"A Little Knowledge Is A Dangerous Thing"

A little learning is a dangerous thing 
Drink deep, or taste not the Pierian spring 
There shallow draughts intoxicate the brain, 
And drinking largely sobers us again.
-Alexander Pope in An Essay on Criticism

"Little knowledge is a dangerous thing." Bits of information are like pieces of a giant puzzle. Each piece provides a glimpse of the entire picture. Making the correct connections is essential but missing pieces can frustrate the entire process. Having bits of knowledge without the ability to relate and unify can indeed be a product of rote learning. However, pretending to have the critical thinking with only a fraction of the information required is equally precarious. In fact, it may not be possible to develop such skills without the mind absorbing the information first. Daniel Willingham writes, "'Learning to learn' is nebulous because it's domain-specific, and it's domain-specific because the ability to learn new things depends on what you already know."

The mind tries to make sense, but it cannot make sense if not provided with enough information. It is not easy to distill nature into one overarching sound bite. Actually, it is impossible. Yet, the human mind greatly craves for that shortcut. "The correct answer is usually simple" is a favorite. Thus, the human mind can collect and sort information, and then devise schemes or solutions that apply to specific situations. It is in this realm that experience does matter. As one grows in experience, exceptions are discovered and in each and every step, one's approach is examined, and the entire strategy is refined.

The intimate link between how one learns and what one knows is usually the challenge of any expert who is trying to teach. This is almost the proverbial problem of which comes first, knowledge or skills. Skills and knowledge are inseparable. This fact applies to any discipline. It applies to chemistry. In the General Chemistry class that I teach, one of the topics perceived as most difficult is acid-base equilibrium. Calculating the pH of an aqueous solution could be tricky. There is the weak acid solution, there is the buffer, there is the equivalence point, and then there is the amphiprotic species. Each one seems to command a different approach, a different shortcut, a different equation. The equations turn out different in each case, but to many students the fact that each one begins with a deep understanding of what equilibrium entails is often the most elusive to grasp. To a student, each situation seems special. Students then begin to build exclusive problem-strategy relationships. If the problem looks like this, then one should answer it this way, if it looks the other way, another approach is required, not realizing that both approaches are developed from the same principles.

One specific example, recently examined by researchers, is how difficult it is for students to appreciate structure-function relationships in chemistry, a fundamental concept in the discipline. The work published in the Journal of Research in Science Teaching has the following abstract:

The major findings of the study are summarized as follows:

One can memorize facts. One can learn strategies. But it truly takes time to learn a discipline. It is challenging to do this all the time within an hour lecture, but it seems important for students to see how experts do think. Constructing a coherent framework requires a lot of support from the instructor. The flow of topics as well as examples seen by students should be designed in a manner that allows for students not to simply absorb bits and pieces of information, but also make connections.

This brings me back to a figure from a paper in EducationNext years ago authored by Guido Schwerdt and Amelie C. Wuppermann, "Sage on the Stage: Is Lecturing Really All That Bad?":

Some can indeed learn on their own. Unfortunately, this is more of an exception than a rule. "Googling" works only through learned eyes. Learning requires a guide. Perhaps, "the sage on stage" does provide the scaffold necessary for students to connect what they are learning. Just perhaps....