Re: [Maxima-discuss] Solving equation step by step

[Richard F. <fa...@gm...>]

There are a couple of approaches to something that might look like what you
are asking about,
but most of them don't work very well.

As Barton says, you can make Maxima very dumb -- a poor typesetting program
-- and try to
guide it with commands. This doesn't "show steps" of the internal program,
really.
 You might guess some steps.
But the steps Maxima takes are not the ones you generally teach students,
so explaining those
steps is generally a loser.
 For instance,  Maxima will convert your problem statement to a canonical
form by executing
addition and multiplication in a polynomial ring or a field of rational
functions. Then apply
algorithms using programs polynomial factorization in a finite field.

Another way, tried in the past, to see if students are on the right track
in solving a problem:

Student types in his/her "new equation" which is the result of some
transformation, and
the program sees if that still has the same solution. In which case it
might be right.  At least
if the student has typed in something that doesn't have the same solution,
it is not
a correct step.

In general this is an obvious loser because it mostly tests the student's
typing ability and
observation of correct syntax of the computer system.  Not a worthwhile use
of student or
teacher time, or a life skill worth attaining.

Or you could have a user interface that allows pointing or lassoing
subexpressions and moving
them around.  Another skill that is hardly worthwhile, and I think the main
reason we even
talk about it is that it is an easily-specified and fun implementation
project for
user-interface fans who want to use tablets, styluses, fingers, and even
speech.
(Alexa, subtract four times eks from both sides of that equation).

Tangential comment..
In teaching a computer algebra system related "lab" to a calculus class,
using Macsyma (c. 1972)
the students were far more interested in how the program actually did
integrals than some kind of
animation attempting to mimic their own heuristic and hand-wavy "methods" as
written in the textbook.  So I taught a little about rational function
integration and the Risch
"algorithm".  But these were students at MIT, so maybe not a common
reaction.  Most
calculus students just want to get a passing grade and then forget the
whole thing.

Good luck
RJF




On Mon, Jul 3, 2023 at 4:04 AM Barton Willis via Maxima-discuss <
max...@li...> wrote:

>
> Maxima's automatic simplifications make it challenging to show these steps
> at the level you wanted. I've shown my best effort, but maybe somebody will
> give you a more complete answer by setting the option variable* simp *to
> false. Setting this option variable to false suppresses automatic
> simplifications, but doing so can make many things not work correctly.
>
> As a math teacher myself, I find Maxima to be quite useful for many tasks.
>
> (%i1) 3+4*(x+2)=5+6*(3+x);
> (%o1) 4*(x+2)+3=6*(x+3)+5
>
>  Steps 1 and 2 Simplifying brackets 3+4x+8=5+18+6x & Simplifying both
> sides 4x+11=6x+23
>
> (%i2) expand(%);
> (%o2) 4*x+11=6*x+23
>
> Step 3:  Rearranging terms with/without variable 4x-6x=23-11
>
> (%i3) %-6*x - 11;
> (%o3) -2*x=12
>
> Steps 4,5, and 6:
>
> (%i4) %/-2;
> (%o4) x=-6
>
> Please let us know if you all have questions or comments about Maxima.
> Again, maybe somebody else will give you a better answer.
>
> --Barton
> ------------------------------
> *From:* jonas mees <jon...@ho...>
> *Sent:* Sunday, July 2, 2023 16:10
> *To:* max...@li... <
> max...@li...>
> *Subject:* [Maxima-discuss] Solving equation step by step
>
> Non-NU Email
> ------------------------------
>
> I am a high school math teacher and want to be able to compare the
> different steps of a solution with my students answers.
>
>
>
> Example equation:
>
> 3+4(x+2)=5+6(3+x)
>
>
>
> Step1: Simplifying brackets 3+4x+8=5+18+6x
>
> Step2: Simplifying both sides 4x+11=6x+23
>
> Step3: Rearranging terms with/without variable 4x-6x=23-11
>
> Step4: simplifying -2x=12
>
> Step5: rearrange factor x=12/-2
>
> Step6: simplify x=-6
>
>
>
> Any help with this is much appreciated.
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