ezLearnz Blog

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?

stepping back from ezLearnz and taking a 60km view on learning in general

I have been very bad at updating ezLearnz activities for the last several months. Sorry! Here’s a quick update: I have found a co-founder (Sean) and spent the summer with him developing ezLearnz and another app that he’s been working on. In September, we decided to take a step back and think about where we wanted to position our apps in the market. We ended taking many steps back, looking at learning in general, and coming up with a vision that is extremely ambitious. Over the next several posts, we’ll start a conversation on our thoughts and conclusions.

The Problem: People want to learn in order to do stuff

When people talk about learning something, they’re really talking about being able to do stuff (even if doing stuff is on an abstract level: one might want to learn philosophy, for example, in order to “do things” with the ideas and concepts of philosophy; or to simply have possession of a particular field of knowledge). Note: this discussion deliberately ignores those who are made to learn (some of those in school) or want to get a degree in order to be (more) employable (some of those in college/university). If the knowledge could just be uploaded to their head somehow, they wouldn’t worry about the learning. Unfortunately, that’s not the reality.

Here are some examples of people wanting to do stuff*.

• Sean wants to learn Haml
• Andrew wants to learn Hobo
  • Context: both are Ruby on Rails developers; it would take them 1-5 hours to learn those programs
• Andrew thinks 3D printers are cool; he wants to build one.
• Sean thinks robots are awesome; he also wants to build one.
  • Context: both have engineering degrees; however, it would take a 0.5-2 years of concentrated study for them to accomplish these things.
• Sean has a dream of getting a philosophy PhD.
• Andrew would love to one day get a PhD in molecular nanotechnology.
  • Context: in both cases, 4-6 years would be required to achieve the degrees.

These examples of wanting to learn things range from the trivial to the epic, in terms of time and effort required to master them. All have one thing in common, however: they require that the guys in our (true) story add to their store of knowledge and skill.

The “problem” part stems from the lack of an underlying foundation for a particular field of knowledge: to take the first example, it would be meaningless for Andrew to learn Hobo without knowing Rails, or Ruby, or software engineering/computer science in general. This does not mean that Andrew cannot start learning Hobo, Rails, Ruby, and the tenets of computer science all at once; in fact, that is the path he took (except for Hobo). However, there were a lot of mental models that were constructed incorrectly and had to be painfully reconstructed as their falsehood came to light. A concenctrated curriculum of computer science in ruby, followed by rails, then hobo, would have taken less time and energy to complete, as compared to the ad-hoc learning path taken. So, in a sentence, content and structure are needed in this scenario.

Another need is the presence of community: it would be easier for Andrew to learn in a group of others enthusiastic about Hobo/Ruby on Rails, with an expert who would be able to answer questions about the subjects at hand.

Later, we will discuss the mechanisms of building a foundation of knowledge, and the solution that ezLearnz’ successor will offer.

*Names have been left unchanged to protect the integrity of the story