Our astronomer writes:

Now and then I come across an interview of some Nobel prize-winning (or otherwise distinguished) scientist with the inevitable question, “What got you started on your path to fame?” Almost always it was an inspiring teacher or mentor, a person who imparted a love of or excitement in doing science. Somewhere in the years between High School and Grad School, between the time when our differences were mostly potential and the time we’re on our way in a particular direction, someone lit a fire. Often there’s a quote something like, “He/She showed me that [insert science here] is more than just a set of results in a dusty textbook, but something that I really enjoyed doing.”

Similarly, in accounts of some part of the history of science it’s almost inevitable that I encounter a sentence like, “so science proceeds in sometimes a roundabout and uncertain fashion, not at all as the textbooks tell you.” Textbooks are not often held up as good examples.

The message, sometimes explicit but often implied, is that our job as teachers and scientists is to inspire and excite. Trying to impart “textbook results” is deprecated. Well, this time I am standing up for the textbook and the type of learning it represents. There is a time when it is just what we should be teaching. We need to ask the question: what are we trying to do? What is the outcome we want in our students?

Consider the lower-level service course, normally considered a bane of existence by both students and teachers. It might be Calculus II and III, Chemistry 101 and 102, Physics A (mechanics) and B (electromagnetism); there are no doubt equivalents in other disciplines. I suggest four possible answers to my question:

• Impart an appreciation of the beauty of mathematics/science, for example something about the rigor and cleverness of the definition of a limit.
• Teach the scientific process, for example showing how the atomic theory was developed based on experiment.
• Develop in the students knowledge and techniques to apply in later classes and in other fields.
• Give some students who are getting by too easily in other classes something really hard to do. (This is often believed outside the Department.)

The first answer is great for developing mathematicians or scientists; however, that’s not what most of our students will be. The second is likewise good for creating scientists; also, it is critical for citizens in a world where science plays an overwhelmingly important part. But I contend that, in these service courses, the third answer is the right one and any other effort must come after. (Unfortunately, given the tight constraints of time and material in service courses, coming after may mean not coming at all.)

I do not mean that all efforts to make the material interesting should be abandoned, nor that (in physics especially) we shouldn’t try to demonstrate that historical misconceptions come out wrong. I do mean that knowing how Galileo, Newton et al. worked things out, or appreciating the abstract beauty of F=ma, doesn’t really help applying the formula in next year’s engineering course. Developing a set of tools means above all practicing their use, often in problems uninteresting in themselves—the sort one finds in textbooks.

Problem drill will not produce the next generation of scientists or research mathematicians. It may produce nothing more than experts in pattern-matching. But something like it is unavoidable if we want to produce competent sophomores or juniors.