• Eventually, many answers are memorized. This results in fast, reliable access and helps us perform complicated skills smoothly.
• The procedure of counting is more compact than an array of memorized facts. Thus the method is learned first, with fluently recalled answers coming only after much more experience.
• The counting procedure can act as a backup.
• The choice to use memorization or a procedure to find an answer depends on the effort needed to perform the procedure, the reliability of the procedure, and incentives surrounding accuracy. 

When performing skills, we use a variety of methods, from following a procedure to retrieving an answer from memory. With increased practice, the memory component becomes dominant for routine situations. Even when we can’t get the exact solution from memory, we may find parts of the answer which we can use to solve the problem faster.

Digging deeper has two benefits:

• It can provide a strategy to obtain the correct answer when memory fails.
• It can assist in non-routine situations where no answer is known.

• Methods that directly assist with learning a domain are necessary prerequisites. Even if a brute-force approach might work, good methods are more reliable than trial-and-error.
• Routine performance is largely handled by drawing on direct experience—not working from first principles.
• If the principles don’t actually lay out the actions needed for routine situations, then they are mainly helpful in non-routine cases.
• These principles will probably only be relevant as your experience within a field grows.