Practice till you get it correct. Then play it two more times.

THIS ADVICE MAY SOUND TRITE. Or, it may appear to be a superstitious ancedote for the belief that the student played correctly by having had good luck. "Au contraire," the piano teacher knows what she is talking about, after all!
According to studies on automaticity by SDSU EdTec students Johnnie Perry and Julie Collett, overlearning leads to automaticity. In a different study, another SDSU EdTec grad student's work lends supporting evidence that overlearning and the activities associated with it can deepen the memory trace and aid in transforming data into memory. Jose Arbona-Soto shared this concept in a presentation on the dynamics of the memory cycle (see below).

When a student receives a stimulus, it enters the brain through the senses (sensorial memory). If the input data are not attended or reinforced through some sort of repetition or development, the data is lost. However, if the brain can attach the data to an existing mental model, then it is moved from sensorial memory into working memory. It can then be developed through pattern recognition, organization or other cognitive reinforcers and become transferred to long-term memory for storage and later, effortless retrieval.

 In the movie, "Karate Kid," the young apprentice was assigned the daily exercise of waxing the car. The process of waxing developed a deftness in the same hand motions used during the fighting moves in karate. When called upon to use the moves in an impromptu challenge by the master, the young apprentice proved to be capable. His motions were effective and skillful. He was able to recall the moves through automaticity. His defense in the spar against his master (teacher) was effective, fluid, and artistic.
Similarly when a piano student is taught drills and finger exercises such as ones in the Hanon and Czerny methods, the student builds skill in usage, finger patterns, dexterity, and finger independence. Finger over thumb crossings are well-learned from scales and arpeggios; chromatic and diatonic scalewise passages found in repertoire are easily articulated because the study of them in drills and exercises has formed the appropriate mental schemata. In short, when mastered, such exercises become the mental schemata that can help transfer newly introduced musical data from sensorial memory to working memory and then to automaticity. It is during automaticity that higher level skills such as interpretation can be executed.
When the brain recognizes familiar tasks, it processes the information and applies the correct rules to the procedure in order to reduce the demand on the working memory and allow for higher order processing of information.
In the study of the piano, the higher order skills are interpretation, articulation, dynamic shading, and tone shaping. Through overlearning, the data can be automized and then when retrieved, the performer is not thinking of the notes; the fingers easily slip into their practiced positions. The performer then begins to focus solely on the higher level skills -- interpretation, dynamic shading, and tone shaping. The artist then, performs, rather than merely struggles through the piece note by note.

Will automacity allow the teacher to assume that memorization of pieces should be by rote, rather than through a careful analysis of tonal stucture? I believe the best practice would feature a combination of the two: analysis in combination with automaticity.
What then, can the music teacher do to lead the learning process? I recommend:

•  Analyze the piece.
• Anticipate likely trouble spots due to fingering patterns "in the cracks," traditional "weak" fingers, tricky rhythmic patterns, and other problems.
• Select or create appropriate drills and exercises to address these issues of technique. 
• Help the student to analyze the tonal structure, motifs, and patterns as much as developmentally possible. 
• Facilitate controlled processing by having the student to drill the troublesome sections slowly and with controlled tempi and continuity. They will have a tendency to accelerate, but remind them that "slow and controlled will later lead to fast and automatic (Collett, p. 3)." 
• Have student to practice it until they get it right, correcting as needed. Do not allow a student to continue to play it incorrectly. (The wrong way can also be "overlearned.)
• After it has been played correctly, have the student to play it three more times (overlearning).
• Place the drilled section back into the song: First with what comes before the section. Next, with what comes after the section.
  

James Bastien makes the case for this type of isolation on page 286 of "How to Teach Piano Successfully." He recommends that the often troublesome passage in measures 77-79 of Fur Elise (Ludwig van Beethoven) should be isolated for focus.

Recognizing it as an arpeggio passage, Bastien identifies the problem of improper execution by 7-8 year olds as a small hand and/or short fingers. I might add, even a knowledge of how to properly execute an arpeggio due to little experience. He recommends both isolation and focus on the three-measure passage in general, as well as separate practice on the skill of arpeggios. See examples.Bastien pp. 285-286.

The study of automaticity and long-term memory refines the Bastien recommendation. The primary focus should be on the execution of the arpeggiated passage 'as written' in the Beethoven, as opposed to mastery of typicalarpeggiated exercises in a technique book such as Hanon, as the Bastien example appears to be. The reason is, near-transfer is more effective than far-transfer exercises. For this reason, I would recommend the teacher use and create another arpeggio drill in the same key using the same notes as the trouble spot. The following is a sample drill that a teacher could create.

This is a teacher-made example which provides for near-transfer, as it captures the trouble-spot as it is written in the Beethoven piece, "Fur Elise."

 Noted pianist and pedagogist, Abby Whiteside, author of "Mastering the Chopin Etudes and Other Essays," disagrees with the prolific overuse of Hanon and Czerny exercises as a panacea for all pedagogical problems.
My own impression is that Hanon and Czerny drills are valuable in that they do assist in sight reading and promoting familiarity with the music language and its syntax (schemata). Hanon-like and Czerny-like drills, can also promote automaticity, if drills are carefully made and/or selected from actual passages (near-transfer). Another adage from the wise piano teacher tells us that, "Repetition, does deepen the impression"...[and lead to automaticity].Noted pianist and pedagogist, Abby Whiteside, author of "Mastering the Chopin Etudes and Other Essays," disagrees with the prolific overuse of Hanon and Czerny exercises as a panacea for all pedagogical problems.
My own impression is that Hanon and Czerny drills are valuable in that they do assist in sight reading and promoting familiarity with the music language and its syntax (schemata). Hanon-like and Czerny-like drills, can also promote automaticity, if drills are carefully made and/or selected from actual passages (near-transfer). Another adage from the wise piano teacher tells us that, "Repetition, does deepen the impression"...[and lead to automaticity].

Constance Ridley Smith, Graduate Student
SDSU Educational Technology