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A reflection about teaching

Alexander Hahn -- Guest Columnist | Wednesday, August 27, 2003

You could be a professor of 20th century French literature interested in the psychological and emotional qualities of certain fictional characters and what these tell us about the human condition. Or you might be a historian of philosophy weighing the impact of Platonic and Aristotelian thought on the development of pre-classical science. Then again, you might be a professor of engineering on the verge of finding a novel way to develop light, nano-fiber enhanced materials of greater tensile strength than steel. Or you could be a physicist, gazing at the cosmos intent to find convincing evidence that the universe has been expanding much more rapidly than classical theory would predict.

You’ve just sent two articles for submission to a prestigious journal in the field. Your summer is now over and the beginning of a new academic year stands before you. With it comes the task of teaching an elementary course in the general area of your scholarly expertise. One fine and sparkling autumn day you step into your classroom and – as on so many occasions before – you are ready to begin. Sitting before you are several dozen sophomores just back from the summer. Having settled into their dorms, they are excited about the upcoming football season and look forward to the weekend’s concert by the Dave Matthews Band. Their passions are light years removed from yours.

You begin a conversation whose purpose is to draw your students in – draw them into an appropriately careful, but increasingly central way, into the fabric, the texture, the meaning and relevance of your subject.

You need to build a bridge. You – architect and engineer – draw up the blueprints and set a timetable. You organize the materials, tools and machinery and get them hauled to the scene. You put in place plans to test components of the structure. The construction commences. Together you lay the foundations. Girders and trusses swing into place. The members of your team shape the planks, first tentatively and soon more confidently. They inspect the beams and begin to get an understanding of the tensions and compressions in the structure. Your goal at the end of the day is for your students to have an understanding of the nuts and bolts and the central themes of your subject and a sense of its beauty and its utility.

The specific strategies will depend on your course and its message. They are the details where the challenges reside. Which parts of your subject do you emphasize in your presentations and which texts and readings will you ask the students to absorb? How do you make sure that your students pursue these with energy? Are your students getting the message that you wish to convey? What are the key concepts? How well are they grasped? How will technical expertise in the narrower sense grow alongside an understanding of the larger fabric? Are you sensitive to the increased sophistication of the unfolding story and the involvement of the students with it? Drifting attention is unavoidable, so how do you mix lecture, discussion and student presentation? How do you structure the students’ activity outside of class? Some subjects require constant contact if they are to be captured effectively. For these, subject matter and student minds should rub against each other like the two rotating discs in the clutch of a car. How do you achieve this? Your conversation needs to mix the routine and the difficult. It needs to inspire confidence as well as wonderment. You want your students to grapple and grasp, to reflect and react and to think and rethink. You need to inject into the conversation an element of who you are and what you are about. How else can it connect and be engaging?

These questions present significant challenges, and your responses to them call for very careful reflection. Your starting point seems easy enough. You select appropriate and stimulating materials, you assess the backgrounds and abilities of your students and you articulate the goals and purposes of your journey together as convincingly as you possibly can. You pay attention to the various points that the Teacher Course Evaluations aim to gauge. A number of issues will require careful reflection and the insights of those of your colleagues who have weighed them with engagement. Technology might assist you. Wouldn’t a discussion about the cardiovascular system profit from an animation of the expanding and contracting ventricles, the inhaling and exhaling lungs and the rushing fluids? If a picture is worth a thousand words, isn’t a moving picture worth a million? Might a PowerPoint presentation help you to organize the flow and pace of the discussion? Or a pre-class WebCT quiz draw your students into the material of an upcoming class? On the other side of this technological coin, however, lies an obligation to limit “face to screen” and to nurture “face to face.”

If your interaction with your students conveys an ongoing sense that you care deeply about their learning, you will enhance their experience and yours. To paraphrase a recent reminiscence of Amar Bose of stereo speaker fame about his teaching at the Massachusetts Institute of Technology: “If they know that you care and if they can reach the solution of problem three after they have understood the approach to problem two, then your students will not only meet your expectations, they will exceed them.” If your students rise to the challenge of being able to absorb sophisticated materials, analyze and organize these and if they rise again to present them articulately, confidently and effectively to the critical audience that they themselves will have become, then they and you will have succeeded.

Alexander Hahn is a professor of mathematics and the director of the Kaneb Center. He can be contacted at hahn.1@nd.edu. The views expressed in this column are those of the author and not necessarily those of The Observer.