This post is in response to a comment that requested an arts-based example. As I explained in answer to the comment, there isn't really much difference in the method of application - just in the material that is being learned. Nevertheless, as it is generally helpful to see more than one example of a concept in application, I will give the example here.
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Suppose you want to learn how to draw in perspective. A good place to start seems to be the following website: http://www.technologystudent.com/designpro/drawdex.htm
From there, say you want to learn how to draw with single-point perspective. Click on "1. Single Point Perspective".
Context: (As it says on the page) "Perspective drawing is a good style to use when drawing in 3D". Single point perspective is the most basic technique. However, using the same skills, more complex drawings can be made. A cube is probably the most fundamental 3D object, and is the one which this exercise is based on. Some SuperMemo items might look like:
Q: What basic style is generally used for making objects look 3D?
A: Perspective drawing
A: Perspective drawing
Q: What is the simplest type of perspective drawing?
A: single point perspective
Q: What is the simplest 3D object to draw?
A: a cube (i.e. 1 line for each dimension, all of equal length)
Procedure: (see http://www.technologystudent.com/designpro/perspec1.htm for a full animation of how to draw a cube in single point perspective. Here is a copied version of the instructions:)
- Draw one side of the cube and select a vanishing point (marked with an 'X').
- Draw very faint lines from each corner to the vanishing point
- Draw horizontal and vertical lines for the 'back of the cube
- Go over the faint perspective of the cube so that the lines that make up the cube are dark and sharp.
This can simply be formulated as:
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Q: Draw a cube in single point perspective
A:
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Rationale: (source: http://en.wikipedia.org/wiki/Perspective_(graphical)#One-point_perspective) The ultimate basis for this type of drawing comes from the fact that the human eye collects conically projected light. Leon Battista Alberti further described defined perspective in terms of planar projections of light, and similar triangles. Overall, the basis lies in physics and mathematics.
Obviously, this part may be of little importance to the practicing artist, which is yet another example of why procedural knowledge can be learned blindly... You don't need to and how or why the method works in order to do it!
Nevertheless, you could formulate these observations as:
Q: What basic mathematical concept did Alberti use to describe the basis of perspective?
A: Similar triangles
A: Similar triangles
Q: Does the human eye collect planar-projected light?
A: No (it is conically projected)
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There are many other, more advanced exercises on this website, and it is worth learning and formulating them in the same way, if you want to practice your drawing skills.
However, I hope that, by comparison with the maths example, you can see that the method doesn't differ all that much, regardless of the material.
Finally, it is not worth reading this blog unless you are going to try applying these methods. After all, you are presumably here because you want to gain the skills required to learn procedural knowledge in SuperMemo, not because you want to theorise on how it should be done, or why it might or might not work. So, start experimenting with your particular material and tell us what you find to be effective.
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Thank you!
ReplyDeleteWhy can't procedural tasks be broken down more incrementally? Step by step parts of an equation or cooking techniques? Like how declarative knowledge is broken down into minimum data objects?
Good question... my justification for not recommending extensive incremental break-down is purely practical. Although it is quite likely that shorter procedures are more stable in memory, it is generally most useful to learn procedures in the form that they will be used in real life.
ReplyDeleteFor example, if you will frequently perform a certain karate combination - e.g. two punches, a kick and a block - you would be best off learning the combination of moves as a separate item to the individual moves (although you can still learn them separately).
By learning the whole procedure as a single exercise (rather than only in parts), you obtain the benefit of being able to execute the method without any need for creative reconstruction of the steps. You can execute the skill without thinking - punch, punch! kick! block!
In music, I have found this to be especially important. You may be able to perform all the required technical feats in isolation, but in a performance, you want the whole piece to flow easily, as a single item.