The importance of detecting the wave front in a knowledge network
For a teacher to be effective at teaching there is one key thing that she needs to get right: Detecting the specific position of the wave front within the network of knowledge of his students.
The knowledge of a student can be thought of as some kind of network. Initially the student does not know anything. As he learns, he starts developing some quanta of knowledge. Such quanta of knowledge are all being linked together by prerequisite relationships that might indicate how you get from one quantum to another. Maybe these relationships are generalisation links, specification links or combination links. The knowledge of a student can be thought of as such kind of network. The current knowledge of the student can be thought of as a wave front in such a network. Knowledge increase will increase/ push out the radius of said wave front.
The must important thing to realise while teaching is that without knowing the exact position of the wave front in relation to the knowledge network it is not possible to do an effective job.
Here is why:
- If the student makes a mistake (m1) way behind the wave front the teacher can simply remind the student of something he certainly knows, but might have just overlooked or forgotten.
- In another case the students makes a mistake (m2) that is depended on a piece of knowledge way after his wave front the teacher can simply tell him to worry about this later since the knowledge to understand it is not yet there.
- Now what about a mistake (m3) at the wave front. That is the learning moment! This is the moment the teacher can push the wave front further out because everything is in place to learn the new stuff at the next radius. So if the teacher understands that the student just made a mistake at his particular wave front (current/initial knowledge) that is where the teaching moment happens. This is where a teacher explains something.