It’s not easy to plan a one hour piano lesson to include ear training, solfege and transposing. (They belong together, bundled with Theory, and enrich the learning environment)
At the Oberlin Conservatory, Theory, Keyboard Harmony, and Eurhythmics were taught separately. Our piano teachers (applied study) adhered to their rigid routine, rarely fitting solfege, sight-reading, improvising, composing etc. into the time-limited hour. Yet, the cross-fertilization of course work, expanded our musical horizons.
The New York City High School of Performing Arts, my alma mater, offered a valuable/mandatory Sight-singing course that continued from 10th grade through senior year. It was enormously relevant as the movable DO (solfeggio) helped me navigate complex scores, and peel away voices.
Piano students who just stick to the music without being exposed to theory, ear-training and other mind-enriching escapades, are basically short-changed. They often view their pieces as finger challenges only–easily becoming Treble clef fixated, tacking on bass lines without a second thought. Naturally, their sight-reading suffers because they’re not internalizing interval movement in various voices, or sensing harmonic flow.
In an effort to stem the tide of such top layer, tracing paper learning, I’ve made a concerted effort to delegate at least 15 minutes of my students’ lesson time to ear training and transposing. (One of my source materials is Fundamentals of Piano Theory by Snell and Ashleigh) 
As an example, I videotaped an adult student transposing snatches from the Preparatory Level workbook, page 45.
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I’ve tossed in a spot-practicing segment where the ADULT student is smoothing out a tricky set of measures in the RONDO: Allegretto, Mozart Sonata, K. 545. (Repertoire should be a springboard for sight-singing, ear-training and theory adventures since they’re interwoven)
(I often slip into solfeggio in parceling voices)
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LINKS:
Solfeggio and Transposing
https://arioso7.wordpress.com/2011/09/19/piano-instruction-solfeggio-and-transposing-video/
The Importance of Sight-singing, Ear-training and Theory in piano study
https://arioso7.wordpress.com/2012/09/21/the-importance-of-sight-singing-ear-training-and-theory-in-piano-study/
Using Piano Repertoire and as a springboard for a theory lesson
How to Improve Sight-Reading
https://arioso7.wordpress.com/2011/04/21/how-to-improve-sight-reading-at-the-piano/
