One of the reasons I love piano teaching so much is that it gives me opportunities to study the learning process, and how each of us learns as individuals. A fascinating example of this often happens when I start working with a new student. At some point, I'll ask the student to slow down at a difficult passage so they can play it correctly. I'm still surprised at how often they'll will resist doing this, saying "my previous piano teacher told me always keep a steady tempo, even if I played wrong notes."
When I hear this, I try to get the pianist to understand the reason behind this advice. Why would their old teacher tell them one thing while I'm telling them the opposite? If you think about it for a moment, you'll realize that the "steady tempo" remark was intended to help them become a better sightreader. If you're sightreading, you're trying to play the music as a performance and in that context, the worst thing you can do is interrupt the tempo every time you come to a difficult measure. So you simply keep going, and leave a few notes out or whatever you need to do to continue the music's flow. This is especially important when you're playing with other musicians.
While practicing, on the other hand, your primary goal is to learn the notes correctly. So in this context, it's vital that you don't "smudge" your way through difficult passages. By all means, anticipate them, analyze them, and play them slowly enough so your fingers get the experience of playing them correctly. Then, you can play at a steady pace.
I'll often do this when I practice Bach. I also do it while improvising over challenging jazz chord progressions. I wouldn't slow down in performance of course, but doing so while practicing enables me to really listen to each note and hear the passage clearly. It gives my fingers a chance to play the correct notes before speeding up to the correct tempo.
By the way, this process of anticipating hard passages in advance is backed up by a study of piano students at The University of Texas. You can read more about it here. Check out point #4: Errors were preempted by stopping in anticipation of mistakes.
Let's take the "steady tempo" advice the way it was intended: to help with sightreading. Don't let it limit you in terms of learning music. Sometimes, slowing down is just what we need!
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