

Definitions, Definitions, Do We Need Them? - profquail
http://rjlipton.wordpress.com/2010/01/23/definitions-definitions-do-we-need-them/

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nzmsv
Definitions are useful for experts in a field. It is much faster to just refer
to a concept by its name rather than explaining it every time.

Unfortunately, definitions are a terrible thing for students. Even more
unfortunately, most books are written in the following style:

1\. Here's a paragraph-long definition that makes no sense to you at this
point.

2\. Here's a proof of this thing you don't yet understand.

3\. Oh, you want to practice? Here's an example problem and a solution. When
you see a problem like this one, plug numbers into this formula in the bold
box.

4\. A bunch more problems to try plugging numbers into yourself.

5\. The discussion on what this thing is actually useful for is outside the
scope of this book. Read about that somewhere else.

The best teachers actually explain how the thing they are teaching works. They
start with a limited concept the student can understand, and then refine it to
make it more formal. Good textbooks do this too. The bad ones start with the
definition in a box.

The problem is that by the time a professor writes a textbook, this stuff is
second nature to them. The prof is an expert. So he/she starts with the
definition, since that is how the professor commonly communicates this
concept. The book then ends up looking like the author is trying to make
him/herself look smart at the expense of the reader. Writing an accessible
book is a rare talent.

Wow this turned into a long rant :)

