A teaching analogy is like a comparison between something you know and something you are learning. Like a comparison, an analogy points out both similarities and differences between the two ideas. Unlike most comparisons, an analogy is primarily concerned with one-directional knowledge transfer: it assumes limited knowledge of the taught idea initially, picking the points of comparison based on their importance to the new idea instead of based on distinguishing between the ideas.

Teaching with analogy is like refurbishing a house instead of building from the ground up. Like refurbishing, much of the effort can be avoided by reusing the good parts of what already exists. Unlike refurbishing, the result is an entirely new idea that does not sacrifice the old idea, and multiple analogies can effectively copy over good parts of multiple ideas to further refine the new idea being built.

Learning with analogy is like reverse-engineering a working prototype. Like reverse engineering, many of the harder parts can be bypassed by borrowing from the idea being copied. Unlike reverse engineering, the result is not a copy of the old idea but rather a new idea applicable in new contexts.

Explanations are like a sequence of very small analogies. Like such a sequence, each step is taught by comparison to something the students already know. Unlike such a sequence, the interplay of the various parts of the explanation might combine in non-sequential and even unpredictable ways.

Teaching without analogy is like cooking without providing ingredients. While it may be possible to forage the needed components of learning directly by exploring the world and how it works, doing so is tedious and inefficient. A skilled teacher may be able to lead the student in paths where the right ingredients can be found, and doing so may be enjoyable for some students, but the end result is needlessly time-consuming with less predictable results.