Path: utzoo!utgpu!water!watmath!clyde!rutgers!umd5!brl-adm!husc6!bbn!gatech!ukma!mtbb34
From: mtbb34@ms.uky.edu (Becky McEllistrem)
Newsgroups: comp.edu
Subject: Re: Learning arithmetic
Message-ID: <8421@g.ms.uky.edu>
Date: 22 Feb 88 04:22:10 GMT
References: <26@dogie.edu> <3340@killer.UUCP> <660@cresswell.quintus.UUCP> <4497@garfield.UUCP>
Reply-To: mtbb34@ms.uky.edu (Becky McEllistrem)
Organization: University of Kentucky, Lexington, Ky.
Lines: 85

In article <4497@garfield.UUCP> martyn@garfield.UUCP (Martyn Quigley) writes:
>In article <660@cresswell.quintus.UUCP> ok@quintus.UUCP (Richard A. O'Keefe) 
>writes:
>
>>operator is.  Talk about *boring*.  Talk about *remote* from the interests
>>of the children.

GGGGGrrrrrrrrrr... you're hitting a sore spot with me in this discussion so
sorry if it becomes a flame, it certainly wasn't meant to be...

   Boring is 1) in the eye of the beholder (most ed majors find computers
      boring too)

         and 2) is dependent on how well the teacher presents the subject....
          if you were bored, then he/she presented it wrongly.
>old "boring" stuff.
>
>
>One reason so many people are weak in mathematics is that as it was taught 
>to them, it was NOT related to their prior experiences.  Hands up everyone

      I'm not sure I understand this statement... Math word problems were
   constantly related to concrete experi  There was nothing involving  games
   or different drill "boards" or concrete ways of INTRODUCING the subject.

   Merely: this is how it's done, because I SAID so and WHY was not something
   a student was to worry about.

 My experience
>of teaching mathematics majors is that none of them taught in this way can tell
>me where to find a group in "the real world", what a group IS, or what it is
>used for.  Ask the nearest mathematics student what an eigenvector has to do
>with his/her/its reflection in a mirror.

And what do you do to help these students... I hope the classes at your math
 education department aren't pure lectures, because that's WHY they don't
have an UNDERSTANDING of these subjects

>
>To paraphrase Piaget, teaching a child something it has not already met in the
>course of its spontaneous development is a waste of time.  You cannot teach a
>concept from a definition.

   I agree with this.  Any classes I've taught so far (and I'm not certified
  yet, but working on it) have gone much smoother, if I use a process-oriented
  curriculum rather than a lecture-teacher-oriented curriculum.  The new math
 would have gone, I think if the students understood WHAT they were doing...
 and that's easier to bring across in a process oriented curriculum...
 
>
>>I think we need three things in elementary arithmetic teaching:
>>	principles:	"This is WHY the addition algorithm works."

    And do you lecture that why or show them that why? Do you cut a square
   to prove two triangles make a square or do you give them some big formula
   that they won't remember?

>
>So why does it?  My experience (as a teacher trainer) is that relatively few 
>elementary teachers know how it works.  As for multiplication or division...

      Tell me about it...

>
>Drills are appropriate if what you want is high performance in a specific task
>such as in piano playing, figure skating or mental arithmetic.  However if
>what you want is the ability to solve problems, then what you give is a lot of
>problems, which, by definition, are not amenable to solution by routine
>methods.

   Sigh, this is just what I'm working against in response to this article...
  What's the use of the drills if they don't understand what's happening 
  BEHIND the process?!!!


                   Becky

P.S. Sorry again if this irritated someone, it wasn't meant to be  a personal
  flame...

-- 
--  "I ALways push the doors marked pull!"- (I don't know who said that.)
--  Becky McEllistrem  (Tadger)
--  mtbb34@ms.uky.edu, mtbb34@ukma.bitnet, {rutgers,uunet,cbosgd}!ukma!mtbb34
--  University of Kentucky in Lexington Kentucky, USA