From: choy@skorpio.usask.ca (I am a terminator.)
Newsgroups: k12.ed.math
Subject: Re: CALCULATORS IN SCHOOL
Date: 25 Jan 1993 17:48:25 GMT
Organization: University of Saskatchewan, Saskatoon, Canada
Distribution: world
NNTP-Posting-Host: skorpio.usask.ca

In article <40924.2B615DB4@puddle.fidonet.org>, Sheila.King@f315.n103.z1.fidonet.org (Sheila King) writes:
|> Dear Christina,
|> 
|> In your message to Brian Bridal you said:
|> 
|> -> I am in Year 5 in Blackalls Public School and I do not
|> -> agree with having calculators out all the time in class.
|> -> They are a help sometimes but the let silly kids be lazy
|> -> and not use their brains.
|> -> My dad teaches too. In some classes, he gives rewards to
|> -> kids who don't use calculators. Some kids end up faster
|> -> without them.
|> 
|> I am glad to see a student such as yourself with such a fine outlook. It
|> seems to me that you understand just what calculators are. As you say,
|> "sometimes a help", but certainly not necessary at all times.

My opinion of calculators is that they are not a problem. I think that
people who understand a math concept do not lose by using a calculator.
Math is a part of computation so it may be natural to move from
calculators to programming.

Students may be lazy by not bothering to learn concepts or by not
bothering to check their work. (They just want to get by "pulling
Homers" (Homer Simpson).) I got 100% on 2 of my algebra finals
because I bothered to stay and check things over. The grade 9 was
nearly 10 years ago, but I remember everyone leaving after 1.5 hours
of the 2 hour exam. One guy who typically got 95% to 100% on the
end-of-chapter quizzes hurried up and left after 1 hr. That's when I
started to go over it again for the first time. I figured to double
check the whole thing after I'd corrected my last mistake. I found
a mistake. Correction. Check remaining answers. Double check restarted.
Everyone else is nearly gone. Some more checking and the supervisor
tells me to hand it in at the office when the time's up. Supervisor
leaves. Another mistake. Correct and check remaining answers. Double
check restarted. No mistakes. One more look with about 10 min to go.
No mistakes. Period.

Within a day or so, my teacher tells me that I got 100. He thought
I'd made a mistake because one of my answers didn't match his, but he
found that everyone was making the same mistake. It was really
the teacher's mistake! When the pressure's off, people don't check
things over, and they can mess up.

The technology of my high school days was such that I didn't shop
for a calculator until I got sick of interpolating trigonometric tables
to the 4th decimal place.

Students need to appreciate and love math and logical thinking. I'm
afraid they don't see such work at the most rigorous levels. My geometry
teacher likes to get into such stuff but he didn't really strain himself
and I never bothered to satisfy my curiosity. But consider the proof
of the theorem "every set is equal to itself". Here's a sample:

Assumptions   Statements                               Reasons

1             1. (x)(y)(x=y<->(z)(zix<->ziy))          Definition of =
1             2. (y)(a=y<->(z)(zia<->ziy))             UE 1
1             3. a=a<->(z)(zia<->zia)                  UE 2
1             4. (z)(zia<->zia)->a=a                   &E 3
5             5. bia                                   A
              6. bia->bia                              CP 5,5
              7. bia<->bia                             &I 6,6
              8. (z)(zia<->zia)                        UI 7
1             9. a=a                                   MP 8,4
1             10. (x)(x=x)                             UI 9

There are a few rules of inference that can be used to prove anything
that's provable. They can be found in any introductory book to logic.

Warning: proofs can get scary. The last theorem I've proven (with some
legitimate shortcuts) after ~30 hr of work runs 59 pages. People should
not occupy themselves with all the fine details of proofs, but they should
know what they can do (as a very last resort) if things just don't work
out. We can quickly probe the depths of knowledge with informal reasoning
and slowly catch up with formal reasoning.

Bet you can't see this stuff on a calculator! WRONG! For the last 5 years
I've been beating up my not so trusty HP28S (I've dropped it too many
times), which can handle symbolic computing. I haven't been keeping up
with calculator prices because I don't go into numerical calculations a
lot, but I think high school students may afford one. It can get them
kickstarted into new thinking. It really disciplines a person to do
fractal programming on a 4 line 32 character display.

-- 

Henry Choy
choy@cs.usask.ca

What rolls down stairs alone or in pairs            This has been brought to 
Rolls over your neighbor's dog?                     you by the numbers 4
What's great for a snack and fits on your back?     and 9 and the letter P.
It's Log, Log, Log!  -- "The Log Song", from            -- Big Bird
                         Ren & Stimpy

Math is tough!       -- Barbie