Date: Mar 21, 2013 4:52 PM
Author: Kaba
Subject: Re: Maths pedagaogy

21.3.2013 22:06, fom wrote:
> On 3/21/2013 2:54 PM, Jesse F. Hughes wrote:
>> Shmuel (Seymour J.) Metz <> writes:

>>>> An unfortunate example is Lang's Algebra, where everything is
>>>> obvious, easy and trivial.

>>> Assertion contrary to fact.

>> I certainly recall Lang's Algebra as being chock-full of the terms
>> "obvious", "easy" and "trivial", and very often these proofs were not
>> easy for me. But I was young and ignorant back then, and I'm no
>> longer young.

> But the question will be this: Do you now
> agree with the assertions of "obvious", "easy",
> and "trivial" after having corrected those
> problems of youth?

The educational value of a book should be judged exactly from that state
of ignorance. The (reasonable) student is the validator of the teacher's
mental model over what is good representation and what is not. A teacher
who acts against validation ("who knows best") is not in touch with
reality and tends to get unhappy students.

It is the nature of information that in short time the student surpasses
his teacher in the student's own narrow field of expertise. Furthermore,
the readers's collective knowledge does this for every page of the book.
This is the perspective from which one should approach writing; you need
to keep improving in your writing (your mental model) until what you get
are throughoutly happy readers.

When you come back to a book long after mastering the content, it is not
the same book anymore. It is merely some writing that aids you to recall
what you already know. The book then becomes a reference. In practice
this means you won't be looking at proofs anymore, or spending much time
with the book itself. What you do instead is to look up some small
details. Judging the book now for its educational merits is too late.