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An Academic Apprentice

Once the path to learning a trade or profession was to become an apprentice. Whether you wanted to become a sea captain, silversmith, or doctor, you found specialists in your field of interest and joined them as an entry-level assistant. Over many years, with enough aptitude, determination, and luck you might work your way up to becoming an expert. Eventually you could take on apprentices of your own, passing onto future generations the skills you learned and likely extended.

An apprenticeship is learning by doing the gold standard of education. A thousand days of continuous exposure to PowerPoint slides about sailing is no substitute for actually changing a sail in a storm on a pitching deck. Books and PowerPoint slides might help with sailing theory, which will be easier to absorb when icy waves are not trying to wash you overboard. The combination of theory in class and practice in labs or in the field has been embraced in almost every discipline.

To get a pilot’s license, for example, one must spend time in ground school and in actual flight, and as well as passing both a written exam and a flight test. Prospective doctors spend countless hours in class followed by sleepless days and nights in a residency program actually treating patients.

Even for students who will not spend any time in laboratories after graduation, lab work is used extensively to extend knowledge and experience. Labs enable students to learn by doing in a controlled environment that is often not possible in the field, without the long-term commitment of an apprenticeship. Labs, however, especially at the undergraduate level, have many shortcomings. Time is always tight and there is often more emphasis on getting the right results than doing any real experimentation. Some things are so difficult to do that they can’t be made into simple lab experiments. There are also limitations to what can be done safely in a lab. A student lab, for example, is a bad place to try thermonuclear reactions or grow a new strain of anthrax. And then there are physical limitations to what can be done. Studying a process that takes a long time to occur cannot be done effectively in a lab.

To avoid the limitations of labs yet still achieve learning by doing, simulations are often used. The very best simulations are so good that they may be used as substitutes for the real thing. Excerpted from “Today’s commercial flight simulators are so sophisticated that pilots proficient on one aircraft type can be completely trained on the simulator for a new type before ever flying the aircraft itself.” And of course when Neil Armstrong set down on the moon, the only previous experience landing the Lunar Module was with simulators.

Simulations are wonderful, but they have limitations, too. I have a simple program that draws regular stars with any number of points by connecting vertices of polygons. Whether you want a familiar fivepointed star or an unusual 55-pointed one, you just key in the number of points and it draws the star. But it accepts every number without question. Ask for a star with -6.39 points and it d'es the math and draws something that it proffers as correct. A colleague of mine wrote a simulator of complex gears that did not fuss about on e-toothed or fractional-toothed gears and was accepting of an enormous gear fitting inside a tiny one.

Simulations also often assume a level of precision that is not possible. A one-kilogram object in a physics simulator has a mass of exactly one kilogram, though except for the platinum-iridium bar in the custody of the International Bureau of Weights and Measures near Paris, France, the kilograms you use in the field will be a bit bigger or smaller. Small differences can have a profound effect on the outcome of an experiment. A simulation is a simulation. It is never the real world.

An apprentice develops intuition over many years by trying thousands of ways to do things and learning from his or her mistakes. Some of those mistakes produce the serendipity that leads to advances in the field. As Albert Einstein said, “Anyone who has never made a mistake has never tried anything new.”

Intuition is what we really hope to develop in our classrooms. Why would we just settle for having a student know the formula for every possible parabola and having him/her ace the advanced placement parabola exam, when what we really want in our students is parabola karma? A student can get parabola karma—or French literature karma, or economics karma—by spending long years as an apprentice or by a few hours, days, or weeks experimenting with an appropriate simulator.

Limitations aside, well-designed interactive simulations allow students to learn not only by doing, but more important by experimenting; exploring the proven, the dead ends, the true, the false, and the unexpected. But college students who have been told for years to do things right need to be taught that it is okay to experiment; that their goal is to develop intuition, not to find the one right answer.

While we fuss to improve learning in the classroom and embrace each new instructional delivery system, we need to remember that our goal is not so much information transfer as it is kindling curiosity, enthusiasm, and the desire for knowledge in our students. Einstein skeptically notes that “It is a miracle that curiosity survives formal education.” If we use IT to get our apprentices fired up, then they will not only survive formal education, they will flourish.

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