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The Teacher's Role

November 2, 2018

Author: Bianca Yang
Email: ipacifics@gmail.com

This post is related to my previous post about the therapist’s role.

In the end of my previous post, I introduced a mechanism for teaching:

[I]n every situation where transfer of information results in a light bulb going off, the information giver’s responsibility was to set up the information receiver to flip the switch themselves.

As someone once described it on Hackernews, the teacher’s responsibility is to set up the student such that his pull function will work when the teacher pushes.

Learning is a highly individual process precisely because of the mechanism I just described above. Each person’s pull will work in different situations. The different situation may be triggered by time. A younger you may not understand what you understand now. A different situation could be learning environment. Trying to read Shakespeare on a car when you’re prone to car-sickness is harder than trying to understand it when stationary. A different situation could be the teacher. Trying to understand a teacher who writes up a bunch of formulas and waits for you to discover the connection between them is harder than understanding a teacher who walks you through the nontrivial foundational steps that define the transitions and relationships between formulas.

That is why it is so important to understand what you are missing when you try execute a pull and you fail. If you want a teacher, it is important to find someone who can identify what waypoints you are missing and build them such that you can make the necessary connections. If you want to be a teacher, you must develop this ability to understand waypoints and how to build them such that people can draw paths between a starting foundation of knowledge to a target base of new knowledge.

Now I want to flesh out this theory of waypoints, or stepping stones. In order to build knowledge, you must have an appropriate path to follow. You also have a radius of understanding for each topic. Let us say that you are trying to understand calculus from algebra. You should have a good understand of variables and symbolic manipulation, but you will need to move more carefully to understand limits, which underlie calculus. What we can say is that you have a wide field of view when performing symbolic calculations but a narrow field of view when reasoning about limits. Thus, in order to traverse the nonphysical world of mathematics from algebra to calculus, you will need to take many, small steps across many, small stepping stones (or bypass many waypoints that are close together) to reach your destination.

When a teacher goes too slowly, that means they are consistently stepping within your radius of understanding. When a teacher goes too fast, that means they have consistently stepped outside of your radius of understanding without placing the appropriate stepping stones to guide you to a new position of understanding. Points on the frontier of your level of understanding are things that you should be able to create your own waypoints to. Stepping consistently on the frontier and giving you time to build waypoints of understanding should be within your competency. Repeatedly stepping outside your radius then coming back to build waypoints should also be within your flow.

As a teacher, your responsibility is to determine each student’s radius and set of waypoints such that you can effectively build connections between their current set of waypoints to a new set of waypoints. A good teacher should be able to construct multiple paths between the current set of waypoints to a new set of waypoints, with each path representing a new way of understanding a concept.

As a student, your responsibility is to improve the speed at which you can build waypoints, to strengthen existing waypoints, and to build new connections between waypoints. One excellent example of building new connections or of strengthening existing waypoints is in Eric Jang’s excellent post on Dijkstra’s in Disguise. For some people who already knew the connections between shortest path finding and Q-learning and ray-tracing, this post helps reinforce those connections. For those who didn’t already have these connections, this serves to build new connections and create robustness in their knowledge graphs. The more ways you can explain and understand a concept, the better you understand it.

I hope this post explained a useful way to understand teaching (and it’s dual, learning) and to improve at it. I welcome feedback through email.