[1.II.23] Damper Pedal
Practice any new piece without the pedal HS, then HT, until you can play it comfortably HT at final speed. This is a critically important method of practice that all good teachers use with all their students. It may seem difficult, at first, to practice musically without the pedal where it is needed; however, this is the best way to learn precise control so that you can play more musically when the pedal is eventually added. Students who practice with the pedal from the beginning will become sloppy players, develop numerous bad habits, and will not even learn the concept of precise control or the real meaning of musicality.
Rank amateurs often over-use the damper pedal. The obvious rule is, if the music doesn't indicate a pedal, don't use it. Some pieces might seem easier to play with the pedal (especially if you start slowly HT!) but this is one of the worst traps a beginner can fall into that will hold back development. The action feels lighter with the damper pedal down because the foot is holding the dampers off the strings instead of the fingers. Thus the action feels heavier when the pedal is released, especially for fast sections. Some students do not realize that where pedals are not indicated, it is usually impossible to play the music correctly at speed if you use the pedal.
For Fur Elise, use the pedal only for the large LH broken chord accompaniments (bar 3 & similar), bars 83-96 and the RH arpeggio passage (bars 100-104). Practically all of the first difficult interruption should be played without the pedal. Of course, everything should initially be practiced without the pedal until you have basically finished the piece. This will encourage the good habit of keeping the fingers close to the keys and discourage the bad habit of playing with too much jumping and lifting of the hands, and not pressing firmly into the keys. An important reason for not using the pedal initially is that technique improves fastest without the pedal because you can hear exactly what you play without interference from previously played notes. You should be actively controlling the tone.
Coordinating the pedal and hands accurately is not an easy task. Therefore, students who start learning a piece HT with the pedal will invariably end up with inconsistent and terrible pedal habits. The correct procedure is to practice HS first without pedal, then HS with pedal, then HT without pedal, and finally HT with pedal. In this way, you can concentrate on each new skill as you introduce it into your playing.
Inattention to the pedal can slow down technical development much more than many students realize; conversely, attention to the pedal can help technical development by increasing your accuracy and adding another dimension to musicality. When you do one thing wrong, it becomes difficult to do all the other things right. When the pedal is wrong, you can't even practice the correct finger technique because the music comes out wrong even when the fingers are technically correct.
The pedal was practically non-existent before Mozart's time; for example, no pedal is used in any of J. S. Bach's music. Mozart did not indicate any pedaling although, today, some pedaling is considered optional in some of his compositions and many editors have added pedal markings in his music. The pedal was basically fully developed by Beethoven's time, although it was not yet totally accepted as a serious musical tool. Beethoven used it with great success as a special effect (third movement of Waldstein Sonata); therefore, he tended to use it a lot (entire first movement of his Moonlight Sonata) or non at all (entire Pathetique Sonata, first and second movements of the Waldstein). Chopin used the pedal extensively to inject an additional level of logic into his music and fully exploited all the different ways of pedaling. Therefore, Chopin (and many later composers) cannot be played correctly without adequate training in pedaling.
See the references for all the different ways to pedal, when to use them, and how to practice those moves (Gieseking and Leimer, Fink, Sandor, Pedaling the Modern Pianoforte by Bowen, and The Pianist's Guide to Pedaling by Banowetz). Try to master all these moves before using the pedal with an actual piece of music. There are some very helpful exercises in the references for practicing proper pedaling. When you do use the pedal, know exactly which move you are using and why. For example, if you want as many sympathetic strings to vibrate as possible, depress the pedal before playing the note. If, on the other hand, you want just one clear note to sustain, press the pedal after playing the note; the longer you delay the pedal, the fewer sympathetic vibrations you will get. In general, you should get into the habit of depressing the pedal a split second after playing the note. You can get a legato effect without too much blurring by rapidly lifting and depressing the pedal every time the chord changes. As with the keys, it is just as important to know when to lift the pedal as when to press it down. Clearly, the pedal must be "played" just as carefully as you play the keys.