This article documents ideas that will be useful in the attempt to reduce the art of pedagogy to a science. The points listed below should be useful for the author of a textbook. Good pedagogues probably abide by most of these rules naturally, but it is also useful to have an explicit listing.
- Always use SI units. Gaussian Units, Natural Units, etc. are not real systems of units. They are conventions which allow you to supress certain dimensionful constants for the sake of brevity at the expense of being correct.
- When defining a word, make it bold. When using a word shortly before you define it, as in when you list all the types of something before you define each in turn, make it italic so the reader knows the definition is soon in coming.
- If you use a trick in a derivation, clearly indicate that it is not obvious so that the reader doesn't waste time trying to think of why it should be clear.
- If you use a trick in a derivation, try to explain how it will benefit the derivation if it isn't immediately obvious. If the explanation of the trick requires a result that comes after the derivation, then say "For reasons that will soon become clear, it is beneficial to utilize the following trick." After the result is obtained remind the reader of the trick and explain why it was used.
- When defining a term whose inspiration is not obvious, either explain what inspired it or explain that it has no inspiration. If the term is used somewhere else in the field or a related field like mathematics, then explain if the terms are related or let the reader know that there is no relation.
- Introduce new topics by grounding them in concepts that are already familiar. It is often a good idea to utilize questions to the reader such as "What if you wanted to...?" As an explicit example, when introducing perturbation theory you could say "What if you wanted to find the energy levels for a quantum system whose energy eigenvalue equation cannot be solved analytically?"
- In conversational prose, you might make up anecdotes that make the topic seem useful. For example, say that someone once asked you a question that they assumed you could never answer, but you used this trick and surprised them. This is only useful if the application of the trick is not obvious because you don't want an anecdote that could be applied to just any topic. This technique is best seen in the work of Feynman.
- In textbooks, clearly indicate any sections that are intended to be used as reference that can't be read straight through at a normal pace. It is often useful to move such reference sections to an appendix.
- Clearly distinguish theory from tricks to solve problems. Sometimes it may not be immediately obvious which category something falls under. For example, in the method of images there is no actual charge at the image location, but when we talk about bound charges, there is actual charge at those locations. So the former is a mathematical trick whereas the latter is actual theory.
- When it is possible to perform a derivation as a continuous chain of equalities, then it should be done this way. If any of the steps are tricky and the chain is long, then it can be broken up for a short explanation. Otherwise the explanation can come immediately after the chain. This keeps the derivation compact and makes it easier for the student to get it all in their head at once.
- When introducing a new variable or notation, always start with an explicit definition. Do not embed the definition in a statement about it. This could lead to confusion.
- Do not save the point of a derivation to the end, even if it sounds like a great idea to make it a big surprise at the end. While this is fun for the writer, it leaves the reader lost for the duration of the derivation.
- Don't be afraid to repeat yourself a few times when there is any chance of confusion.
- Never say that something is obvious. If it is indeed obvious, then the reader will know that it is obvious. You may still say something like "This is a direct consequence of the last theorem," which indicates that it is obvious if the reader knows where to look.