One of the reasons for introducing the contrast between Intuitive Declarative and Blind Procedural learning was to deal with the concept of rote learning. In particular, rote learning can be considered a primary form of procedural learning.
What is rote learning?
All users of SuperMemo know the importance of repetition in learning. However, there are two distinctly different functions for which repetition can be used. On the one hand, rote learning involves the acquisition of knowledge through repetition. Conversely, SuperMemo uses repetition as a maintenance tool for previously-acquired knowledge.
Examples of rote learning:
- In school, most children learned their multiplication tables through an endless (and mindless) process of re-reading and recital. Despite any work done to reconcile multiplication with arithmetic (i.e. that 3x = x + x + x) it was primarily this mundane repetition that bored the numbers into their heads
- Every budding musician's first few years consist at least partly of practicing scales, arpeggios, etudes and other such exercises - over and over (and over) - until the fingers know how to play them, and the mind doesn't need to get in the way
This method of learning is focused entirely on practical application. As long as you can defend yourself in a fight, it is not required that you explain the theory behind your technique. As long as you can play your piece in the orchestra, in tune and in time, it's not necessary that you be able to name and describe all the muscles involved in playing. This type of learning is does not require strong understanding.
In contrast to this process, repetitions in SuperMemo occur only after skill or knowledge has been acquired. In the case that you have thoroughly studied something such that you can fully understand and apply it, SuperMemo simply ensures that you "lock in" this improvement so that you need never return to your notes and wonder what on Earth they mean (which otherwise happens very often to students studying large amounts of material). Spaced repetition does not increase your understanding, nor does it reduce it - it simply maintains it at whatever level you have achieved by the time you formulate your items.
The somewhat subtle difference between these two forms of repetition is the first point of misunderstanding with potential new users of SuperMemo. The assumption is that "repetition = rote learning". In fact there are two types of repetition, each with different functions. In particular, rote learning is the acquisition of skill through repetition.
How it Works
The basic principle which makes rote learning effective for acquiring a skill is the variation principle. This is the fundamental principle that a new skill is easiest to learn when it is but a slight variation on an already-learned skill. In rote learning, the first time you try to execute something, you only get part of it right. However, you then repeat the part that you know, and then try adding a bit more to it.
For example, you try to play the first line of a musical piece but only get the first two bars sounding good. So what do you do? You practice the 3rd bar in isolation, and then try to add it on the the first two bars. Then you learn the fourth bar, and so on. Overall, it looks something like:
- Play the first bar ok
- Play the first bar again, and also play the second bar
- Play the first and second bar again, this time getting the dynamics right in the second
- and so on
This is of course the simplest situation - no new techniques to be learned, no difficult passages, just learning of notes. However, it illustrates the basic rationale, which is that each time you repeat the skill you add on a little bit extra.
When you first feel the thrill of riding a bike, it is all you can do to keep in a straight line. However, after a few more goes you can also steer and brake without smashing into things or jumping off the bike.
When you learn your multiplication tables, it often happens that you can remember the first 2 or 3, but have trouble with the rest. e.g.
- 1 x 3 = 3
- 2 x 3 = 6
- 3 x 3 = 9
- 4 x 3 = ...?
However, after some time of saying the whole x3 table from 1 x 3 to 12 x 3 over and over (and over) again, you add on a few more lines each time. The parts you learn may not necessarily be in order. So, you might learn 10 x 3 before you learn 7 x 3. However, you are still using repetition and the variation principle to add on, bit by bit, to the basic skill that you started with.
Now, it is of interest to note that in mathematics education "Children have a tendency to learn algorithms by rote without developing any understanding of what they are doing" (Hiebert, 1986). This statement beautifully illustrates that skills can be acquired through simple rote repetition, without any supporting understanding. Now, this quote is obviously pointing to the negative effects of learning maths without declarative support. However, the cure is not to stop children learning procedures by rote - the method is obviously effective - it is simply to make sure to also teach the context and rationale of those procedures. Apart from being able to apply these, students should also be able to choose when to apply them, and understand why they work.
Terminology and other Meaningless Verbal Knowledge
The last part of this post may turn out to be the strangest. And that is because I propose that any knowledge acquired through repetition alone (i.e. rote), without association to other concepts (which is the primary indicator of understanding), is procedural. As a simple test, if there is something that you cannot remember on the first attempt, but need several goes in the Final Drill to learn it, it is probably procedural.
A particularly large and relevant example of this type of knowledge (especially in SuperMemo) is terminology and other general vocabulary. Knowledge of which word is used to represent which idea is almost always learned through repetition, rather than through an intuitive understanding that the word makes sense. For example, you learn that "orange" is the word for that large fruit with the unique colour to its skin.
Why is this fruit called an "orange", and not a "coconut"? It just is and you better practice the word a few times or you will forget what it means the next time someone says it. Certainly, you can learn the etymology of the word and understand (declaratively) where it was originally derived from, but you don't have time to do this with every new word. And let's face it, how many children know or care about the etymology of words like "mum" and "dad"? That's just what they're called, and with a bit of effort, they're not too hard to say.
- This continent is "Africa". Why?
- This person is called "John". Why?
- This mathematical symbol is called "pi". Why?
- This bone is called the "tibia'. Why?
As you can see, asking "why?" to any of these is irrelevant in most situations. Even if you did find out why, you would still have to learn the word, separately.
The only real exception is words where the etymology of words is obvious. Because I am part Greek, and have lived several years in Greece, there are many scientific words that I can understand immediately. For example, I knew the meaning of the word "polychromatic" the very first time I heard it, because it is made of the Greek words "poly" (many) and "chromatic" (colours). So something that is polychromatic has "many colours". In this case, I learned this word declaratively. Unfortunately there are not so many other cases where this can be done. Even compound words like "pancake", which ostensibly comes from "pan" and "cake", don't really make that much sense, since a pancake is not really a cake anyway.
(http://www.wired.com/medtech/health/magazine/16-05/ff_wozniak?currentPage=all)
This Wired article on SuperMemo and Wozniak describes how Ebbinghaus experimented with nonsense syllables such as "bes, dek, fel, gup, huf, ke4k, be4p, bCn, hes". Though many psychologists would probably treat these as declarative, I contend that they are probably not. At least in practice, they can be treated as procedural, and that is what's important for us. However, I would also hazard a guess that an fMRI would confirm that this type of knowledge is not processed in the brain in the same way as when you think about something that you understand, and has many associations to other knowledge. The intuitive justification is that when learning vocabulary, you are simply acquiring the ability to say the right word when presented with certain information.
This Wired article on SuperMemo and Wozniak describes how Ebbinghaus experimented with nonsense syllables such as "bes, dek, fel, gup, huf, ke4k, be4p, bCn, hes". Though many psychologists would probably treat these as declarative, I contend that they are probably not. At least in practice, they can be treated as procedural, and that is what's important for us. However, I would also hazard a guess that an fMRI would confirm that this type of knowledge is not processed in the brain in the same way as when you think about something that you understand, and has many associations to other knowledge. The intuitive justification is that when learning vocabulary, you are simply acquiring the ability to say the right word when presented with certain information.
Thus, the names of countries, capital cities, parts of anatomy, and any other technical jargon all form procedural knowledge. In fact, practically all words in language are learned procedurally, except perhaps those words that can be readily and obviously derived from other words.
Redundancy
Redundancy is an important and useful tool for maximising the stability of your memories through association. When I separated the ideas of Intuitive Declarative and Blind Procedural, I did not mean that you should only learn one or the other. In practice you must learn both, in order to reinforce the same knowledge from different perspectives. It is important that you learn these as two different representations of the same knowledge, rather than learn a single all-encompassing "intuitive procedural", so to speak. As I said in response to a comment on another post, you should keep the training of skills and learning of knowledge separate. It's just like saying that in language learning, vocabulary, grammar, spelling, punctuation etc should all be formulated into separate SuperMemo elements - not because one is more important than the other, or because they are unrelated, but because it allows for better focus and more efficient learning.
Thus, you will naturally find instances of procedural learning that seem to require a lot more thought than others, even once they have been mastered. The trick is to artificially separate out the different components so that they can be learned separately and then used to support each other.
In summary, rote learning is when you acquire knowledge primarily through repetition rather than through association to other knowledge. If you learn something by rote, you should thereafter treat that knowledge as procedural. Also, all knowledge is inherently fluid and often contains parts that require blind execution and parts that require intuitive understanding. Learn both, and use them to support each other.
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