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Chemical Eye on Degrees of Learning
by Preston MacDougall


January 28, 2006

"The toe bone is connected to the foot bone. The foot bone is connected to the ankle bone." So went your first class on human anatomy, which, if you are like me, you mastered by singing the material over and over while sitting on the teacher's lap.

You didn't have to take any notes, just hit the right ones.

jpg Learn, think...

"Learn. Think. Create."
So says the more animated subject
(Preston MacDougall) in the photo.

If you have had a second course in human anatomy, you would have learned about phalanges, metatarsals, and so on, although much less lyrically. In between, the acclaimed Swiss psychologist, Jean Piaget, would have said that your cognitive development advanced from the pre-conceptual stage to one of concrete operations.

Piaget characterized the next stage of cognitive development as one of formal operations - essentially solving problems logically using abstract concepts. He often cited chemical and mathematical reasoning as examples of this latter stage. His studies, not to mention my test grading experiences, indicate that it is not fully realized in all people.

It is a difficult transition, particularly if teachers, during a student's concrete operations stage, made rote learning too much like a passive form of entertainment. Problem solving is fun too, but the reward comes at the end (a correct answer), and increases both with the complexity of the problem, and with the degree of independence from the teacher. The same "Eureka!" emotion that awaits the serendipitous explorer, whether in the lab or out in the field, also awaits the diligent problem solver. Only the magnitude differs, as measured by number of exclamation points in their research, or course, notebook.

In other words, memorizing every diagram in Gray's "Anatomy of the Human Body" does not a physician make. Medical schools, much like engineering schools, are annually infused with those students who have excelled at learning, and are eager to develop their skills in solving complex problems. We have a healthy population, and economy, largely because our nation's professional schools are the envy of the world.

Although it isn't included among Piaget's stages of development, I believe there is yet another transition - from formal operations to one of de novo creativity. For example, to solve complex mathematical problems requires facility with formal operations. But to solve the really hard problems, such as Fermat's last theorem, often a new way of thinking must first be created to solve the problem with. This is how British-born Princeton mathematician, Andrew Wiles, finally proved, in 1994, that Fermat was right over 350 years earlier.

Instead of bulky psychology terms, you can think of there being three stages of problem solving: learn, think, create. Whether we realize it or not, we go through these stages every time we encounter new problems in daily living. Some people are naturally gifted at solving problems involving inter-personal relationships, such as Dr. Phil, while others became masters of the atomic domain after years of education and research at premier universities.

Recurrent shortages of skilled workers in key technological fields point to weaknesses in our economy, and in our education system. The initial government response was the No Child Left Behind legislation. This will address the "learn" part of the equation, but I am not so sure about the "think" and "create" parts.

An important consideration for teaching a subject, to students who are at different stages of problem solving, is the evolving nature of the subject itself. For instance, when students are learning chemistry, it snugly fits right between biology and physics. But at the "master of the atomic domain" level, chemistry has more in common with mathematics, literature and music. The latter involve creative synthesis with numbers, words and notes, instead of with atoms.

I am reminded of a little red book that I picked up at a flea market in Beijing. My Chinese friend, who was my age and grew up during Mao Zedong's Cultural Revolution, was taken back in time. He showed me what he was taught to do over and over and over again. He picked up the book between his thumb and forefinger, then cocked his elbow and straightened his arm, three times, shouting "Xue. Xue. XUE!" (Each xue is pronounced shu-weh.) This translates as "Learn. Learn. LEARN!" and refers only to what is in the little red book.

January 29th marks the first day of the year 4703 on the Chinese calendar, and the Cultural Revolution is fading into that long history. In modern times, Chinese universities have learned much from their Western counterparts. Recently they have even had success in recruiting faculty from Ivy League campuses. In fields such as nanotechnology and materials science, Beijing's Tsinghua University lands highly in world rankings.

If you are not a student or a teacher, you might be wondering how this affects you. The answer, in case you haven't figured it out already, is that the education bone is connected to the economy bone.



Preston MacDougall is a chemistry professor at Middle Tennessee State University. His "Chemical Eye" commentaries are featured in the Arts and Public Affairs portion of the Nashville/Murfreesboro NPR station WMOT (

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