Let us assume for a moment that all I really know in the world is the following:

  • The set of integers
  • The operator +
  • The results of addition of two identical numbers, 2 with 2 any number of times

Or, 2+2=4. Now I can use this knowledge to recognize and solve certain similar equations:

  • 2+4=2+2+2=6
  • 4+4=2+2+2+2=8

By extension, I can solve other sums such as:

  • 8+4=4+4+4=12
  • 8+8=4+4+4+4=16

Very simplistically, I can replicate a pattern (2+2=4), derive other patterns (4+4=8) in an ever evolutionary manner.

What happens if I now posit that I learn how to multiply identical numbers:

  • 2X2=4
  • 2X2X2=4X2=8

But hold on, I see a similarity or pattern here because I could get the numbers that result from the above two products by summing the first number by the number of times the value of the second number. So if 2X8 is 16, I could arrive at 16 if added 2 to itself 8 times…or if I added 4 to itself 4 times. So that probably meant that 4X4 is also 16.

In the first instance, I was generalizing (and it worked in this instance), but the second one required me to step out, gain the knowledge of multiplication of 2 identical numbers with themselves, experiment and draw similarities or differences (2X4 is not the same as 2+4) based on outputs.

What happened here are three things:

  • I started from a fact represented symbolically using a language and notation I accepted and learnt through experimentation and generalization
  • Then I learnt another fact that was similarly represented
  • Once I learnt both, I discovered that there was another similarity to be found linking the two operations

The facts could have been learnt from a book or a conversation on the web or in-person with my teacher or in of multiple ways. Or they could have been patterns I saw elsewhere and provided my own symbolism for. The cognitive construct that I formed or learnt at a symbolic level served gave me the intelligence to compare and find a third pattern. In this example it was numbers and math operators, it could easily have been any other situation. I don’t even need to be aware of axioms and principles and any formal knowledge to symbolise and evolve these patterns. However, they may be necessary to formalize as I evolve.

Let’s call these patterns or collections thereof knowledge and the capability to compare and evolve, intelligence. When these patterns are collected in a cohesive collection, they may acquire a unique symbol or may get enshrined in a tool or process that may signify that collection of knowledge or of complexity. Learning could then be defined as the process of acquiring and relating patterns, that of demonstrating intelligence, that of actionable knowledge.

Some of my patterns could stop evolving and some could evolve extremely fast. Some could get discarded. Some patterns could conflict with others and some fit exquisitely with other patterns. Some of my patterns could get augmented, refined or discarded as I receive or solicit new patterns through social interaction or experience or introspection. Some patterns could potentially be useful, but not immediately so and would be reserved for future reference. Some patterns could be very sensitive to initial conditions (that 10 to the power -10 change) as in Chaos Theory. Self organization is mentioned by George as another process where the way these collections are organized may itself need to change when new inputs come in or the environment changes.

So far so good. The process of learning so described is what social constructivism also appears to describe. However George mentions that key limitations of behaviourism, cognitivism and constructivism is that they do not “address learning that occurs outside of people (i.e. learning that is stored and manipulated by technology)…(and) how learning happens within organizations”. For the latter point, perhaps there may be disagreement. We need only to look at Communities of Practice to see how this could potentially occur. For the former, well, we use those patterns in our everyday life (e.g traffic lights?) as an environmentally present source that forms part of negotiating knowledge.

Connectivism makes the process of forming connections to acquire and relate patterns in pursuit of learning an explicit focus, while social constructivism makes the negotiation of knowledge in a social and cultural context as the explicit focus. George demands this as an entirely new approach because of a significant change in underlying technologies.