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Class Notes
	Learning one step at a time (Published February 25, 2002) By H. WELLS WULSIN

In the ’90s comedy What About Bob? Bill Murray in the title role has a head filled with a crock-pot of ludicrous and laughable personality disorders. During his therapy sessions, Bob and his psychiatrist hold hands and waddle in circles, practicing a new treatment plan dubbed "Baby Steps."

What Hollywood sees as farcical psychotherapy also aptly describes the process through which we all learn – one small block at a time. Often inflated ambitions urge us to leap forward in great bounds, but lasting knowledge is rarely achieved through anything but steady, measured pacing.

The incremental nature of education is seen in every discipline, but it is especially pronounced in the sciences, where each concept builds on the one preceding it. To understand the chemical properties of a substance (say, ice), one must understand the configuration of the molecules, which requires understanding the shape of the molecules, which requires understanding the atoms within the molecule, which requires understanding the constituents of the atom. A student analyzing an acid-base titration must draw on myriad prerequisite topics: reaction equilibria, stoichiometry, equation-balancing, concentration calculations and topics all the way back to the first day of the course.

Caught in a swirl of new ideas in a fresh subject, it is not always clear to a student what gaps need to be filled to proceed to the next level of comprehension. It is here that the teacher’s perspective and tailoring eye become critical. After all, teachers are not exceptional in their store of raw information. The local bookstore, a branch library or a high-speed Internet connection will quickly deliver much more authoritative and extensive information than even an entire year of top-notch lectures.

If we need teachers (and we certainly do!), we need them because so often in the learning process we don’t know ourselves what it is we don’t know. Understanding does not result from rapid-fire exposure to large quantities of information. As students, we need to be shown the jewels picked from the pebbles. To arrive at our destination, we need a guide who knows where we are beginning.

These starting coordinates have been frustratingly elusive in my first year of teaching. Time and again, I have missed the mark in trying to pinpoint what my high school students know. I was shocked to discover that many of them lacked basic tools for learning science, such as being able to multiply fractions, convert metric units, use a triple-beam balance or draw a model of an atom. A student who does not understand scientific notation cannot write down the number of molecules in an ice cube any more than a carpenter can drive a nail through a two-by-four without a hammer.

Without the prerequisite tools, trying to learn advanced techniques is futile. So while a good teacher must maintain high standards of excellence and keep high expectations for student performance, it is also incumbent on the teacher to give students hand-holds that are within their reach.

Two years ago I borrowed a friend’s snowboard, thinking I could quickly master the graceful snow-carving technique. I hit the slopes, and after an hour of falling on face and on rear, I was bruised into submission and gave up, defeated.

Over the most recent President’s Day weekend, I gave it another try in western Maryland, starting this time with a group lesson. Our instructor had no secret tricks for how to snowboard, but instead she took us to the bunny slopes and let us practice – first sliding, then stopping, then turning one direction and, finally, tracing smooth curves back and forth.

By progressing sequentially from basic to advanced levels, acquiring each new skill was perfectly easy. My previous attempt, when I tried to leapfrog the fundamentals, taught me nothing except how hard it hurts to fall down.

Even when my poor aim miscalculates my students’ starting position in the classroom, I can still be confident that, with sufficient time, we will move toward a deeper scientific understanding of the world.

So often, science is seen in lay circles as a realm inaccessible to the commoner – the domain of bespectacled white-haired men wearing lab coats and pocket protectors. Many children and adults have had painful experiences with science (I confess that one or two have occurred in this classroom), which may have dampened their interest or undermined their confidence in science. But the beauty, and the power of science, is in its simplicity.

If science is a land a thousand miles away, then the journey to get there begins with a single step and continues with nothing else but step after step after step.

Last week during a unit on chemical reactions, a student called out when I diagrammed a nitrogen molecule on the blackboard: "How do you know to draw three bonds?" At first it frustrated me. In our unit on molecular structures two weeks ago, we had already covered that question. I avoid backtracking over old material, but looking out at a sea of squinted eyes and furrowed brows, I realized I needed to review this topic again.

Quickly I wrote the steps to find the number of bonds an element forms: use the periodic table to find the group number, use the group number to determine the number of valence electrons, use the valence electrons to find the electrons needed for a full octet, and that number will give the number of bonds formed.

Every step is simple, but when put together, they produce answers to questions that at first glance seemed impossible.

I smiled as I heard a murmur of "Oooooohhhh’s."

They saw it: To solve such problems, a student need not be gifted or brilliant or even average. With a little practice, you quickly become comfortable with the road, and soon the journey is not so treacherous after all.

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Send stories, advice, or questions to H. Wells Wulsin at wulsin@gwu.edu.

Copyright 2002, The Common Denominator