WeightedGrader

Weighted Graders

If a question has n answer blanks, the default weight to each answer 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 of some answers are incorrect.
• The weighted grader allows you to assign the weight you want 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. (This is not yet documented here.)

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

Problem Techniques Index

PG problem file

Explanation

loadMacros("PGanswermacros.pl"); # usual initialization, 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());

Answer Evaluation: Be sure to load PGanswermacros.pl or PGstandard.pl (which loads PGanswermacros.pl). 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.

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

PG problem file	Explanation
DOCUMENT(); loadMacros( "PGstandard.pl", "PGcourse.pl", "MathObjects.pl", "weightedGrader.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");	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_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.

Problem Techniques Index