Many people think that the lesson is where the crucial learning happens, but the lesson is only once a week, while the practice is many more times per week! Therefore, instead of the "learn in the lesson, then practice what was learned" mentality, it's more like "discover and improve during practice and I will guide and support you during the lesson".
There are two main aspects in considering practice:
(1) Getting to the Piano
(2) How to Practice Efficiently (once you are at the piano)
Getting to the Piano
Make Piano Practice a Priority
Just because you like practicing doesn't mean you will. I would love to play the piano all day long and have many new books that I have yet to read and play through, and it only happens when I prioritize it. How? See the next point.
What Works for You? Create a Schedule, Set Reminders, Post-It Notes, etc.
Just because you enjoy practice and want to practice, doesn't mean that you will. Even for me, I definitely need to block out time to practice, otherwise it does not happen.
There is no one-fits-all solution to this. For some, setting a routine like practicing every weekday at 4 pm would work well, and for others that would not be possible.
Consciously Learn to Enjoy Practice
If it is a "chore" to practice, it may be okay in the short term, but it is not sustainable for the long term. Might be okay for elementary school students as they grow into knowing what they enjoy, but middle school and especially high school students will not benefit if they do not appreciate making music.
How to Practice Efficiently (once you are at the piano)
A. Starting a New Piece
Before playing any notes, we will want to take a look at the form of the piece. Students may be tempted to count the number of pages in a piece... but identifying the form helps you see the large picture and importantly, any repeating sections. Most music has some sort of repeating section (even if it's not an exact repeat) so that helps to organize your practice and make it seem less daunting.
A2. Fingering & Rhythm
These are the two aspects of music that are most difficult to correct or "re-wire" in your brain if learned incorrectly. Also, you can get away with poor fingering (especially while playing slow) but it will ultimately lead to bad habits and sloppy playing when trying to play faster.
Look for repeating patterns or ideas in music. Music is not random and virtually always has various repeating ideas! While not necessary, stronger theory knowledge allows you to analyze patterns deeper (identifying harmonies and cadences used, meanings of each accidental, etc.).
B. Core Practice Phase
B1. Quality over Quantity: Create a Focused Plan
More is not always better. Using a combination of your Tonara assignments for the week and amount of time you have available to practice for the day, make a plan that includes all the points below.
B2. Practice by Phrase - Don't Just Start from the Beginning
Although the form identifies larger sections of the piece, you'll also want to focus on the difficult spots -- generally no longer than 2-4 measure phrases. Also notice that many phrases will be similar with slight variation, make sure to be able to identify what is going on.
B3. Use Metronome to Solidify Beat and Gradually Increase Tempo
While metronomes serve the primary function of keeping a steady beat, they also serve a secondary function that is just as important -- allowing you to go faster ever so slightly, and provides a number that you can use to keep track of your progress for each section or phrase.
B4. "Erase" Mistakes: Accuracy in Practice = Accuracy in Performance
Accurate practice will lead to accurate performance. Do not just play "whatever" or extremely sloppy thinking that you'll fix it later. Start with good habits from the beginning -- accuracy in notes AND musicality -- and your music will shine come performance time. If you do make a mistake somewhere, address it by figuring out why you played the wrong note (wrong fingering, missed key signature, etc.), then "erase" it by playing that 2-4 measure phrase correctly many times in a row. That helps to "erase" the mistake. Most people just play it correctly once, but that only means you played it correct 50% of the time -- once incorrectly and once correctly.
B5. Listen to Professional Recordings
Listening to recordings by different performers will help give you different ideas as to how to interpret the piece. You should listen both actively (while studying the sheet music) and also passively (while doing other things).
B6. Distinguish Finger Muscle Memory from Brain's Knowledge of Piece
By sheer repetition, you will develop muscle memory, and often your fingers will be able to play without you even really thinking about what's being played. While initially this seems cool, it is actually very risky without the brain understanding what's going on! Once muscle memory is interrupted for any reason, the brain must kick in and if it is lost, you won't be able to keep going. This is why active and focused practice is important, and starts with the analysis of patterns from the very beginning of learning pieces.
B7. Basic Variation
Simply playing the piece "as written" over and over has limited benefits. Changing it up keeps your brain flexible, which helps you learn it more securely and also helps with performance. Basic variation includes changing the rhythms (playing 8ths as swung, for example) or articulations (switching staccato and legato, for example). Or, playing a playful piece as lyrical or pretending a fast and exciting piece is actually a slow and depressing one.
C. Polishing a Piece / Preparing for Performance
C1. Creating Your Own Opinions & Interpretations
After listening to various recordings and doing your own analysis and considering the composer as well, find your own interpretation, your own opinion of how this piece should be performed. At this point, this is (hopefully) a well-informed decision, including feedback your teacher has given you. While you can use professional recordings as references, they are not things you should strive to copy.
C2. Fallboard (or Desk) Practice
By playing on the fallboard (key cover) of your piano or a table/desk, you can practice fingering while playing the piece in your head or listening to a recording (and not being interrupted by wrong notes). This is also a good way to practice firm and active fingers, as you will get a nice "poppy" sound from the fallboard or table if you are playing with the correct touch.
C3. Mental Practice & Visualization
If you are preparing for a recital, examination, or competition, mental practice is one of the most underappreciated strategies. Not only playing the piece in your head (and without the sheet music if it is to be memorized), but visualizing the place of performance (stage, exam room, etc.) and who will be present (parents/audience, evaluator/judges, etc.) And just like regular practice, don't just play from beginning to end, even in your head! Use variation and starting from different sections to your advantage.
C4. Advanced Variation & Improv/Arranging
The possibilities here are endless! Play your repertoire like a lead sheet! Improvise the melody over the same chord progression or keep the melody and reharmonize the harmony. Weave in and out of variation and as written. This keeps your practice fresh, even when you feel you have "mastered" the piece. (Which of course, have you really??)
C5. Step Away and Refresh, Enjoy!
Sometimes you just need a break. After playing a certain piece for too long, it can get stale, even if you liked it a lot to begin with. Could be a short break of just a couple days, or a bit longer, but sometimes coming back to a piece after a vacation gives you a new perspective on the piece and breathes new life into it. While the performance of a piece only takes a few minutes, you spend many hours practicing it -- so enjoy while you practice!!