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.

-----------------------------------------------------------------------

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.

Blind Procedural

Intuitive Declarative (review):

In the last post I described what I consider to be the ideal outcome of declarative learning. Namely, to improve your intuitive understanding to a point where everything fits in harmoniously and makes good sense, without contradictions.

It is not enough to be able to give the right answer at a repetition - you must have a firm grasp of what you are saying. A good rule of thumb is that if your answer field allows for several synonyms or alternate descriptions that all mean essentially the same thing (e.g. big/large/massive/enormous, etc.) then your item is declarative. It's not the words that you say, but the concept that you are recalling. The words you use as representation are only aids to recall; they are not the knowledge itself.

The Blind Path

For a long time I had a dilemma while studying engineering at university: I would study my subjects with a reasonable amount of effort and with the purpose of developing as strong an understanding of my subjects as possible. I generally achieved my aim and often understood material better than my peers. I was able to answer lecturers' questions, help other students and learn new material more quickly. However, to my dismay, students that literally did not understand what they were doing (they told me so, and asked me for help!) were surpassing my marks. Annoyingly, I knew why, but I didn't know how to fix it.

Engineering requires an understanding of how things work. It also requires the ability to use tools (e.g. mathematics, computer programs, and physical tools) to make things work. As you can guess, I was better at the former, while my peers were better at the latter. The problem was that I didn't want to be like them and forgo my understanding in return for ability.

You see, my style of learning would be to start at the basics and relentlessly try to understand the details and how they fit with what I already knew. I tried to devour skills through good understanding (which I now see was futile). Conversely, my peers were more efficient and simply tried to find the shortest route to finishing their assignments by skimming pages for formulas that might work, and crunching numbers without caring about what the numbers meant.

Obviously, I did have some skills and my peers had some understanding or we wouldn't have passed the grade. However, through this experience I realised that it is possible to learn declarative and procedural components in isolation. After all, I had learned the declarative component (with few skills), while most others had learned the procedural component (with little understanding).

The lesson: Like my procedurally-focused classmates, you don't need to understand something in order to be able to do it. You can study procedural knowledge "blindly".

Other Examples

• Knowledge without skill: No matter how well you can explain the subtleties of ([insert your skill here] e.g. music, sport, painting), it doesn't mean you can do it. From here comes the (somewhat cruel) taunt that "those who can't do, teach".
• Skill without knowledge. Many great leaders in history have never learned formal management theory. Likewise, many basketball players haven't studied physics, even though this science describes many important factors of their sport. You can walk, talk, breathe and eat without thinking about it

Hence, although skills and knowledge are both important, it is possible to learn them independently. Furthermore, it is more efficient to learn and formulate them independently due to the minimum information principle.

Use Feedback

Do not try to understand the rationale behind a technique, how it might be improved, when it is applicable, and so on, while you are learning the skill. These things are important, but leave them for another time. You can't learn everything at once.

Instead of focusing your attention on understanding things, focus on the actions you're performing and adjust them according to your feedback. For a musician, this would be the quality of the music being played. For a programmer, this will be the console and the outputs it gives, including the error messages. For a graphic artist, this could be the effectiveness of the image. If you're not sure what feedback you should be paying attention to, don't try and think about it too much. You will improve more quickly by simply setting a goal and training for it.

Instead of seeking understanding, you must learn to move blindly through the methods your are training and listen to your feedback.

All comments are welcome. You can get RSS more easily now by clicking on the link on the right hand side bar.

Intuitive Declarative

The next few posts will be on the contrast between "intuitive declarative" learning and "blind procedural" learning. Hopefully, they should help you further clarify the difference between the two knowledge types, as well as give some ideas as to the best modes of learning.

------------------------------------------------------------------------------------------------

In this post, I ask “What is the ideal outcome of declarative study?” in order to contrast it with procedural study

According to Bloom’s taxonomy, the ideal outcome should be to:

1. Know simply facts and be able to bring them to mind when necessary

2. Understand these facts in context and be able to explain them

3. Apply them in problem solving or when learning another concept

4. Analyse them, explain them in terms of other concepts, and arrange them into a structure

5. Be able to synthesise them into new ideas

6. Be able to evaluate them and decide on their worth and relevance, according to some framework

From my personal experience, the best outcome of declarative study has been to provide me with strong intuitive understanding of my subjects. By intuitive, I specifically mean “learned intuition”. Not the type of intuition that allows you to know something without thinking, but the type that is based on experience.

For example, if I spell a word wrong, it feels wrong. If someone asks me whether the USA or New Zealand has a larger population, I don’t just automatically answer “USA”. It feels like the right answer because everything that I know agrees with it – global politics, Hollywood, history, geography, currency conversions, etc. I wasn’t born with “English spelling flashcards” or “country population items” installed in my brain. However, by associating meaningful examples to my learning, I have developed an emotional connection with my knowledge that allows me to internally evaluate such responses.

Some subjects are generally considered non-intuitive. For example, Richard Feynman famously said, “If you think you understand quantum physics, you don’t understand it”. Likewise, Arnold Sommerfeld said of thermodynamics, “[It] is a funny subject. The first time you go through it, you don't understand it at all. The second time you go through it, you think you understand it, except for one or two small points. The third time you go through it, you know you don't understand it, but by that time you are so used to it, it doesn't bother you anymore.”

I have studied both thermodynamics and rudimentary quantum physics and I have found that what these statements really mean is not that you can’t understand them - if no one could understand anything, there would be no one studying these fields! The point they make is that you can’t associate knowledge from inside these subjects to the other things that you know. You can’t, for example, say that light is made of little particles, like matter. Nor can you say that it is made of waves. The term “wave-particle duality” that is used to describe how light actually works illustrates perfectly our inability to connect its behaviour with something we are familiar with. Almost everything in these subjects is a completely new concept, which makes it difficult to make analogies to the outside world.

Despite all this, I have achieved a considerably strong intuitive grasp of the topics I have covered in these subjects. After much study, it no longer makes sense to me to think of light as a wave or a particle. Nor does it make sense to think of perpetual motion machines that violate the laws of thermodynamics. I have learned a new sense of what is reasonable and what is possible. This is what I mean by intuition. Through the learning process I have changed the way I look at the world, the way I think about things, and what I am capable of understanding.

Therefore, my answer to the initial question is that the ideal outcome of declarative study is to build strong intuition. The links between ideas should be clear. Their applicability should be understood. You should be able to explain the same ideas in a variety of ways.

In the next post I will continue describing this "Intuitive declarative" idea, so that I can ultimately contrast it with the idea of "blind procedural" learning.

Thank you for support on the previous post! All comments are welcome.