The vision proposed by Stephen Downes …
Hence, in connectivism, there is no real concept of transferring knowledge, making knowledge, or building knowledge. Rather, the activities we undertake when we conduct practices in order to learn are more like growing or developing ourselves and our society in certain (connected) ways.
and by George Siemens
Connections create meaning
explain all my learning experience. Just an example.
As a students in Physics I got A in a course based on the Fourier Transform, a basic, wonderful and ubiquitous mathematical instrument.
Later on, when working on my thesis I was glad to see that the Fourier Transform was needed to work with digital medical images: “Finally, I can use something of that I have studied!” I thought.
It was a shock when I discovered that the (scholastic) knowledge of the theorems and the related demonstrations, of the Fourier Transform was almost useless: I missed completely the basic concept.
Successively, I realized that I missed a lot of connections and that without those connections the idea of Fourier Transform (together with the theorems and the demonstrations) was just an asteroid lost in the space of all the possibilities.
I missed even the more general concept of mathematical transformation.
I missed the essence of mathematics, despite my former good grades.
Probably, from my teachers point of view, knowledge of the Fourier Transform was successfully transferred in my mind but in my later experience I began to realize its essence and usefulness only when trying to find connections in a real context in order to solve a real problem that I strived to solve. I began to feel comprehension just waiting in face of my problem and letting connections come out, spontaneously. This part of my understanding was absolutely spontaneous, it had to grow. It took time.
Afterwards, I was able to look at this mathematical device as at a wonderful toy useful to describe an incredible number of phenomena. I was also able to see the beauty of symmetries and how the perception of such symmetries were useful to find other new connections.
The propositional knowledge of the Fourier Transform is partial and by no ways sufficient to use it in real life. A more effective knowledge, and a never thorough one, needs a system of connections with other concepts, some abstract and some real, and this system of connections can obly grow in your mind because you have to experience it.