Archive for category: Science of Learning
1) THOU SHALT NOT KID THY SELF.
In Shakespeare’s Hamlet, Polonius gives his son Laertes the advice to above all else to be true to himself. Honesty with one’s self is a lifelong process. In the world of music practice it can begin with the simple step of writing down how much you practice. Even if you never total the time or even give it a second look, you have established a measure from which to judge your efforts.
Goal setting is critical for any endeavor. If the requirement is to have a piece up to tempo by a certain date, you can break down the steps necessary for the accomplishment. If these intermediary steps are not met, you must be honest with yourself that the larger goal is in danger and likely not to be met unless additional effort is made. If a secure memory is the goal and little has been committed to memory a week before the deadline, don’t kid yourself, a secure memory is not likely to be the outcome.
We will bear the complete responsibility for our success or failure for the vast majority of our life. While as a student, it is easy to be dependent upon your teachers to order and plan your work and goals. However, you are a student for only a short time and will have to order and plan your work for decades after your student years.
While it helps to record our activities so we have a written record of what we did, rather than relying upon a faulty memory, we can learn so much more about the practice of practice with just a little thought and planning. If you treat your practice as a scientific experiment in learning, your learning specifically, over time you will make significant gains in the efficacy of your work. I was motivated to learn about cognitive psychology because of my very slow learning and poor progress as a young student. What I learned allowed me to improve my practicing and learning efficiency by orders of magnitude. I have been a slow learner and a fast learner, being a fast learner is much more fun!
The last thing we want to happen is to become neurotic about our record keeping and cease to enjoy this journey of discovery, so only keep those records which you find helpful in your understanding of what you did and the results your efforts yielded. However, keep in mind it is easier to have too little information than too much. Sometimes your data may only point to an interesting observation but because you failed to collect enough information you cannot know for certain. So at first try to collect as much information as you can and after you have a better sense of what you need to know to reach your conclusion you can begin to focus your collection more closely.
Here are a couple of examples of how we can do some very simple experiments, with ourselves as subjects, and our learning styles/habits/procedures as the point of query.
When starting with a brand new piece of music we are immediately faced with the task of figuring out how to approach its unique problems. It is often suggested that you begin by playing through the work. This helps in getting a sense of the structure, common musical patterns, and areas of difficulty. Assuming you have done whatever you feel necessary on this issue, we can begin at the beginning.
With your very first page of music you have several choices as to how to handle the music. Will you play it from beginning to end before repeating it? Play it half way? Phrase? Line? Measure? How many times will you repeat your chosen unit before moving on? How do you know which combination of all these variables is most appropriate for you today with this particular piece and its unique problems? While cognitive science can give us some general guidelines as to capacity of our short-term memory, the effects of repetition, recencey, latency, etc. on how we move information from our short-term memory to our long-term memory the application is more art than science. Only with careful self-observation can we become aware of what may be our particular needs at a specific moment.
So try this experiment with a multiple page piece which remains roughly consistent in difficulty throughout.
On the first page, play the first unit of music, whether it is a phrase or line. If it takes longer than about 15 seconds, play a shorter unit. Play it three times without speeding up and observe your progress. Do you feel you are at least familiar with the music now? Play it a fourth and fifth time. Did you make any more significant progress? Continue this process throughout the whole page. With each unit observe at what repetition point you felt your progress slowed, that is the point further effort started yielding less improvement compared to earlier efforts.
On second page of music double the length of material. If you were playing one line, play two; one phrase, this time do two phrases. Now compare the results with the first page. Do you still have the same sense of “familiarity” as you experienced on the first page? Did the progress in learning increase or decrease? Are beginning to notice a “sweet spot” in the repetition count before your improvement slows?
On the third page, treat the whole page as your unit.
At this point it is probably becoming quite obvious which level of breakdown allowed you to absorb and retain the most information. So far we have addressed two possible variables in our practice, the length of material and the number of repetitions. How long of a section we work on and the number of repetitions we find most useful are impacted by your understanding of music theory, technical demands relative to your technical abilities, and your focus and attention.
Continue working through the whole piece using the unit size you found most advantageous. When you have completed the work one time, put it away for a day, you need some time for this information to be processed and the time will give the slight variations in repetition and attention to become less of an issue for the next part of the experiment.
On the second day, repeat the entire process using the section length you settled upon on the first day. Observe the progress you make per repetition. Has the “sweet spot” moved? You will no doubt find yourself speeding up some now, try to keep this under control. Playing faster by definition will make the music harder, which introduces another variable to our experiment. We are looking to see how quickly we can absorb new music, not how quickly we can speed it up… yet.
So, at this point we are beginning to get a sense of how many repetitions it is worth doing before moving on to the next section at the very earliest stages in the learning process. For your own understanding of the learning process it is a worthwhile exercise to use the rejected breakdowns on two other pieces to better understand why they did not work as well and what their inherent weaknesses were for you. However, just because they were inappropriate at this early stage does not mean they will not be useful later on.
You should make a notation for your records of the following: composer, work, relative difficulty for you (was it below your current ability, comparable to recent works, or harder than what you have been playing), selected working unit length, some type of note about the density of the music (more dense usually means smaller units), average or range of repetitions which yielded the best results, and also observe if you found that after a certain number you actually got worse.
Since for most of us, our musical aspirations exceed our ready technical equipment, we inevitably spend a fair amount of time working on increasing our tempos, sometimes by very large margins. There is a school of thought which says we should not attempt music which is significantly above our current playing ability. I think the answer to this is very subjective and very dependent upon the personality of the individual. Some people may find challenges which take long hours of effort, with no certainly of success very discouraging. However, I find life quite boring without multiple skill bending projects going on simultaneously. This next experiment may prove more useful if you of the later group, but I think even if you are more comfortable with less difficult challenges you may find some useful understanding here.
Now that we have worked through our piece at least twice and as many as four times with the chosen breakdown unit, we have become quite aware where is the hardest material. Nothing will ruin a piece faster than a difficult couple of dozen measure which always lag behind the rest of the music in performance. So in keeping with Rule #4 of Practicing: hard stuff first.
We first must find a base line tempo, a speed we can play the passage with no less than a 95% success rate. In all likelihood, this will a much slower tempo than you image it needs to be. Record this tempo in your notes. After we find the speed which we are just able to play successfully, we need to find a tempo which is “easy” to play. The primary, if not the only determinate of difficulty is speed. If you played the section at the rate of one note per hour, you would certainly find it easy, no matter how dense the music was. If you had ten minutes to play a note, I dare say it still would be easy. We are essentially looking for a speed which is slow enough that we can think about everything we are doing and yet fast enough we don’t take all day to get through it once.
A funny thing happens when you start looking at some of these numbers in how they relate to other human activities. In weight training a similar procedure can be done. When doing a new lift, athletes will look for a weight which they can lift only once. Eighty percent of that weight however will yield them a weight which they can lift 7 – 10 times, which is often a repetition number they are also looking for.
Eighty percent of your maximum successful tempo will often yield you a speed which is near that sweet spot of slow enough to study and think and fast enough to repeat often. Your results may vary some, I would only use results slower than 80% though, never faster.
Now for the experiment. Play through your passage at this tempo. Make sure the unit is short enough you can get through it in 30 – 45 seconds. It is important that you remember in detail what you did so that you can learn from the experience. After successfully playing through the passage move your metronome up one standard notch. (I will discuss standard metronome numbers vs. smaller increments at a later date.) Continue to move the metronome up with each successful completion. If you start making mistakes, repeat the speed. If the mistakes continue, slow down 2 – 3 notches and continue to move up the tempo once the problems are fixed. Observe what happens as you approach your baseline. Do you find a sudden increase in difficulty or do you roll right past it? Continue raising the tempo until you find the number you can’t move past. You can check this by slowing down a couple notches and trying again. If you continue to fail, you have reached your limit for the day. If you can, continue to move up until you fail again, this will probably mark the end. Record the numbers which you had all of these experiences. Again put the music away for the day.
The very next day repeat the entire process, however this time the proceeding’s day top speed becomes your new baseline. Again, start at no more than 80% of that number and work your way up the metronome. Observe and record if you experience a sudden increase in difficulty and your final speed.
Do this for several days. After you have 5 – 7 days worth of data what observations can you make? Which days experienced the largest increase in tempo? How much slower was the progress in the later days? If it helps graph the numbers, over time you will start seeing some very predictable results.
The next stage would be to repeat the entire process on some new material, however this time start at 70% below your baseline and observe the results. There is a flaw in this approach however, by starting slower you will be assured of having more repetitions before you reach your baseline… or will you?
As a final stage start at 50% of your baseline. Do this with two different sections. In the first section go up one notch at a time and in the second go up two notches at a time. There can sometimes be very different results, a lot will depend on other factors such as the difficulty of the music.
There are many other experiments which we can do at various stages in the learning process and by applying just a dash of scientific method can teach us a lot about how we learn best. Hosting practice camps during summer months can also give you the opportunity to show your students how to learn how they learn.
Trace decay vs. interference.
There are two schools of thinking regarding the cause of forgetting. The first, trace decay, came out of Ebbinghaus’s work. He showed that time was the primary cause of a loss of memory.
There have been other approaches to the question of memory and forgetting. Scientists such as F. C. Barlett used stories instead of word lists to look at the effect time had on memory. He would have subjects read brief stories and then test their recollection of those stories at various time intervals up to 6 months. Though Barlett initially set out his work as a criticism of Ebbinghaus , especially in his use of non-sense syllables; Barlett’s work showed similar types and degrees of memory loss as could be explained in Ebbinghaus’s work.
Another explanation for forgetting was developed in later years and that is the “interference theory”. Briefly, it states that material learned both before and after the target material interferes with the retention of the designated material. A typical example of this type of study would be the following: 3 groups of subjects, one learns the paired group of words A-B and C-D (car – dog and tree – road). The second learns A-B and A-C, and the third would learn just A-B. The groups would then be tested on their ability to accurately recall the various lists. The results typically were the A-B only group would do the best. The A-B and C-D group would do noticeably worse on their A-B list as well as their C-D lists. The A-B and A-C group though would do the worst over all. They would intermix their two lists. This is not unlike the problems we often encountered in repetitive sections in music where the repeated sections have slight variations. It is a common problem to intermix the sections, ultimately having trouble extracting one’s self from the section.
It is a common experience that repetition impacts memory. The more a passage is repeated on day 1 of practice, the better condition it is in when the next day’s work begins. But how much practice does it require to maintain “X” amount of material? How much retention is gain for each repetition? At what point does the diminishing returns outweigh the value of the additional retention?
Ebbinghaus did a series of double tests to find the answer to these questions. He learned 6 series of 16 syllable lists, repeating each list either 8, 16, 24, 32, 42, 53, or 64 times. The next day he repeated the tests, the results were remarkably consistent across all levels of study. Through the course of his study he found that it took an average of 31 repetitions to learn a list of 16 syllables. So the lists learned 8, 16, and 24 times were not learned to his standard of error free reproduction. However the 42, 53, and 64 repetition lists were significantly over studied for his standard.
The next day he relearned the lists and recorded the amount of repetitions and time it took to learn each list to his standard. The results across all lists was an average savings of 12.7 seconds with each test set of 6 lists falling within the narrow range of 12 and 13.7 seconds saved. The average savings per list (out of the 6) was 2.1 seconds and the average time it took to read a list was 6.6 – 6.8 seconds. On average, across the entire exercise he experienced a savings of one repetition for every three repetitions done the preceding day.
And as for the question of diminishing returns, the greatest savings occurred at the 42 repetition level. Some of this he attributed to: “An increase of the readings used for the first learning beyond 64 repetitions proved impracticable, at least for six series of this length. For with this number each test requires about 3/4 of an hour, and toward the end of this time exhaustion, headache, and other symptoms were often felt which would have complicated the complicated(sic) (I think the translation should have said “results”) of the test if the number of repetitions had been increased.”
So when your students asks “Do I really need to play it again????” You can say quite confidently: “Yes, Dr. Ebbinhaus says do it 42 times!” It is indeed true that repetition is the mother of all learning. In coming articles we will look at the effect of thoughtful repetition.
The first area of memorization Ebbinghaus looked at in his dissertation was the effect of the length of the list of non-sense syllables he learned. His first observation was that lists of 7 or fewer required just one reading to be reproducible by memory. This observation is later verified by other researchers as the usual size of the short term memory. The short term memory is often described as having the capacity of 5 – 7 “chunks” of information and lasting no more than 15 seconds.
As the number of syllables increased to 12 the average number of repetitions required for the first errorless reproduction increased to 16.6. Adding just 4 more syllables added nearly 14 more repetitions. The next addition of 8 syllables (24 total) added another 14 repetitions and the final addition of 15 syllables (39 total) added only 11 (55 total) repetitions.
Number of syllables/ Number of repetitions necessary for first errorless reproduction (exclusive of it)
in a series
7 / 1 12 / 16.6 16 / 30.0 24 / 44.0 39 / 55.0
While we could say that if the final group of 39 syllables had been learned in groups of 7 or fewer it would have taken far less effort to get to the first errorless reproduction, we will see in later parts of his dissertation the effect of practice on retention. Retention is the only thing which matters after all.
One of the very first studies in human memory applying scientific processes was published by Hermann Ebbinghaus in 1885 with the essay Uber das Dedachtniss (Memory, A Contribution to Experimental Psychology (English translation title)). Ebbinghaus used himself as the subject in his experiments in learning lists of non-sense words (from a list of 2300 words). Based upon his experiments he described three important theories which can be helpful today in understanding the learning process. They are: 1) interference theory in which earlier learning is covered over by later learning, 2) trace decay is where images or knowledge suffers changes which alter its character, 3) forgetting involves a “crumbling” of various components as opposed to a general obscuring.
Ebbinghaus used himself as the subject of his experiments because he wanted complete control of motivation factors and an awareness of any possible distractions from his experiments. After creating lists of three-letter non-sense words he would read them out loud at a steady rate of 150 per minute and consistent intonation usually emphasizing every fourth. He would continue to read the lists with periodic tests until he was able to reproduce the list without hesitation, a perfect reproduction of the material. He also controlled for external factors such as time of day and personal levels of distractedness. After doing thousands of tests, he performed statistical analysis on his results.
The ability of humans to store information is enormous, however the rate of retention, ability to accurately recall, and rate of forgetting varies greatly and is the area of greatest concern when we look at learning methods. Ebbinghaus examined the rate of rote learning he experienced with his lists. One question he sought an answer to was the effect of repetition on the rate of learning. What was the relationship between practice (repetitions) and learning; how did more practice effect the outcome? What happens when a list was learned a second time; what was the residual impact of initial work on subsequent efforts?
To find the answer to these and many other types of questions he employed lists of non-sense words and practiced them for 8, 16, 24, 32, 42, 53, or 64 repetitions. He would then relearn these lists the next day measure the results. “Learned” is defined as one successful performance of the material by memory. The use of non-sense words was to reduce or eliminate any associative characteristics with meaningful words. The purpose of the study was to look at the rote learning of non-associative and non-sense syllables.
After looking at the rates of learning 16 syllable sequences with 8, 16, 24, 32, 42, 53, and 64 reps he found an average saving of 12 seconds in the re-learning after 24 hours for each repetition. A single repetition of about 7 seconds of work saved 12 seconds of work the next day.
Ebbinghaus also looked at the rate of forgetting (his famous “forgetting curve). A 13 syllable list was re-learned after a 20 min break through 30 day interval. The forgetting metric is the difference between the numbers of reps for the first trial minus the number for the second trial expressed as a percentage of the first trial. The retention rate was found to be after 1/3 hr 60%, 1 hr 45%, 8 hr 35%, 24 hr 34%, 2 days 30%, 5 days 28%, and 30 days 25%. Most of the forgetting occurred within the first 24 hours and even after 30 days enough memory remained to reduce the time it took to relearn the list by 25%.
Ebbinghaus also looked at the position a word appeared in the list and the consequences of its serial position on retention and re-learning. There are two functions he found present. Recency is the recall of recently learned material and primacy is the recall of the first learned. First studied material benefits from the lack of conflicting material and increased rehearsal.
This is a study of purely rote learning of non-associative/nonsense information. It doesn’t show the retention of associative or meaningful material. It does however provide a baseline of learning. Rote learning is the most mechanical learning process and represents learning at its most basic level.
Ebbinghaus showed, through his careful testing of his most reliable subject, himself, a model of learning which still informs our thinking nearly 150 years later. We see the relationship between learning effort and forgetting and learning effort and retention.
In upcoming articles I will look at several aspects of his work which I found helpful in understanding some of the basics of human memory which were relevant to my study at the piano. I know that some of you may find this stuff as dry as dead bones, but I hope at least a few may share some of the AHAAA moments I had as I learned something about how I learn.
I recently re-read The Art of Practicing by Madeline Bruser. While the author occasionally would swerve into a more empirical mind set, much of the time was spent in what my great late friend Ralph Bus would have called the “ooo eee”. Being a bit more analytical and empirical in my thinking, I usually do not get much out of this “new age” approach to problem solving.
When I was much younger and feeling very intimidated by my classmates at college I asked “Why can they, and I can’t?” This question propelled me for most of the next 20 years to find the answer to that question. It was actually a very difficult subject to explore and find meaningful information. The vast majority of cognitive psychology research which I was able to find focused on language as a subject matter. The cognitive processes used in the study of music and the learning of an instrument are orders of magnitude more complex than learning a list of words. Only in the past decade or so has the field of music psychology begun to take shape. Yet, despite the difficulties in finding useful research which could shed some light on the learning of music, I was able to develop a pretty complex and nuanced understanding of the mechanics of learning music.
The human mind is a very complex electro-chemical machine and while most of its functions are still unexplainable,
enough is known to create a number of working models of the how and why of the human mind and memory.
Years ago I started to outline a book on this subject which I will use throughout this series. Some of the ideas I will present may strike you as too mechanical to be used in an artistic endeavor but becoming an efficient learner is no different than developing an efficient technique. We don’t hesitate to work on scales and etudes in the hope of having a better mechanical command of our instrument. It is very difficult to play artistically if you are fumbling around mechanically. Understanding how the human mind learns, retains, and recalls information will help us learn, retain, and recall our music more efficiently and effectively.
In the same way that concert artists often make very poor teachers because they often don’t fully understand how they do what they do or how they learned to do it, they may not be aware of how their learning processes may be unique to them, giving them a great advantage in learning literature. Through the course of these articles I will explore what science can tell us about how we learn, retain, and perform our music.
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