[extropy-chat] Maths ability

[Herb Martin]

> -----Original Message-----
> From: extropy-chat-bounces at lists.extropy.org 
> [mailto:extropy-chat-bounces at lists.extropy.org] On Behalf Of 
> Samantha Atkins
> Sent: Sunday, March 05, 2006 8:51 PM
> To: ExI chat list
> Subject: Re: [extropy-chat] Maths ability
> 
> I could be wrong but I think there are times when kid's brains seize  
> up over something new to learn that somehow goes against the grain.   
> For me it was "imaginary numbers".  I was really good at math (the  
> more abstract the better) but my brain rebelled that any of my  
> blessed numbers could be "imaginary".  I had to do some serious on  
> the spot meditation/psychological rewiring to get past this seizing  
> up.  I somehow knew that if I did not that I wouldn't trust 
> math ever  
> again or my ability to understand it.  It was real work to get past  
> that little brain glitch.  

I know that the above is an example and not a
direct request for sources on Complex Numbers,
but since I am currently reading Penrose's
"The Road to Reality:..." and preparing to take
the GRE Mathematics subject exam I recently found
a DELIGHTFUL book:

	"Visual Complex Analysis"

This book is very readable by anyone who either
wants to know about complex numbers, or who has
ever learned about them and perhaps forgotten.

It is readable due largely to several elements of
the author's style:  teaching through reference
to pictures and using both geometric and complex
analysis to explain both the pictures and the 
solutions, along with a goal to have a conversation
with the reader -- to make the reader feel as if
one were having a conversation with a friend who
is knowledgable, patience, helpful, and somewhat
delighted by the beauty of the math.

> I suspect that a lot of people hit those  
> in various subjects and never get past them.

You are certainly correct.  The most common such
glitch for young students is when they are
'taught' "long division" before being required to
learn the multiplication tables.

"Long division" is not really about division, so
much as it is multiplication and subtraction: a
guess is made, a multiplication is performed,
followed by subtraction -- if the term is suitable
the process continues, else a new guess is 
substituted and the previous step repeated.

Children who don't KNOW those multiplication tables
are constantly (until they give up) trying to guess
where all these "magic numbers" originate.

Generally this happens (in the US) in the 3-4 grade
and those children who fall prey to such terrible
teaching (by parents or teachers, but the fault lies
with the adults not the students) typically believe
themselves "bad at math" -- usually for life.

There are certainly other points of failure, but this
is likely the one that accounts for the largest 
group of people who honestly believe they are "bad at
math."

--
Herb Martin