Procedural Knowledge

Today we come to the topic of this blog: Procedural Knowledge!

This means learning how to DO things. This type of knowledge includes skills, techniques and methodology. Many procedures require physical coordination, such as sport, music, driving, typing, using specialised mechanical equipment, etc. Others are more knowledge-based procedures, such as finding the solution to mathematical problems, using grammatical rules in practice and playing computer games. In this second category it is important to include all deductive uses of knowledge. As I said in the last post Declarative Knowledge includes only non-deductive knowledge. NB: Examples of deductive and non-deductive knowledge are given below.

Whatever type of skill is to be learned, few people have managed to figure out how to methodically use SuperMemo to learn and retain them for the long term. A primary purpose of this blog is to outline the method I have been using for the last couple of years to learn primarily violin, but also guitar, maths, engineering concepts and computer games.

Firstly though, I will continue to outline the nature of Procedural Knowledge in order to clearly distinguish it from declarative knowledge (see previous post). Most often, the distinction between declarative and procedural is described as "knowing what" versus "knowing how", respectively. However, I don't find such descriptions at all useful for understanding the underlying nature of these knowledge-types and consequently how to formulate them in SuperMemo.

Therefore, here is my version:

DEFINITION 2: Knowledge that can only be tested through performance is procedural

I find this definition to be infinitely more useful, at least in a SuperMemo context. In order to test if you still have the ability to play a major scale on the violin since your last repetition, there is nothing for it but to take out the instrument and play the scale! Several online users have discussed other methods for learning procedures, such as recounting an enumerated version of the steps in a process. However, this clearly does not satisfy the definition above since it a mental visualisation rather than an actual performance. Importantly, there is little reason to think that such a method could reinforce anything other than the ability to visualise. If you want to reinforce a skill at repetition time, you must perform the skill. Naturally, this brings about huge constraints. You can't use SuperMemo to practice driving unless you have it with you in the car. You can't use SuperMemo to practice Karate unless the software is with you in the training hall. And so on. However, these are necessary constraints, for the reasons given above. I repeat, at every repetition you must DO what the skill demands - you cannot just imagine it.

However, it is interesting to take on those types of knowledge at the boundary and decide how to classify them. Take, for example, the knowledge of the enumerated steps of a procedure, such as the ability to open a can using a can opener:

1. Take the can-opener out of the draw
2. Hook it onto a can
3. Twist the handle until the lid is off

Any experienced user of SuperMemo would have no problem formulating such information into items. However, think about how such knowledge would be tested. Obviously, the student would think of the answer in her head and click Show Answer... she wouldn't go downstairs to the kitchen and physically pull the can-opener out of the draw. There is a recognition of what correct action should be taken. But there isn't any actual performance of the action. Therefore, from the definitions I have presented for declarative and procedural knowledge (see post) we can see that this is declarative knowledge. Suppose that instead of taking the above action, the student visualised taking the correct steps. Now, I would not say that this is totally inneffective. However, I would say it is not sufficient. The only reference for grading would be the student's own memory, or a photo or video. However, suppose that the can opener needs to be held at a specific angle, or is easier to open with several large turns rather than many half turns... such things can only be realised and rectified during an actual performance. Naturally, there is not much room for error in opening cans, but in the types of valuable knowledge that we would input to SuperMemo, there generally would be a higher degree of complexity, which cannot properly be imagined. There is no substitute for actually doing it! Having said that, there are some procedures that are so basic they do not have to be learned or practiced - memorising the steps is enough. However, do not trick yourself into thinking that you are learning procedural knowledge.

For the next example, I will also contrast deductive and non-deductive knowledge. Consider the following items:

Q: 3 x 2

A: 6

Q: 6 x 10

A: 60

Q: 3 x 7

A: 21

Q: 6 + 2

A: 8

Q: 8 x 10

A: 80

Such knowledge is generally declarative (after reading on, come back here to figure out why I say only "generally"). On the other hand, knowledge of the following item is procedural, although based on the preceding declarative items.

Q: 3 x 27

A: 81

Anyone with basic arithmetic skills can work out the last example. However, this skill is based on their knowledge of the first five items, without working them out. There are, of course, more complex cases where one thing needs to be worked out, then fed into the next equation, and so on. However, in any case where the final answer is not simply known, but needs to be worked out using other non-deductive knowledge, the problem can be considered a procedural one. To actually get the final answer, you don't recognise that "3 x 27 = 81"... instead, you perform the calculation to determine it. From this explanation we can see that to some people the following item would be declarative, and to others it would be procedural:

Q: 3 x 17

A: 51

For those that know the answer by heart such knowledge is declarative. For those that need to work out the answer, the knowledge is procedural. Consider a detective trying to find the culprit of a crime. To the criminal such knowledge is declarative - the criminal knows who he is - while to the detective such knowledge is procedural - it must be worked out from known data.

Just as a declarative item can be characterised by the semantic links between question and answer, a procedural item can also be characterised. In particular,

A procedural knowledge item is characterised by the purpose the procedure serves.

To put it simply, if you know two ways of achieving exactly the same thing then one of those ways is redundant (once again, redundancy is not necessarily bad).

Suppose you work out "3 x 17" as follows:

1. 3 x 10 = 30
2. 3 x 7 = 21
3. 30 + 21 = 51

Now, you can also work out the answer like this:

1. 20 x 3 = 60
2. 3 x 3 = 9
3. 60 - 9 = 51

Both methods are equally long and come to the same result. Thus, one of these is redundant. Redundancy can be important for preserving the integrity of important memories, but can be a waste of time for simple cases such as the above. Also note that some of the steps may declarative for some people, and procedural for others. A young child may need to work "30 + 21" on paper, while others may spit the answer out instantly.

Declarative and Procedural knowledge are often closely intertwined in practice, often making them difficult to separate for formulation in SuperMemo as separate items. The ability to play classical violin pieces requires knowledge of music theory (declarative) as well as practical skill (procedural). The solution to a mathematical problem can only be found by first recognising the problem formulated within the specialised notation (declarative) and then applying specific methods for its solution (procedural). However, inasmuch as each type of knowledge needs different forms of reinforcement (recognition vs performance), you do need to learn how to distinguish between the two and treat them separately.

Hopefully you now have a somewhat deeper understanding of the practical differences between procedural and declarative knowledge. Now that the groundwork is laid down we can move on to the fun stuff - real examples of SuperMemo items that give one the ability to retain procedural knowledge just as easily as the declarative sort!

All comments and questions are welcomed.