Re: [WWdevel] interval_cmp

[Davide P. C. <dp...@un...>]

> In a calculus problem, I want students to find critical points and  
> indicate if they correspond to maxima, minima, or neither.  And I  
> don't want to give away in advance how many points there are.  So I  
> was trying to coerce interval_cmp to do this for me by having it  
> evaluate a set of "intervals," viz.,
>   interval_cmp( "(-2,min),(3,max)", 'unions'=>'no',
> 		'strings'=>['none','min','max','neither'] );

I'm not sure why you are using interval_cmp for this when you could  
use the List object directly.  E.g.,

	Context("Numeric")->strings->add(none=>{},min=>{},max=>{},neither=>{});
	ANS(List("(-2,min),(3,max)")->cmp);

There's really no need to mislabel this as an interval check when it  
isn't.  You are really checking for a list of lists, which is just  
what List() is designed for.  (I agree with John that the semantics  
of the traditional answer checkers are more direct, but the Parser  
versions do allow more flexibility, when it is needed.)

> This works very well, until there is no maximum (or no minimum), in  
> which case
>   interval_cmp( "(-2,min)", 'unions'=>'no',
> 		'strings'=>['none','min','max','neither'] );
> has trouble: as student entering (-2,min) has her/his answer marked  
> wrong with the message "The parentheses for your list should be  
> removed."

I was not able to reproduce this.  Are you using current versions of  
all the Parser files?  (In particular lib/Value/AnswerChecker.pm)

In any case, there was a problem dealing with this that I have fixed,  
so you should get the AnswerChecker.pm that I have just added to teh  
CVS archive.  The issue is that when a student types a list like  
"(1,max)" it is not clear if they mean the list containing two items,  
1 and "max", or the list containing one item, the list "1,max".  The  
default had been the former, which is probably a bad choice, since  
that turns out to be rarely what is intended.  I have changed the  
answer checker to use the latter, and added a flag to allow the  
former behavior in those cases where it is desired.  This should not  
adversely effect existing usages, as it only happens when the student  
explicitly includes the parens.  Anyway, that should clear up your  
problem whether you use interval_cmp or the List object directly.

>  1. Have I overlooked a better way of checking this type of problem?

I think using List() directly makes more sense.

>  2. Is there some feature of interval_cmp that I can change to get  
> a more
>     intuitive (at least from the perspective of a student) behavior?

I think my change to the list checker will take care of this.

>  3. Is there an easy tweak to interval_cmp that will have the same  
> effect?

No need at this point.

> I also have a problem where I want to check the answer "(0,min), 
> (a,max)", where a is a constant.  My rather coarse solution was to  
> copy the interval_cmp evaluator into the problem, calling it  
> my_interval_cmp, and add the variable 'a' to the Parser Context.   
> Is there a better way of doing this?

There wasn't a way using interval_cmp, so I added new "var" and  
"vars" flags that allow you to do

	interval_cmp("(0,min),(a,max)",var=>'a');

One of the problems with using this approach is that the warning  
messages will now say that you are looking for a formula rather than  
a constant.  but in your case, since the items in your list are  
themselves lists, you should not get any type mismatch errors (since  
lists can be practically anything).  The Parser doesn't know what the  
legitimate values for your list are, so can't issue warnings when the  
student types something different.

If you want to provide more meaningful error messages, you can supply  
your own type checker as follows:

	Context("Numeric")->strings->are(none=>{},max=>{},min=>{},neither=>{});
         Context()->variables->add(a=>'Real');

	ANS(List("(0,max),(a,max)")->cmp(
	  typeMatch => sub {
	    my $student = shift;
	    return 0 unless $student->type eq 'List' && $student->length == 2;
	    my ($x,$t) = $student->value;
	    return ($x->type eq 'Number' && $x->class ne 'Formula') && $t- 
 >type eq 'String';
	  },
	  entry_type=>"a critical-point specification",
	));

	$showPartialCorrectAnswers = 1;

This overrides the type checker and supplies your own that checks  
that the student answer is a list of the desired form (a number  
followed by a string value).  The list checker will call this on each  
answer, and will report an error if the result is zero (or false).  I  
also supply an entry_type string that will be part of the messages.   
You will get messages like "Your first critical-point specification  
is incorrect" and "Your first value doesn't look like a critical- 
point specification (it looks like a ...)" in the situations where  
these apply.

A more complicated approach would be to define your own Parser  
syntax, say "-2 = max" or "-2 => max" or some such, and then ask for  
a list of those.  The "=" or "=>" would be an operator, and it could  
return a list formed by its two operands, so that the equality  
checking would as expected.  It wouldn't be too hard to do, so if you  
want that, let me know and I'll give it a shot (I'm not doing it now,  
since I already spent most of the morning on this, and I have to get  
back to work :-).

John's suggestion of an array of text entries with pop-up lists also  
looks like a possibility, though you would have to handle the pairing  
of numbers with menus yourself, and allowing the points in any order  
(and not repeated) and so on.  The Multipart object can certainly  
handle that, though there is some work to do.  I haven't tried nested  
multi-parts, but if that worked, it would simplify things  
considerably (use a bunch of ordered multi-parts for the pairs of  
number with pop-up, and then collect those into an unordered multipart).

Davide