Smart Skills

In the "Intuitive Declarative" and "Blind Procedural" posts I described the ideal outcome of these types of learning. In this post I will try to further clarify and harmonise these ideas with a more general approach.

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Separate and Re-combine

The rationale behind the minimum information principle is that by learning knowledge in component form (i.e. by splitting complex material into several parts and learning them independently) you can acquire information more efficiently (since loads on the working memory are lighter), represent knowledge more clearly (since smaller components are easier to represent) and gain higher stability in long term memory.

However, in practice the divisions between these components are more or less arbitrary. Moreover, in the real world, knowledge must be applied in a much more fluid and connected manner and not "item by item" as in repetitions. The reconciliation between component-based learning and the corresponding “fluidness” required in application comes from the associative nature of the human brain. In practice, this takes effect when older knowledge is reformulated to take newer learned concepts into account, and when new information is represented as combinations of already-learned concepts. Through these techniques, each piece of knowledge becomes closely-connected to the rest of the student’s understanding, instead of existing as isolated facts.

All of this is already familiar to most users of SuperMemo. Nevertheless, there was some confusion as to the reason why procedural learning was recommended to be learned independently to understanding. Essentially, this recommendation was just a way to implement the above techniques in a procedural learning context. Thus, during acquisition, the separation of procedural and declarative components makes learning more efficient through simplification. At repetitions, the separation of procedural and declarative knowledge allows each to be formulated in self-contained items. However, during application, these boundaries dissolve and the procedural and declarative knowledge become much more fluid. In the end, mastery depends on a combination of both skill and understanding.

CPR

More specifically, there are generally three parts of a technique that must be learned:

1. Context: Where does the new technique fit into prior knowledge? Why are you learning this method? How does it extend what you know? Notice that any answers to such questions in no way advance your skills or your understanding of how the method works. However, they are the basis for your intellectual motivation for learning.

2. P

   rocedure: This is the blind part, where you actually gain the skill. To do this, find a worked example, or a video of someone else performing the skill, or any other form of instruction and observe the series of steps carefully, but do not worry about why they are done for now. Then, try doing it yourself - try solving the maths problem, or playing the musical phrase, or juggling the four balls, without looking at your source materials. If it doesn't work first time, look back at your instructional material and figure out what step you skipped or executed incorrectly. Then go back and re-try it, "listening" carefully to any form of feedback. Keep going until you have gained some skill. If you seem unable to progress at all, try something easier. In any case, don’t "waste" your time trying to understand what the steps are for. For now, just try to improve to where you can carry out the method without "cheating" (i.e. looking back to your materials for help).

3. Rationale: Finally, this is the part that every careful student worries most about (and where most of the comments to the last post were directed), and rightly so. It is the part where you analyse the procedure, step by step, to find out why each step is there, how important it is, and what would happen if you changed the step. It is where you derive the formula yourself instead of taking it for granted. It is where you consider if there are any potentially better ways of doing the same task. However, this should only come after the previous step. After all, what would be the point of being able to explain something that you can’t actually do?

Clearly, step 2 is the procedural part, and steps 1 and 3 form your declarative understanding. Yes, you should learn all parts, but not all at once, and preferably in this order. The main problem with learning the rationale before the procedure is that you fall under the delusion that you know how to do something, because you understand it so well. Beware of this delusion.