WeightedGrader
Weighted Graders
If a question has n answer blanks, the default weight for each answer is 1/n. 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 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.
Standard Problem Grader: give full credit if all answers are correct and zero credit otherwise.
| PG problem file | Explanation |
|---|---|
#######################
# Initialization
loadMacros("PGanswermacros.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
Answer Evaluation: We use
|
Weighted Grader: assign different weights (percentages) to each answer in a problem.
| PG problem file | Explanation |
|---|---|
DOCUMENT(); loadMacros( "PG.pl", "PGbasicmacros.pl", "PGchoicemacros.pl", "PGanswermacros.pl", "PGauxiliaryFunctions.pl", "PGgraphmacros.pl", "PGcourse.pl", "MathObjects.pl", "weightedGrader.pl", ); install_weighted_grader(); TEXT(beginproblem); |
Initialization: We need to include the |
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");
|
Set-up: 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 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( "PGbasicmacros.pl", "PGchoicemacros.pl", "PGanswermacros.pl", "PGauxiliaryFunctions.pl", "weightedGrader.pl" ); install_weighted_grader(); $showPartialCorrectAnswers = 1; TEXT(beginproblem()); |
Initialization: We need to include the |
# 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";
|
Set-up: 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 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
Since weighted answers with the credit answer option are non-standard, insert a |
