Many students find physics more difficult than any other subject of study. What makes physics hard - as well as exciting, challenging, and rewarding - is the the combination of attitudes and skills needed to learn and practice physics successfully. It is not enough to memorize the concepts of physics. They have to be understood and successfully applied to both familiar and unusual situations. Solving a physics problem - textbook or real - has to begin with qualitative understanding of the phenomenon, formulation in gradually more mathematical terms, until the problem is reduced to a clearly defined mathematical question. Then the mathematics has to be evaluated accurately, with no technical error and with an eye on the physical meaning of the formalism. The mathematical result has to be interpreted, leading to quantitative and also a higher level of qualitative understanding.

This is not an easy program. It requires intuition, mathematical skills, creativity, accuracy, memorization, understanding, focusing on details, and perceiving the general picture - a very broad range of skills and attitudes.

Good physics teaching must simulate this variety of approaches on any level. Physics is not a purely descriptive subject, its essence cannot be perceived without some problem solving. Students must experience that abstract calculation can in fact predict the behavior of real systems. Physics is not mathematics either, its subject is the real material world, not a system of man-made axioms. Performing a calculation alone is not physics, no matter whether it is a simple substitution exercise or some elaborate advanced mathematical evaluation. The mathematical formulation must originate from physical intuition, the result should say something about nature.

Several requirements follow from these features :

1. Teaching must have significant focus on qualitative understanding, guiding students from common experience, demonstrations, student experiments to increasingly accurate formulation of the problem. The qualitative description should smoothly lead to mathematical formulation.

2. Uncompromising correctness. Qualitative is not a synonym of loose and inaccurate. The discussions must result in a set of accurate statements - verbal and mathematical - which are correct on a certain level. Any description is a simplified, limited description of real phenomena, the analysis is about a model of nature, not about nature itself with all its complexity. This is not a problem if the assumptions and limitations of the description are clearly stated. The same situation may be described on different levels, but all of them can be correct if the conditions are stated clearly.

3. Physics teaching is a spiral: The same phenomenon is discussed on increasingly advanced levels. This is very important, the simpler description prepares for the next level. It does not become obsolete either, simple problems should be approached with simple tools. Simplicity promotes understanding.

4. Seeing is believing: Demonstrations, student experiments, references to everyday observations and experiences are very important.

5. Drawing is more powerful than text and equations when it comes to truly understanding difficult concepts or situations. One can easily write a long paragraph without much meaning. It is much more difficult to draw a sketch of the situation without actually understanding it. Likewise, it is possible to write a look-alike equation (hoping for partial credit) but it is difficult to graph that equation without some thinking about its meaning. Therefore, sketches and graphs must be part of the language of any physics teaching.

Last revised: February 20, 1996