The following are a list of activities that have proven fruitful and interesting in most circumstances, and I hope that they will be able to aid you in dispelling the inevitably occasional boredom that accompanies our profession, and enrich the minds of any students who could benefit from them. I'll state that not all of the things on this list are mine - some have been adapted from ideas by wonderful colleagues I've had the pleasure to know from around the world (both in person and in cyberspace), and I've attempted to give due credit where merited.
1.) Have them give you a lesson. So they didn't practice this week; Physically being unable to execute the motions required to play something are different from the intellectual understanding of knowing how a piece should "go". Play them portions of their repertoire and let errors abound. Rhythm, dynamics, and notes should be all over the place.
Two skills will be honed here: listening and communication. The former is something that should have been engrained already, but the latter is something that is often an entirely overlooked skill in the piano lesson. The average student will probably be able to hear that something is off, but their attempt at correction will likely be overly-simplistic, or come in the form of a single blanket statement ("This note should be a D"), that targets the symptom of the error, but not the disease.
Now is your chance to arm their thought process and diagnostic skills with a more pointed specificity. One way this can be done is by implementation of mature musical vocabulary: Perhaps (in reaction to a note mistake), they will simply say "You're supposed to play an F# here". Your response? "We're missing an accidental here" Play the piece obviously too slow? They will say "It's too slow!". You say "The tempo is too slow!!" (Yes, you DO risk sound like a pedantic poseur, but this is a lesson after all.) Guiding students along the specifics of any given vocabulary in whichever field will sharpen their minds and give clarity to their thoughts.
Additionally, you can have them reshape simple commands into the form of questions, which will automatically require them to think harder and broader. If you play a piece which is supposed to be lyrical and cantabile with a harsh and percussive tone, you'll likely get a "It's supposed to be soft". Ok - at least they are listening, but how can this statement be reshaped into the form of a probing question? "What are the dynamics?". Definitely better, but could we go even further? How about "What does the character/emotion of this piece feel like to you, and do your dynamics, voicing, and articulations express that to me?. This lets them string together many thoughts, and makes them think about the ultimate purpose of dynamics and articulation.
Not only will this type of work increase awareness in piano playing, but honing communication skills during piano lessons can easily carry over into all areas of students' lives.
2.)Have an "Articulation Dictation". This one is fun. We all remember doing melodic and harmonic dictations in music school, but those might be a bit over the top for our purposes. Better to begin with qualities of sound that are easily recognizable. Find a sight-reading book and white-out the articulation markings (Or, better yet, print some sight-reading flashcards from teacher-guru Diane Hidy's website), and give them a clean slate: notes and rhythm, but nothing else. Perform it for them while adding an abundance of slurs, staccatos, crescendos, fermatas, and dynamics to the excerpt. Play it multiple times, and have them pencil in what they hear. Having to aurally recognize these symbols that are often visually taken for granted is much more difficult than flash-card like activities, and engrains them much better into the memory. For students who are advanced enough, even a bit of theory can be thrown into the mix: If the passage is major, lower the third, and ask them to put in the correct accidental they heard that made it sound minor.
3.)Have a "Practice Practice Session" I originally heard of this concept from Daniel Epstein - professor of piano at the Manhattan School of Music. He would have his students come in for a whole lesson and do nothing but watch them practice, take notes, and at the end give them constructive advice about how they could better spend their time. (The teacher Dan Severino also has an excellent article on his blog titled 'The Silent Piano Lesson").
When you do this, you will likely be absolutely horrified at what you hear, and want to intervene immediately. Resist. If the student stops completely, then give some minimal instructions on how they should carry on. Very often a student will start playing from the beginning until they hit a rough patch, then begin again from the beginning - continuing ad infinitum. They likely won't utilize any of the practice techniques we spend whole lessons drilling (Hands separately, slowly, blocked, small sections, isolation, etc). About halfway through the lesson, you can give them some ideas for further practice, and then continue to watch in silence. Being told to do something at home and being encouraged to do it in the lesson are completely different things. This technique is something that may take multiple lessons before improvement can begin to be noticed, but it really is one of the surest ways of diagnosing whether or not instruction has been absorbed.
4.) Give a Piano Literature Class. I've often been amazed at how sometimes a new student will show up and play something for me (sometimes quite well), and not even know the name of the composition, not to mention the composer. Does the student who feels deeply about the Chopin Prelude she is playing know that this is just one star in the solar system of Chopin Preludes, in the galaxy of Chopin, and in the universe of the piano repertoire? These days with smartphones, nothing could be easier than giving students a sneak preview of the vast amount of music they can explore online, and introduce them to different genres, styles, and composers. You can talk about which characteristics make Schumann Schumann, and why Schumann cannot be Bartok, etc. You can then quiz them by having them listen to one piece by Bach, one by Chopin, one by Prokofiev, and one by Schoenberg, and asking if they can identify which is Bach and why (based on what they heard). Learning to listen for specific things in music is a way to inspire independent listening at home.
5.) Discuss Time-Managment Strategies - This somewhat related to #3. (I will devote a separate post exclusively to practicing and time-management). Practicing is a solitary and often boring and lonely activity. Unlike soccer, dance, or debate team - practicing has no built-in structure; no hardly defined schedule. It is little wonder that it's not apparently obvious how much practice actually needs to take place outside a lesson for improvement. Take out a sheet of paper and have them write their Monday-Sunday daily schedule, with all actives, etc. Find a block of time every day where they can devote exclusively to practice, and then discuss exactly what can be done during this time. Practicing (like anything), can seem much less daunting when one realize's that it can be chunked down in manageable blocks, and with different activities scheulded for differnet times (Scales and technique the first 10 minutes, Bach the next 20, theory workbook on Thursdays, etc.) While most students and parents already know there should be some regimented structure for pracitce, many don't go through the motions of putting it down on paper. This will likely not go as exactly as planned, but the act of having them put it down on paper is a huge step in the right direction.
6.) Record your Student Playing Something and Listen Back Together. All professional musicians put themselves through the agony of recording themselves so they can listen back for improvement. Some of us also tell our students to record themselves. (My fanatically dedicated teacher at Indiana University - Emile Naoumoff - would film all of our performances in studio class on his iPhone and immediately afterward upload them privately to Youtube, sending us email links to the performances for us to review). But how often do we spent the time to listen back to performances WITH our students - hitting the pause and rewind buttons, and probing them to articulate exactly what it is that does not sound quite right - OR - noticing the encouragement in their spirit when they hear it was not as bad as they though it was?? Collaborative listening and discussion is an integral part of music making and should not be ignored. If you want to take this a step further, you can instruct them to write comments about their own performance, as an adjudicator would in a festival or competition.
7.) Have Fun With the Metronome. The pianist Louise Earhart (Current president of the MTAC), once introduced a fascinating procedure to me: Take an electronic metronome, set it to a moderate tempo, and have the student clap loudly, and so exactly in synch with the beat that you reach a point where you can't even HEAR the metronome. What has happened is that the internal pulse has taken over, and the body is doing all the time-keeping independently. This might take a bit of time, but is incredibly fun when it happens. Then you can have the student clap different rhythmic variations in this manner. Other ideas are to take a piece that has already been thoroughly mastered and have the metronome click first to a sixteenth note, then and eighth note, then to a quarter, then a half, etc. Doing this may give the student a heighten sense of subdivision - an indespensible tool for any musician, and will also be an incredible exercise in patience!
A less creative (but no less valaube) option is to go through the tried and true method of taking a difficult passage, setting the metronome to the slowest speed, and gradually working up the tempo notch by notch. Hearing a passage many times, at many different tempi is like looking at a painting from many degrees of distance: each step you take reveals a different type of details about the composition.
8.)Compose. This is probably better as a long-term home assignment as opposed to something that can be done in one lesson, but it can certainly be started in a lesson. Memorization and identification of such theoretical elements like time signatures, key signatures, chords, etc, are really only the tip of the comprehension iceberg in comparison to having to actually create music from scratch. Nothing reinforces concepts (of any kind) as much as having to actually decide when and where to utilize them. Although this may depend on your student's current level of ability, a good way to start would simply be to pick a mode and key, and jointly browse through the rich array of accompaniment possibilities on the piano for the left hand (This alone is such a great learning experience, and can take a long time). Once the mood has been set and this is done, the concepts of what makes a successful melody can be introduced, and the student can experiment with that. After these basics are in place, you can talk about where you want the main stresses to fall - which will lead to selecting a time signature. At this point we can set up our staff paper page basics, and the student will likely be filled with motivation to go home writing.
That last sentence may seem overly optimistic, but allow me to share personal experience: Every year, I teach multiple college group-piano classes. True to human nature, a few minutes before the end of class, bags are packed and people start looking at the clock. An exception to this is on the days when I assign a composition assignment and we begin in class: when the time comes for class to be dismissed, virtually every head is quietly buried in staff paper, blatantly unaware of the time. I pushed the limits to see how far some of them would remain unaware (or apathetic) to what time it was, and about 20 minutes after the end of class, about half remained.