Re: [MLUG - DISCUSSION] beginner slide rule wanted

[Michael <EMAIL:PROTECTED>]

I never used a sliderule (though I've seen others do so) but I can do 
most basic problems quicker in my head than on a calculator. I usually 
can't tell you how I arrived at my answer though.. which means I have a 
great deal of trouble at most math classes. I can't step by step through 
a problem as is usually required.

As young as fifth grade I remember getting in trouble for making up my 
own methods for solving problems. I was acussed of cheating, my parents 
called in, etc. Major bummer. I never grokked math classes either. I 
need to know why something works to really understand it.. just telling 
me the steps without explanation doesn't work for me. Having so many 
teachers unable and/or unwilling to explain why to me was never a help. 
I can't follow steps I don't understand. No doubt one reason I'm one of 
the geeks that have to understand computers from the hardware up. :)

Oh well. I've always grokked string and array style data better than 
numbers anyway. :)

> Is this different than it used to be?  Sure, people like you and me can
> immediately say approximately what 23704 x 3864 is, and we could do that
> back when we were teenagers, but most people can't do that, and most
> people couldn't do that when we were teenagers.  Psychology students can't
> do that kind of computation now, and they couldn't do it 25 years ago
> either.
>
> Here's what I think - and this is a really important idea that should be
> considered widely.  I'm sure you'll agree.  We need to teach kids to do
> this kind of in-the-head arithmetic.  We should cut way back on the
> traditional arithmetic problems and focus on approximation.  When we need
> the right answer, we don't do it by hand, so why teach kids to approach
> problems that way?  How do we make changes in our school systems so that
> arithmetic can emphasize approximation?
> 
> For one, we should be teaching kids to add columns of numbers from left to
> right, not right to left.  Same for multiplication of pairs of large
> numbers.  Long division is good as it is, I guess.  What else?
> 
> How can we make this really happen?
> 
> 
> 
>>So every year I walk students through the Tower of Hanoi Problem with a
>>small number of disks, establish that the number of moves it takes for
>>the n disk problem is 2^n - 1, and then ask for people to guess how long
>>the 64 disk problem takes if you can do 1 move per second.
> 
> 
> I do it as (2^10)^6 * 2^4 which more than 16*(10^3)^6 = 1.6*10^19 seconds.
> But how long is that?  There are 3600 seconds per hour and 24 hours per
> day so there are about 8.6*10^5 seconds per day and about 3.7*8.6*10^7 or
> 3.2*10^8 seconds per year.  So that means (1.6/3.2)*10^(19-8) = 5 x 10^10
> days to solve.  That is 50 billion.
> 
> 
>>The modal guess is usually off by a factor of 50 billion or so.  I
>>submit that an error anywhere near this large would never happen to
>>anybody who knew how to use a slide rule.
> 
> 
> Is that because they usually say that it will take one full year?  It
> isn't an easy inside-the-head kind of problem.  I would struggle to get a
> good answer and I'm pretty good at that kind of thing.
> 
> 
> 
>>That's not to say that I think a slide rule is the only way to learn
>>about how to do stuff like this, just that it is *a* way, and it's not
>>clear to me that many better ways have come down the pike since the 70s.
> 
> 
> Well, you have to think about the basis for slide rule calculation:  It's
> the sort of thing I was doing above:  Using engineering number notation
> (is that what they call it) where we use things like 3.65 x 10^2 instead
> of 365.  Make students do this a lot and you'll be most of the way there.
> 
> Give them a lot of multiplication problems that look like this:
> 
> 1.3 x 7.2 =
> 
> 8.4 x 3.9 =
> 
> Make them give only two significant digits and make them do it in their
> heads.  We can teach them to do this and it will be worth it.  They can
> use it in almost any occupation.  They can even use it when grocery
> shopping.

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