David asked about technically basic repertoire used by Chopin in his pedagogic work.
Thinking about teaching repertoire of Chopin we must firstly remember the time he lived and taught in - there were not as many possibilities in any field of people's activity as today... - therefore the amplitude of studies using by him could not been as large as it commonly happen today.
Chopin's mostly used piano technical compendiums were "Preludes and Exercises" and "Gradus ad Parnassum" by Muzio Clementi, concurrently he liked the Studies of Ignaz Moscheles, of J. Cramer and brilliant virtuoso works of Johann N. Hummel. Only his truly greatly talented students (for example - Jane Stirling) have played his own Studies op. 10 and op. 25. But his most appreciated collection of the musical pieces that, in his opinion, truly can improve the piano technique - were the both parts of "Das Wohltemperierte Klavier". It is worth interest - let you consider the technical complicity level of many Preludes there!
Actually - "Gradus ad Parnassum" by Clementi, the 48 Preludes and Fugues of Bach and works of Hummel - were of the key importance for technical forming of the pianist before he/she may start to play Chopin's own Studies and other works.
It should be clear that he could not work with his students on the Liszt's Transcendental Studies or his Studies after Caprices of Paganini because these both colossal sets HAVE BEEN COMPOSED just after Chopin's death... We know that Chopin did not like Liszt's music, still we have to consider the fact that all, nowadays the most beloved and - artistically seen - most valued pieces of Liszt have been born AFTER Chopin's death. In any case his pupils have played some pieces of Liszt: Tarantella after Rossini, and his transcription of the final sextet from 2nd act of "Lucia of Lammermoor" by Donizetti.
However the knowledge of Chopin's technical repertoire might shed some light on his teaching, in my opinion, after about 5 - 6 years of intense practical experiments with some evident elements of his Method, I may say that the most important things here are:
Creating the possible clear image of a spirit the pianist would like to fulfill with the each one played sound, so - there cannot arise exactly any artistically EMPTY sound. Seeing from the artistic point of view THE EMOTIONAL EMPTINESS (I mean, THE COMPLETE NEUTRALITY) cannot work as emotional background in any play. We have to be sure - the sound of music works as a material medium (only) that transports something greater from the performer's fantasy to the listeners' mind. However the problem of emotional resonance has not been yet understood in the theory of piano teaching as the point of interest, as the real and important problem - for many years this question is present as one of the most intriguing matters, generally, in the pedagogic and educational theory (Dewey).
As the next point I would see the creation of a vivid vision's of the each one played sound. The pianist cannot just push down or press on the keys focusing his energies (physical as well as mental one) somewhere in the depths of a keyboard. The pianist must create a situation in which he will get a feeling of smooth and easy joining the internally mobile sound with the next, and next, and next one of the similar character. Being internally IMMOBILE one cannot be able to produce the effect of MOBILITY in the performed music! The emotional resonance acts always and everywhere!
One should to be sure that emotional indifference would be easy disclosed and negatively evaluated on the concert stage by public and/or juries (if at exams, competitions, etc).
To easily realize these both points above practically, the pianist should search for and find such Zone in dynamic & coloristic scope of the sound that he/she really can listen to with the authentic PLEASURE. Practicing without such "controlling device" the pianist might realize many tasks chaotically, working on too many problems at the same time, which cannot bring many positive results. Finding the proper dynamic Zone of the sound he/she will install the rationality in the energy management in his/hers instrumental habits. Getting the basic sound of his/hers own, the pianist will be able to seriously thinking about these aspects of the matter I wrote in the both former sections above. The action will get a sign of excellence and the way toward artistic self-realization will be open.