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Custom Answer Checkers: PG Code Snippet

This is the essential PG code to write problems that check "arbitrary" conditions on the student's answer.

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Problem Techniques Index

PG problem file Explanation

Initialization: Standard. You might want to use, although it is not necessary.


$ans = pi/3;
$val = cos($ans);

Setup: To set up the custom answer checker we will override the answer checker routine for the MathObject that we're using to check the answer. Thus our answer object should be of the same type (e.g., Real, Formula, etc.) as what we want the student to be entering. For example, here we're going to ask for a value of x such that cos(x)=cos($ans). Thus we set up the answer to be a real number.

In this sample, we've taken advantage of a bunch of overloading that MathObjects do: the line $ans = pi/3 is doing the same thing as $ans = Real("pi/3") or $ans = Compute("pi/3"), because pi is already defined as a Real, and the division / is overloaded for MathObjects.

Similarly, $val = cos($ans) takes advantage of the cos() function being overloaded to produce a MathObject when the argument is a MathObject. Thus this is the same as $val = Compute("cos(x)")->eval(x=>$ans) (which would be necessary if $ans wasn't already a MathObject).

Enter a value of \(x\) for which \(\cos(x) = $val\):
\(x = \) \{ ans_rule(25) \}

Main Text: We don't have to make any changes or additions to the text section of the file.

$showPartialCorrectAnswers = 1;

ANS( $ans->cmp( checker=>sub {
my ( $correct, $student, $ansHash ) = @_;
return cos($correct) == cos($student);
} ) );


Answer Evaluation: Then when setting up the answer and solution section, we override the default answer checker in the answer. The replacement is a Perl subroutine that takes as its arguments the correct answer, student answer, and answer hash that is being processed in the answer comparison. Its return value should be 1 if the student's answer is correct, and 0 (false) otherwise. When doing the relational check, you should always put the correct answer on the left and the student answer on the right, e.g., cos($correct) == cos($student) should be used, but cos($student) == cos($correct) should not since the relational operator works from left to right which would mean that the student's answer would be determining the settings (such as domain of function evaluation) instead of the correct answer.

We could also specify the answer checker as a separate subroutine by writing

sub mycheck {
  my ($correct, $student, $ansHash) = @_;
  return cos($correct) == cos($student);

ANS( $ans->cmp( checker=>~~&mycheck ) );

(The ~~ in the above is remapped to a backslash in the course of the PG translation of the problem.)

One final point: we can set an error message in the answer checker by using Value->Error("message"). This will set the message that is displayed to the student and exit the checker with an incorrect return value. For example:

sub mycheck {
  my ($correct, $student, $ansHash) = @_;
  Value->Error("Try again") if cos($student)==sqrt(3)/2;
  return cos($correct) == cos($student);

ANS( $ans->cmp( checker=>~~&mycheck ) );

Problem Techniques Index