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Knowledge trees: a Mechanism of Learning

This post is the second in a series on the subject of learning, where we take a look at the mechanism of learning, or building a foundation of knowledge.

To switch topics for a bit, let’s look at the mechanism of learning. In the example of mathematics, one usually learns in the following progression:

1. Arithmetic
2. Algebra
3. Calculus

Each of those subjects require the previous one as a prerequisite, and each has sub-units. So, by saying that algebra requires arithmetic as a prerequisite, we are really saying that you should know how to add, subtract, multiply, divide, etc. before trying to learn algebra (which itself is really a collection of math concepts).

Let’s represent this whole concept as trees of knowledge, with their connections being the prerequisites, and the nodes being the subjects (we can even refine this definition by observing that each subject is really a tree consisting of sub-units, etc). At first, there are a few essential subjects that everyone must learn; these subjects—reading, writing, ‘rithmetic—are a prerequisites to all the others that one might wish to learn.

So with this concept in place, we can make a few generalizations:

Everybody has a knowledge tree.

In our example from the last post, both Andrew and Sean have completed primary education and received a technical university degree. Sean is also completing his Master’s in philosophy.

There is also a global knowledge tree

It represents the sum of all human knowledge.

To learn more, one grows his knowledge tree by “grafting” on a branch.

Continuing the previous post’s example, a whole range of branch sizes exist:

1. In the first case, the required learning is simply a practical implementation of areas in which the guys have solid theoretical understanding. This is why it requires little in terms of time or energy.
2. In the second case, completely new areas of both theoretical and practical knowledge are required, so the knowledge trees have to grow by a substantial amount.
3. The third case is similar to the second, with more knowledge required, as well as proof to other people of one’s knowledge.

We can organize the knowledge tree by assigning meanings to the axes.

The following meanings can be assigned, although none are cut and dry:

1. Quantitative vs. qualitative (exact vs. vague in the graph above)
2. Purely abstract vs. only observational
3. Theoretical vs. practical
4. (Passive) understanding vs. (active) application
5. Level; depends on the prerequisite (this is the only one that can be easily parsed from current university/college syllabi.
6. A further complication of this kind of classification is a “child” of two disparate academic subjects. For example, you can have a history of philosophy, as well as a philosophy of history, and these are two different subjects.

For now, I am working on a classification of various subjects that is not assigned to an axis. I am using the Wikipedia’s page on academic disciplines as a starting point.

As an aside, is anyone aware of any academic research efforts in this area?