The knowledge of academic subjects like mathematics, science, history, and literature is self-organizing when it is open online. As we have put knowledge openly online over the past decade, it has organized itself into its cognitive relationships within the web’s network structure because the knowledge itself is a network. Looking at the image with this post, we can imagine it as a network of the subject of mathematics, with basic number laws clustered in the center, geometry and algebra forming adjacent clusters (with their interconnections), calculus, trigonometry and the other math topics grouped toward the edges and interconnected to complete the patterns.
The two ways today’s smartphones offer mathematics to learn are:
- 1) apps, like the one suggested in the red circle — isolated from related online math materials and confined to the smartphone into which it has been downloaded
- 2) the entire open mathematically network on the web. At this point the apps are usually slicker, but the presentation from the web on mobile phones improves steadily.
The image with this post is a scan from Analysis of Biological Networks (Junker and Schreiber, 2008). It depicts, as the caption explains, an example of a biological network, and is based on the data set from DIP for interaction of human proteins. The authors introduce their chapter on “Networks in Biology” by explaining that biology looks at systems at levels from molecular, to cells, to tissues, to organs, to organisms to phylogenetic relationships — and that:
At all these levels of detail, relationships between the elements are of great interest. These relationships can be described as networks, in which the elements are the vertices (nodes, points) and the relationships are the edges (arcs, lines …). (p. 3)
Individual apps downloaded into a student’s smartphone can have tutorial value. Nothing wrong with that. However, the increasingly fast and compelling mobile access to the internet is where cognitive relationships and context will form the arena of future learning. The apps can come through the internet too, but only the internet will provide the relationships that underly knowledge.