\chapter{Explicitness and Structure}

When teaching, make key points, steps and techniques explicit.
- make points explicit

also, make *approaches* explicit.
Explain what you're doing.
If you're using some philosophy of teaching,
*say so*, and indicate it:
let students understand *how you are teaching*

\section{Explicit}
- highlight key ideas
- techniques
  when use a technique, don't just use it,
  *state that this is a technique*
[EG, if teaching a 1st rigorous course,
 don't just prove the contrapositive:
 say that you're doing so and that it's a useful technique,
 esp. in XYZ circumstances.]

\section{Structure}
mneumonic
people will structure it anyway;
you're providing them with a structure.

Ideally, material and structure should work together.
In practice, material often doesn't have very coherent structure:
there are key themes, but many auxiliary ideas that don't fit.

How to deal with this?
- You can twist material to fit structure (ugh)
- Omit material that doesn't fit
- Include material that doesn't fit,
  and accept that it'll be lost a bit more

\section{Why don't people teach like this?}

b/c it requires work and introspection

It requires not only mastery and understanding of the material,
but \emph{explicit} understanding and introspection.

people generally teach by demonstration,
and students learn by imitation

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\section{Objections}

``All these explicit points are overwhelming, and should be omitted.''

Then the material is overwhelming.

Frequently teachers say that slowing down and covering material more
thoroughly is both more enjoyable (for themselves and students) and yields
better understanding.

That said, I believe that explicitness makes learning so much easier that
one can generally proceed at the same pace or even faster.
If points are omitted, students don't understand the material
and the pace of learning slows down: you can't build on poor foundations.


There is nothing wrong with covering material in little depth
\emph{if you do not require greater depth}.
(However, rushing b/c want to cram doesn't work.)

Pithily, ``the journey is the destination'': the value of a course
is frequently not the big result at the end,
but learning the field.
