Maybe good practicing—and good teaching, for that matter —is just simple math: addition and subtraction, multiplication and division, over and over again in ten thousand combinations.

This occurred to me recently when I was working on a set of Bach preludes and fugues for an upcoming concert. Practicing Bach always demands all sorts of creative arithmetic as I break it down in different combinations every day: first right hand alone, then left hand alone, then with hands together while adding fermatas in all the awkward places, then subtracting the fermatas and the right hand but adding the metronome, and so on. Pure practice math.

Actually, this is pure science. The science is based on a cognitive theory called the Information Processing System, which divides the brain functions into various categories of tasks and storage. The first job of the Information Processing System is to deal with all the sensory input that is constantly bombarding us. This is the background noise around us (the lawnmower next door), the visual stimulation we are faced with (the notification alerts popping up on my computer screen), the felt and other sensory inputs that are a regular part of our world (the cats howling at my feet), the internal noise and conversation within us (I need to call my sister and get the towels out of the washing machine). This input is unlimited and relentless, which is perhaps why sensory-deprivation tanks are so popular and appealing.

On the other end of the system is our long-term memory, which cognitive theorists tell us is also unlimited. The long-term memory is where information, skills and memories are stored. While we have been repeatedly told that human beings only use 10% of our brains that isn’t exactly true. We don’t actually know how much of the brain we use, but none of us ever come close to maxing out our long-term memory capacity.

Any time we have truly learned something, it is in our long-term memory. The question is how it gets there.

The piece in between is our working memory. The job of the working memory is to sort through all the sensory information that comes in and to decide what to attend to and what to throw away. This is the part of the learning model that chooses what gets stored in long-term memory. Not everything that filters through the working memory ends up in long-term memory, but everything must start there. The working memory is juggling tasks and information when we are engaged in things like playing the piano, or driving our cars, or teaching our lessons, or reading a book. In short, the working memory is where things get interesting, because although we can’t max out the capacity of our long-term memory, the working memory has serious limitations. In fact, cognitive theorists often refer to the working memory as the bottleneck of our brains.

There is a famous article about the working memory from 1956 by the psychologist George Miller entitled, “The Magical Number 7, Plus or Minus 2,” which basically states that we can handle about seven different things in our working memory at any given time, give or take one or two. What is fascinating about this theory is that this seems to be pretty consistent across people, regardless of intellectual level. There is simply not a wide variance in working memory capacity. We can learn some tricks make more efficient use of our working memory, but even so, there are real limits. It is what it is.

Recent studies have questioned Miller’s Magical Number 7 and suspect that this number is actually too high and it more like four or five for most of us. Which brings us back to practice math.

Traditionally, pedagogical practices haven’t given much thought to the mathematics of our musical work with regards to the limits of the working memory. Instead, more commonly, we have been taught that if we don’t adhere to every aspect of the score from the very beginning—no matter how many disparate elements!—we are committing a grave sin, and the music will never recover. It is not unusual for teachers to start harping about dynamics even as the student is struggling with notes and rhythms. It is as if teachers fear that there is some inherent danger if students start by playing everything with a generically healthy mezzo sound. Or at the very least, a bad habit will be formed. More than anything, piano teachers are terrified of the infamous bad habit.

I am here to tell you that there no danger. In fact, it’s smart practice math—and a very good habit as well— to mix and match elements, building and rebuilding the music in different combinations, all the while keeping a respectful eye on our how much the working memory can handle at any given time. Not only does such thoughtful practice prevent mental breakdowns, but layered and rich repetitions create more pathways in the brain, making us more flexible and creative musicians in the end. It’s all about that magical number 7, or more realistically, the limits of juggling 4 or 5 different elements. Take, for example, Lila.

Lila is six years old with six months of piano lessons behind her. Having learned an impressive list of rote pieces, she has a fairly good grasp of the keyboard, can accurately and quickly name all the keys and her finger numbers. But when her teacher puts a piece of simple music on the rack in front of her things start to get sketchy. Suddenly, she is required to make sense of notes and rhythms, finger numbers and also that silly picture of a dog in the corner. One part of her brain is trying to decipher bass clef (All Cows Eat Grass), another treble clef (F-A-C-E), another rhythm (That dot next to the half note is supposed to mean something different, she thinks, but she isn’t sure.), and still another part is attempting to read those finger numbers printed above some of the notes (Why only some of the notes? It’s puzzling for sure.) And what about that dog? Why is he there in a piece called “Sandy Beaches?” To make matters worse, the teacher keeps interrupting with something about “forte” and “piano.” Little Lila starts to cry.

This scenario happens literally every day in piano studios across the globe (I’d love to find a way to blame this on Trump, but it is a world-wide problem.). Furthermore, this very scenario has been repeating itself now for multiple generations of music students. It is pretty much the reason when a stranger hears I am a piano teacher they inevitably say something like, “I took piano when I was a kid, but I think I just didn’t have any talent.”

The real tragedy is that this scene is so preventable with a little pedagogical and practice math. And it has nothing to do with talent.

What would avoid this meltdown is some basic subtraction, and then a bit of division. Start by asking Lila lots of questions to help her make sense of the information on the page: Which hand begins? Where is the setup on the keyboard? What is the first finger for the right hand? Why is that dog there? Does he like beaches?

Then begin, not with the notes—or heaven forbid, the dynamics—but rather with the rhythm. Together tap the rhythm: right hand taps the right-hand part, left hand taps the left-hand part. Remember Lila is a beginning pianist. It is already a full cognitive load to manage the hand-eye coordination of the right rhythms with the correct hand, not to mention that pesky half note with a dot next to it.

Lila is six, although in the end that matters not at all. A 66-year-old beginning pianist would have the same issues. A 48-year-old practicing fiendishly difficult Bach is also faced with similar limits of her working memory. I can successfully negotiate the notes, fingerings, articulations and rhythms of the right hand (see that’s already 4 things to juggle!) if I ignore the final Vivace tempo and any attempt at voicing the subject. It is simply smart practice math that until some of these things are automatized and chunked together in my brain, I need lots of practice time and repetition. Eventually—one hopes—these separate technical challenges will add together and become a single unit in the working memory. Only then will I have the cognitive room to deal with musical shaping and voicing, to adjust to the strange piano I will face at the concert in few weeks and to make friends with any performance anxiety I might experience under pressure. At least that’s the idea.

Until then, practice math.

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