using Formula in answer in a scaffold section causes incorrect answer evaluation

[ofloveandhate]

Hi! A colleague and I are developing Calculus content this summer, and we've arrived at a real stumper of an issue in a Webwork problem. The problem uses scaffolds, and the particular issue is that:

• a user is expected to enter a formula $m(x+h)+b$, like $10(x+h)-7$
• the user enters 10(x+h)-7
• the system tells them their answer is incorrect, and that the correct answer is 10(x+h)+-7.

i've observed that I can make the issue "go away" by doing any of:

• removing the preceding Section::End() Section::Begin("...")
• making a Formula object inside the previous Section and using it, rather than using [__]{Formula("")} inside the PGML.

I'm really baffled as to why this is happening, and would appreciate some help.

---

The server is running 2.17. I do not manage it.

Code. The problematic line is marked with PROBLEM HERE.

## DESCRIPTION
##   ****
## ENDDESCRIPTION

## KEYWORDS('Power Rule')

## DBsubject('Calculus')
## DBchapter('Derivatives')
## DBsection('Power Rule')
## Date('07/20/2024')
## Author('W. Shull')
## Institution('UWEC')
## TitleText1('')
## EditionText1('')
## AuthorText1('')
## Section1('')
## Problem1('')

########################################
# this file automatically moved
#	from setproving_grounds/ProductRuleIntroduction.pg 
#	to setderivatives_product_rule_-_training/ProductRuleIntroduction.pg 
#	on 2023-07-01 15:08:39.906823 by silviana amethyst.
# if this problem uses static images, they should also have been moved from that location to here.
# if not, look in the source directory for images that didn't make it.
########################################


DOCUMENT();        # This should be the first executable line in the problem.

loadMacros(
  "PGstandard.pl",
  "MathObjects.pl",        # the new parser
  "contextFraction.pl",
  "parserMultiAnswer.pl",
"answerHints.pl",
"PGML.pl",
   "scaffold.pl",
  "PGcourse.pl",           # Customization file for the course
   "customCSS.pl",
   "parserPopUp.pl",   # <--------------------------------------NEEDED FOR DROPDOWN MENUS
);

loadMacros("niceTables.pl");

TEXT(beginproblem());
$showPartialCorrectAnswers = 1;

$same_derivative = PopUp(
  ["Choose one", "yes","no"],
  "yes");

Context("Numeric");
Context()->noreduce('(-x)-y');
Context()->noreduce('(-x)+y');

$y1=non_zero_random(-10,10);
$m1=non_zero_random(-10,10);
while($m1==1){
    $m1=non_zero_random(-10,10);
}
$b1=non_zero_random(-10,10);

#SRAND($psvn); #FIX RANDOM VARIABLES ACROSS MULTIPLE PROBLEMS

Context()->variables->add(u=>"Real", h=>"Real");

###################################
# Main text
###########################################
#  The scaffold
Scaffold::Begin();
###########################################
Section::Begin("Part 1: Definition review");

Context()->texStrings;
BEGIN_PGML

Let's review the definition of the derivative:

[@ openDiv({ "class" => "importantFormula" }) @]*
[```f'(x)=\lim_{h\rightarrow0}\frac{f(x+h)-f(x)}h```]
[@ closeDiv() @]*

Let's try applying this to some functions we know. We will start with the constant function [`f(x)=[$y1]`].

Retype that here: [`f(x)=`] [_]{Formula($y1)}

END_PGML
Section::End();

Section::Begin("Part 1: Definition review & constant");

BEGIN_PGML

Based on what you know from algebra, what is the slope of [`y=[$y1]`]? [_]{0}

(If you're not sure, go to Desmos.com, type the equation, and find [`\frac{\mbox{rise}}{\mbox{run}}`] between any two points.)

END_PGML
Section::End();

Section::Begin("Part 2: Constant from the definition");

BEGIN_PGML

Let's see if the definition of the derivative gives us the same answer!

If [`f(x)=[$y1]`], then [`f(x+h)=[$y1]`], so:

[```
\begin{eqnarray*}
f'(x)
&=&\lim_{h\rightarrow0}\frac{f(x+h)-f(x)}h\\
&=&\lim_{h\rightarrow0}\frac{[$y1]-[$y1]}h\\
&=&\lim_{h\rightarrow0}\frac{0}h\\
&=&\lim_{h\rightarrow0}(0)=0\\
\end{eqnarray*}
```]

Is this the same answer as before? [_]{$same_derivative}

END_PGML
Section::End();

Section::Begin("Part 3a: Other straight lines");

BEGIN_PGML

If [`f(x)=[$m1]x+[$b1]`], then based on what you know from algebra, the slope of the line is [`f'(x)=`] [_]{$m1}.

Meanwhile, [`f(x+h)=`] [_]{Formula("$m1(x+h)+$b1")->reduce}  PROBLEM HERE

END_PGML
Section::End();

Section::Begin("Part 3b");

BEGIN_PGML

[```
\begin{eqnarray*}
f'(x)
&=&\lim_{h\rightarrow0}\frac{[$m1](x+h)-[$m1]x}h\\
&=&\lim_{h\rightarrow0}\frac{([$m1]x+[$m1]h)-[$m1]x}h\\
&=&\lim_{h\rightarrow0}\frac{[$m1]h}h=[$m1]\\
\end{eqnarray*}
```]

Is this the same answer as before? [_]{$same_derivative}

END_PGML
Section::End();

  Scaffold::End();
Context()->normalStrings;

$showPartialCorrectAnswers = 1;

COMMENT('MathObject version');
COMMENT('Complicated chain rule problem in the code');
ENDDOCUMENT();

[dlglin]

After some fooling around with this, it looks like having a PopUp in a scaffold interferes with creation of future MathObjects. I have created issue #881 about this. Someone who knows more about the inner workings of PG will have to look into it.

In the meantime you have the available workaround of defining the Formula earlier in the problem. It looks like putting that anywhere before the Section::End() for the section containing the PopUp will work.

[ofloveandhate]

Thank you! It felt like a bug, ha. Thanks for making an issue for it, and for the workaround option.

[drgrice1]

Another work around that would allow you to keep the code structure of your problem the same would be to change line 53 of your code from Context("Numeric"); to $eqnContext = Context("Numeric");, and then add Context($eqnContext); to line 125 (right after the Section::End(); call that contains the section with the question Is this the same answer as before? [_]{$same_derivative}). Note that if you add more to the problem after the later pop up question, you would also need to add that line again after that section.

See issue #881 that @dlglin posted for more details on this bug.