Difference between revisions of "WeightedGrader"
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| − | Answer Evaluation: |
+ | Answer Evaluation: For the non-credit answers, use <code>NAMED_WEIGHTED_ANS( 'label', evaluator, weight );</code> instead of <code>ANS( evaluator );</code>. For the credit answer, use <code>CREDIT_ANS( evaluator for volume, [list of names of answer blanks to provide credit for], weight );</code>. |
| − | The code given assigns |
+ | 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. |
| − | The weights should be positive integers that sum to 100. |
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Revision as of 17:29, 26 November 2009
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 = "x = $a y, \quad y^3 = x \quad (\mbox{with } y\geq 0)"; # already displaymath mode
$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 |
# answers
$integrand="pi*($a*y)**2 - pi*(y**3)**2";
$differential="dy";
$lowerlimit="0";
$upperlimit="sqrt($a)";
$volume = ((4*pi)/21)*($a**3.5);
# answer weights for integrand, differential, lowerlimit, upperlimit, and volume
@weights=(50,2,4,4,40);
# answer evaluators
@ans_eval=(
fun_cmp($integrand, vars=>['x','y'], limits=>[[1,2],[1,2]]),
str_cmp($differential),
num_cmp($lowerlimit),
num_cmp($upperlimit),
num_cmp($volume)
);
NAMED_WEIGHTED_ANS('optional1', @ans_eval[0], @weights[0]);
NAMED_WEIGHTED_ANS('optional2', @ans_eval[1], @weights[1]);
NAMED_WEIGHTED_ANS('optional3', @ans_eval[2], @weights[2]);
NAMED_WEIGHTED_ANS('optional4', @ans_eval[3], @weights[3]);
CREDIT_ANS(@ans_eval[4],['optional1','optional2','optional3','optional4'],@weights[4]);
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 |
