernicus we briefly study the work of Tycho Brahe. Students learn how to use parallax measurements to determine the distance to astronomical objects. They use this method (along with simulated observations in Starry Night) to find the distance of the moon, sun, and Halley's comet from Earth. They also use a computer simulation to examine the relationship between the astronomical systems of Ptolemy, Copernicus, and Tycho.
Next is a sequence of activities on Kepler. Students use computer simulations to explore Kepler's idea that the planets were confined to spheres nested between Platonic solids. They also examine simulations that illustrate the development of Kepler's theories on planetary motion. They construct an orbit for Earth using a compass, straight edge, and three observations of Mars. Finally, they complete a lab exercise in which they apply Kepler's three laws of planetary motion to a variety of problems.
A sequence of activities on Galileo's telescope observations and physical theories is next. Students use computer simulations to reproduce Galileo's measurement of the height of mountains on the moon and see how Galileo's observation of the phases of Venus refuted the standard Ptolemaic theory. Students use a computer simulation of Galileo's sunspot observations to determine the rotational speed of the sun, and also apply Kepler's laws to the motion of Jupiter's moons to find the mass of Jupiter relative to that of the sun. Simulations and experiments are used to investigate medieval ideas about motion as well as Galileo's ideas about falling bodies and neutral motions (close to the modern concept of inertial motion).
The final sequence of activities deals with the theories in Newton's Principia. Students use simulations and mini-experiments to learn about Newton's laws of motion. More simulations illustrate how the right centripetal acceleration can produce a circular orbit, and how an inverse square centripetal force can reproduce all three of Kepler's laws. Finally, they examine Newton's argument that projectile motion on Earth is qualitatively the same as the motion of the moon, illustrating the universal nature of gravity.
For the first project students are given observational data for a fictional solar system. From this data they must construct both Ptolemaic and Copernican orbits for their home planet/star, as well as for two other planets (one inferior, one superior). After calculating the orbital parameters they must draw diagrams representing the orbits for each of the two systems. This project assesses student conceptual understanding of these two astronomical systems, as well as factual knowledge about astronomical terms and calculation methods. In the second project students must write a paper defending the Copernican system against an attack from a fictional Aristotelian (I wrote the attack myself, but it I used arguments derived from 17th century primary sources, mainly Galileo's Dialogo). This project assesses student understanding of Galilean/Newtonian physics and how these physical concepts led to the overthrow of the old Aristotelian/Ptolemaic system and justified the acceptance of the Copernican/Keplerian system.
Student response to this course has been very good. The students seem to enjoy the activities and they like working with the computer simulations (especially Starry Night, but they like the simulations I created as well). Overall I have been very pleased with the way this course has gone and I plan to continue teaching it this way indefinitely.
Paul Wallace has written a textbook for this course which I have modified. We plan to publish the textbook in a few years (it's not quite publication-ready at this point, although the students have been pretty happy with it).
Anyone interested in this course and the simulations and curricular materials I use should go to http://facultyweb.berry.edu/ttimberlake/copernican/ where the open-source simulations (but not Starry Night) and activity/lab worksheets can be downloaded for free.
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