WeightedGrader

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Weighted Graders

If a question has n answer blanks, the default grader, which is the average problem grader (avg_problem_grader), will use 1/n as the weight for each answer. We describe several different ways to weight answers differently.

  • The standard problem grader assigns full credit if all answers are correct, and zero credit otherwise. This all-or-nothing grader should always be used for matching, multiple choice, and true / false questions, otherwise students will be able to deduce how many answers are correct by the partial credit reported by webwork.
  • The full-partial grader gives full credit if the last answer is correct, no matter what the other answers are, and partial credit (like the average problem grader) otherwise.
  • The weighted grader allows you to assign a weight to each answer blank in a problem.
  • The weighted grader with the credit answer option allows you to specify one answer blank to be the final answer which, if answered correctly, will provide full credit for all other answer blanks in the problem.
  • The incremental weighted grader, which awards a certain amount of credit for answering a certain number of parts correctly, is described in Example 1 (answer evaluation section) on the page PopUpListsLong


Standard Problem Grader: give full credit if all answers are correct and zero credit otherwise.

Problem Techniques Index

PG problem file Explanation
#######################
#  Initialization
loadMacros("PGstandard.pl");

#  Usual setup and main text go here

#######################
#  Answer evaluation

install_problem_grader(~~&std_problem_grader);

$showPartialCorrectAnswers = 0;

ANS($a->cmp());
ANS($b->cmp());
ANS($c->cmp());

Initialization: Be sure to load PGstandard.pl, which automatically loads PGanswermacros.pl which has the standard problem grader.

Answer Evaluation: We use install_problem_grader(~~&std_problem_grader); to give full credit only if all answers are correct, and zero credit otherwise. We should probably also hide feedback on whether answers are partially correct or not by setting $showPartialCorrectAnswers=0;. The standard problem grader is recommended for true / false and multiple choice questions to prevent students from guessing and receiving either feedback or partial credit that tells them whether their guess was correct.



Full-Partial Grader: give full credit if the last answer is correct, no matter what the other answers are, and partial credit (like the average problem grader) otherwise.

Problem Techniques Index

PG problem file Explanation
#######################
#  Initialization
loadMacros(
"PGstandard.pl",
"PGgraders.pl",
);

#  Usual setup and main text go here

#######################
#  Answer evaluation

install_problem_grader(~~&full_partial_grader);

$showPartialCorrectAnswers = 1;

ANS($a->cmp());
ANS($b->cmp());
ANS($c->cmp());

Initialization: Be sure to load PGgraders.pl

Answer Evaluation: Use install_problem_grader(~~&full_partial_grader); to install this grader. Everything else is as usual. If the student answers the third question correctly, they will receive full credit no matter what their other answers are.




Weighted Grader: assign different weights (percentages) to each answer in a problem.

PG problem file Explanation
DOCUMENT();

loadMacros(
"PGstandard.pl",
"MathObjects.pl",
"weightedGrader.pl",
"PGcourse.pl",
);

install_weighted_grader();

TEXT(beginproblem());

Initialization: We need to include the weightedGrader.pl macro file and immediately install it using install_weighted_grader();.

Context("Numeric");
Context()->variables->add(t=>"Real");
Context()->strings->add(A=>{},B=>{});

$r = random(2,4,1);
$answer1 = Real("pi * $r**2");
$answer2 = Formula("($r - 1) * x**2 * t") -> reduce;
$answer3 = String("A");

Setup: To show how this works with MathObjects, we add some variables and strings to the context.

Context()->texStrings;
BEGIN_TEXT
Enter \( \pi $r^2 \): \{ans_rule(10)\}
Enter \( $answer2 \): \{ans_rule(10)\}
Enter A: \{ans_rule(10)\}
END_TEXT
Context()->normalStrings;

Main Text: Answer boxes are as usual.

$showPartialCorrectAnswers = 0;

WEIGHTED_ANS( ($answer1)->cmp(), 40 );
WEIGHTED_ANS( ($answer2)->cmp(), 40 );
WEIGHTED_ANS( ($answer3)->cmp(), 20 );

ENDDOCUMENT();

Answer Evaluation: Use WEIGHTED_ANS( evaluator, weight ); instead of ANS( evaluator );. The code given assigns 40% to each of the first two answers, and 20% to the last answer. The weights should be positive integers that sum to 100.







Weighted Grader with Credit Answer Option: assign different weights (percentages) to each answer in a problem, and provide one answer blank that, if correct, will supersede all other answer blanks and award full credit.

PG problem file Explanation
DOCUMENT();

loadMacros(
"PGchoicemacros.pl",
"PGanswermacros.pl",
"PGauxiliaryFunctions.pl",
"weightedGrader.pl"
);

install_weighted_grader();
$showPartialCorrectAnswers = 1;

TEXT(beginproblem());

Initialization: We need to include the weightedGrader.pl macro file and immediately install it using install_weighted_grader();.

# problem set up
$a = random(2,9,1);
# $region will already be in displaymath mode
$region = "x = $a y, \quad y^3 = x \quad (\mbox{with } y\geq 0)"; 
$lineofrotation = "the y-axis"; 

Setup: Everything is as usual.

BEGIN_TEXT
The volume of the solid obtained by rotating the region enclosed by 
\[
$region
\] 
about $lineofrotation can be computed using the method of disks or 
washers via an integral
$BR
$BCENTER
\( \displaystyle V = \int_a^b \) 
\{NAMED_ANS_RULE('optional1',50)\}  
\{NAMED_POP_UP_LIST('optional2',['?','dx','dy'])\}
$ECENTER
$BR
with limits of integration 
\( a = \) \{NAMED_ANS_RULE('optional3',10)\} and 
\( b = \) \{NAMED_ANS_RULE('optional4',10)\}.
$BR
$BR
The volume is \( V = \) \{ans_rule(50)\} cubic units.

$PAR
${BITALIC}
Note: You can earn full credit if the last question   
is correct and all other questions are either blank 
or correct.
${EITALIC}
END_TEXT

Main Text: The answer box for the credit answer (the actual volume) is as usual; however, the other answer boxes are not as usual. In particular, you must use \{ NAMED_ANS_RULE( 'label', width ) \} or an appropriate variation for all answer boxes other than the credit answer.

At the bottom of the text of the problem, include a note to students that explains how they can earn credit.

# answers below are incorrect to maintain 
# the integrity of the original problem
$integrand="pi*x**2";
$differential="dx";
$lowerlimit="3";
$upperlimit="5";
$volume = pi*$a**3;

NAMED_WEIGHTED_ANS( 'optional1', fun_cmp($integrand, vars=>['x','y'], 
limits=>[[1,2],[1,2]]), 50 );

NAMED_WEIGHTED_ANS( 'optional2', str_cmp($differential), 2 );

NAMED_WEIGHTED_ANS( 'optional3', num_cmp($lowerlimit), 4 );

NAMED_WEIGHTED_ANS( 'optional4', num_cmp($upperlimit), 4 );

CREDIT_ANS( num_cmp($volume), 
['optional1','optional2','optional3','optional4'], 40 );

COMMENT('Gives partial credit for correct answers to initial questions
or full credit for answering only the the final question correctly.');

ENDDOCUMENT();

Answer Evaluation: For the non-credit answers, use NAMED_WEIGHTED_ANS( 'label', evaluator, weight ); instead of ANS( evaluator );. For the credit answer, use CREDIT_ANS( evaluator, [list of names of answer blanks to provide credit for], weight );. The code given assigns 50% to the integrand, 2% to the differential, 4% to each of the limits of integration, and 40% to the value of the integral. If the student correctly calculates the volume and either enters only the volume or all other answer blanks are correct, then full credit is awarded. The weights should be positive integers that sum to 100.

Since weighted answers with the credit answer option are non-standard, insert a COMMENT() that explains how answers are evaluated. This comment is only visible to professors browsing the problem library.




Problem Techniques Index

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