Appendix 1

Criteria for a good explanation

A good problem solution is not just a collection of equations and numbers. In fact, in many of the problems in this course you will not use equations at all. A problem solution combines the features of an essay and mathematical proof:

it clearly and coherently communicates your thinking about a problem to someone else; and

it presents a logically valid chain of reasoning based on established principles.

Just as you can tell the difference between a good essay and a poor one, or a good geometry proof and an inadequate one, you will learn to distinguish between good and poor scientific explanations. If you have studied the solutions at the end of this chapter, and compared them to your own explanations, you may have noted certain characteristics of a good explanation. Let's be as precise as we can at this point about the criteria for a good scientific explanation. Then, you should use these criteria as a checklist to criticize and improve your solutions to the homework problems for this and subsequent chapter.

Description versus explanation

When asked to explain, some students only describe. A description tells what happened; an explanation tells why it happened, in terms of fundamental principles.

A description:

"The charges spread out all over the surface of the metal."

An explanation based on fundamental principles (Coulomb 's law, properties of metals):

"Because like charges repel, and the electrons are free to move, the excess electrons spread

out over the surface of the metal."

A basic goal of science is to explain a wide range of phenomena in terms of a small number of powerful, fundamental physical principles. Aim to reach this goal in your own work.

Time steps

To explain a process, it is necessary first to divide it into steps. These steps may correspond to very short time intervals, but are conceptually necessary to a clear explanation. Compare your four step explanation of charging by induction (section) with the following sentence:

"Touching the back of the foil with a finger removes negative charge, leaving the foil positive."

It is possible that the writer understood the whole process, but he or she has not made this clear. Many questions remain unanswered: Why was the back of the foil negative? Why would touching the foil remove negative charge? Why doesn't this negative charge simply flow back onto the foil again?

Diagrams

Practicing scientists draw diagrams all the time. They use diagrams as a tool to support and guide their own thinking, as well as a device for explaining their ideas to others.

Students are frequently reluctant to draw diagrams. As reasons for their reluctance students say things like "I'm not good at drawing," "It takes too much time," "It's redundant, because I have to explain everything in words and equations anyhow." A common thread in these statements seems to be the perception that a diagram is a decoration, not a tool. Many students have not yet learned to use diagrams in a way that can guide their own reasoning and prevent many errors. Often a good diagram can bear the major burden of explanation, with little or no accompanying prose required to make the point.

A useful diagram is the centerpiece of a good explanation. What makes a useful diagram?

Readability

A diagram must be large enough to see and interpret easily. Do not draw little teeny diagrams in the margin of your paper. Make the diagram big enough that all the important information can be included in it, and can be interpreted easily by a reader. A diagram should not be ornate. Use simple, clean lines.

Labels

By labeling all distances, charges, and forces in a diagram, you bring together in one place a great deal of information that is scattered throughout the problem. Once it is recorded on your diagram

you do not have to search for it again. Labels help to prevent serious errors, such as using "d" rather than "dx" as an integration limit. Carefully labeled diagrams significantly reduce the number of errors made in problem solutions.

Include only relevant details

A c1uttered diagram is hard to interpret. For clarity, include only relevant information. For example, show only excess charges, but do distinguish between charge on a surface and charge inside an object. Do distinguish between free and bound charges—do not make your drawings of polarized molecules in an insulator look the same as a drawing of a polarized metal.

These distinctions are important physical distinctions, so diagrams must reflect them unambiguously.

Precise use of words

Scientific words have very precise meanings, and they must be used precisely. Unlike everyday speech, where it is permissible to substitute many different words for each other, there are very few synonyms in science. If you use the wrong word, your statement may be meaningless or utterly incorrect. Here are some important words that are frequently misused by novice students:

Force, acceleration, velocity, displacement, distance, momentum, work, energy, temperature, heat, charge, charges, dipole, field, induce induction, ionize, ionization, neutralize, polarization, polarized, potential

For example, a charged object is not the same as a polarized object. Force and charge are utterly different concepts; they are connected conceptually by the fact that a charged object can exert a force on another charged object.

Here are some examples of meaningless statements from students' papers:

"The charge attracts to the positive dipole."

"The metal block is induced by the touching of a positive charge."

Checklist for scientific explanations

• Not just description

• Based on fundamental physical principles

• Processes separated into steps

• Diagrams

Readable

Relevant details

Labels

• Precise use of words

Use this checklist to help in constructing good solutions to homework problems.