We believe that students function best when they are in control, thus we have designed the course such that students accumulate points rather than average them. Most students believe that they can get just about any grade they wish to work for, although the quantity of work may seem prohibitive. Students have access to the gradebook at all times. Students who, in another setting, might well accept a C in a relaxed manner, may be driven to work harder in order to achieve a B or an A. We believe that students have an unusual sense of control over their grades, even though this course is obviously a difficult one. We believe that, in general, this is a good feature.

Some students believe that they are responsible for achieving as high grades as possible, and may well be pressured to work to an unreasonable degree to achieve A’s. Thus, the freedom to retake tests and do extra credit assignments may not afford these students a greater sense of control. These students can self-destruct in such an atmosphere, achieving A’s while learning to hate the subject. Teachers and parents must exhibit considerable sensitivity in helping students to set and accept reasonable goals.

Mainstream education which focuses on answers may be entirely misdirected. Given a collection of experiences, we believe that the ability to come up with appropriate questions is at least as important as the ability to reason answers and far more important than the ability to recite answers. The best scholars are those who have developed the ability to think through a problem and come up with the most useful questions. Answers may be easy to come by once the questions are clearly phrased.

Our students begin the course prepared to look for answers but not for questions. We seek to help students develop the ability to ask appropriate questions which is why we answer so many questions with other questions. As the year progresses, students who approach teachers with questions find, to their surprise, that the presence of the teacher stimulates questions of greater clarity and answers follow. As they ask questions, they often say, “Never mind, that’s a stupid question,” when actually, it was the clarity of the question which made any teacher’s response unnecessary! We may react by saying, “Sometimes you just have to stand next to a chemistry teacher and answers just jump into your head!” Actually, we believe that as the student approaches the teacher, better questions appear in the student’s head, and better answers tend to follow.

Our students entering chemistry appear well prepared to deal with certainties in a scholarly fashion. If A = B and B = C then A = C. This type of neat solution seems to have preoccupied the students’ early years and then suddenly, there are significant figures. The rules for significant figures are not difficult. The concept is not difficult. But psychologically, our students appear unready to accept uncertainties. The very notion of significant figures is contrary to their vision of science and of education.

Some years ago we introduced a project which unintentionally contained an ambiguity. In order to simplify the mathematics, the atomic masses of the atoms were rounded to integers. Students came to an atom with a mass of 40 and could not distinguish whether the atom was Ca or Ar. At the time, we decided that we would correct this mistake for the next year’s assignment, but this year we were forced to respond with, “I guess it could be either one. How would you indicate that.” Well, this was a pretty long assignment, spanning about three weeks, and the “or” which crept into the results table kept slapping the students in their respective faces and refused to go away. Our students were unprepared and unable to function logically with that little “or” in there.

After a week of agony we realized that the situation would not be alleviated next year by correcting the assignment. It would just go back into hiding. So we responded by focusing on the teaching of ambiguities, the use of logical operators such as “or” and “xor”, and if-then statements, the uncertainty in measurement and the uncertainties in language. In fact, we later expanded the assignment to contain many different levels of uncertainty.

We also have one class devoted to a lecture/discussion concerning, if a tree falls in the forest …

The three pronged solution involves

1. the nature of sound and the need for a receiver such as an ear to convert silent sound waves into the perception of noise. [straight science]

2. the ambiguity of the word “tree” and the requirement that a certain type of nervous system is needed to extract the concept of a tree from the mass of interconnectedness out there. [crooked science]

3. the uncertainty that there ever was a forest based upon the “brains in vats paradox”. [very crooked science]

We even have one day in which our chemistry teachers compete, via their students, in a lab contest. Teachers are not allowed to advise their own students, but may help other teachers’ students. Since these teachers are hoping that other students will do poorly, there is a tendency to, … how shall I put it, … to lie. To protect these students, teachers are required by law to lie in everything they say. This does not prevent them from nesting information in “if-then” clauses with “or” and “and” or “xor” and “imp” statements. The effect is somewhat chaotic but our students get a pretty good dose of dealing with ambiguities throughout the year. This particular contest is an alloy of The Great Harvard-Princeton Titration Contest, the Army-Navy football game, with a dash of our own special brand of eccentricity thrown in.

We no longer protect our students from ambiguities but rather, we hope for more mistakes so that unintended ambiguities will creep in to ruin our neatest assignments.