Friday, June 19, 2009

Matrices of the general connectivist model of distance learning

Roel Cantada

The matrices of the general connectivist model of distance learning are composed of a 3-mode matrix and three 1-mode square matrices.

The 3-mode matrix is made up of the following 2-mode matrices:

  1. actor x learning environment
  2. actor x concept
  3. learning environment x concept
The 1-mode square matrices are:

  1. actor x actor
  2. learning environment x learning environment
  3. concept x concept
Since this is a signed network, these ties could take on negative values as well.

The network model can also factor attribute data with vectors (i.e. n x 1 matrices) that could be vizualized as partitions or sizes of nodes. These are represented in the graph as node properties in general. For example if the actor mode is made up of groups of students engaged in collaborative learning, then the individual students can be partitioned into their groups. There would be a vector of group numbers.

With this model, we can ask a lot of testable questions like, is there a correlation between the change in actor x learning environment ties with the change in the actor x concept ties? What is the probability that y can be known given x sub 1, x sub 2, x sub 3 ... x sub n precedent?

We can compare a learning network centered on an LMS with one centered on a wiki. We can compare the density or average degree of the personal network of one student with another. We could trace paths from start of the course to the end i.e. when goals are achieved, and compare the paths taken by different students to identify the most efficient path.

We can diagnose a misunderstanding by comparing concept networks, or using bayesian network analysis to seek factors that may have contributed to mistakes. We can prescribe better paths, better nodes based on adaptive techniques. User modeling can reside in the concept mode while the mechanisms will reside in the learning environment.

And we can ask all or one of these questions in the model and see the effect of it to the entire network. It is a holistic analysis.

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