Re: [Phys-l] Should equation solving be done with calculators and robots or by hand?

[Steve Highland <shighlan@uslink.net>]

I think my earlier posts may have given the impression that I want to go too
far in reducing algebra manipulations in physics problem solving.  My goal
is to make better use of robots to take care of 'chore' sorts of tasks that
steal attention and time that I think could be better devoted to expressing
physical reasoning in words and interpreting the *meaning* of answers.

Piles of algebra just aren't what I'm looking for in solutions to physics
problems.  That seems to be what a lot of students crank out, though.  I
want language instead.

> Joel Rauber wrote in part:

> As an example, I think it is worthwhile for students when they first
> learn about matrix inverses to have to compute a bunch of inverses by
> hand. Certainly 2x2's and 3x3's if not a few 4x4's, and maybe try to
> find the inverse of some non-invertible matrices.
>
> If all you have ever done is hit the matrix inverse button , you will
> miss some real understanding regarding linear algebra and matrix
> mathematics and understanding regarding elementary row and column
> operations.
I like your matrix inverse example but I think the main benefit to doing a
matrix inverse by hand is just to get a feel for how much labor you save by
having it done for you by a machine.  I don't see how doing the elementary
row operations teaches anything very deep.  (Maybe I'm missing something?)

How about the quadratic formula?  Does using the quadratic formula by hand
in a projectile problem teach the physics better than using an equation
solver? I don't see any advantage to doing it by hand.  Using an equation
solver saves time and reduces errors.

Would anyone argue that today's students should learn how to interpolate
values between entries in tables of trig functions like I was taught when I
was a kid?  Calculators have made that totally obsolete.  Why shouldn't more
powerful calculators make these other chores obsolete as well?


> | I've noticed the math
> | > department at our university is beginning to be less enamored with
> | > graphing calculators and using them for teaching the algebra and
> | > calculus classes.  I think this is happening for a reason.
> | 
> | What is this reason?
> | 
> I can only speculate, but I think it is because they felt that less
> understanding of the material was happening.
I'd like to know more about this if possible.  I can imagine other reasons,
especially of the 'technoglitch' sort.  One can burn up a lot of time trying
to track down typing or keystroke errors when one or two students' machines
don't seem to be doing what all the others are.  Making everyone wait while
trying to figure it out can be a big headache for all involved.

Learning all the ins and outs of a piece of technology takes quite a long
while.  I've seen things go wrong that I've never been able to figure out.
> _________________
>
>
> On a related note, I don't like the way that a lot of newer calculators
> work, for example, some of the newer "algebraic" calculators take trig
> functions by the sequence hit sin -> open paren-> number-> close paren.
> presumably in order to make the entry look like how you see it in the
> textbook.

> For older calculators the sequence is enter number -> hit the sin
> button.  This is preferable, IMO, as it reinforces the idea that sin is
> a function (or mapping) or an operator that acts on an input to give an
> output.  (Not to mention that it involves less key strokes).

I thought this change had something to do with maintaining the correct
hierarchy of operations but maybe I'm wrong about that.

Proper use of parentheses is a huge problem for students, whether they use
robots or not.  I think this needs a lot more attention in their algebra
courses.


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