This PG code shows how to include three different kinds of answer hints:

• General answer hints that help students get started on a problem and are always available via "Knowls".
• General answer hints that help students get started on a problem and are made available after a student has submitted an answer at least once (a "Show hints" checkbox appears near the "Submit Answers" button) via a BEGIN_HINT / END_HINT block of text.
• Specific, customized answer hints that appear in the answer feedback messages box after a student submits a particular answer that activates a pre-programmed hint via the answerHints.pl macro and a post-filter with answer hints for the answer checker.

You may also be interested in ErrorMessageCustomization

PG problem file Explanation
DOCUMENT();
"PGstandard.pl",
"MathObjects.pl",
);

TEXT(beginproblem());


Initialization: We need to include the macros file MathObjects.pl and answerHints.pl, which only works with MathObjects answer checkers (not old answer checkers). General answer hints only require the standard macros, but specific (customized) answer hints require the answerHints.pl macro.

Context("Numeric");
Context()->variables->are(t=>"Real",u=>"Real");

$f = Formula("2 t");$answer = Formula("6 u");


Setup: We restrict the variables to t and u

Context()->texStrings;
BEGIN_TEXT
If $$f(t) = f$$, then $$f(3u)$$ = \{ ans_rule(10) \}
$BR$BR
\{
value=>'Substitute 3u wherever you see t in the formula for f.')
\}
END_TEXT

$showHint = 5; BEGIN_TEXT$PAR
If you don't get this in $showHint tries, you can get a hint. END_TEXT BEGIN_HINT Substitute $$3u$$ wherever you see $$t$$ in the formula for $$f(t) = f$$. END_HINT Context()->normalStrings;  Main Text: Knowls (little bits of knowledge) provide an always present link to a hint that, when clicked on, expands to reveal the hint or, when clicked on again, retracts to hide the hint. The value of a knowl should be plain text (math mode may cause problems, as it did for me using ww 2.9). It is possible to get math to display, but it requires using a few escape tricks: value=>escapeSolutionHTML(EV3P('Substitute \$$3u\$$ ...')), base64=>1). In particular, note the use of escapeSolutionHTML(EV3P()) to do extra interpretation of the string formatting and also note the use of double backslashes \$$\$$ for the math mode delimiters. No special macros are needed for Knowls. For hints that are revealed to students only after a certain number of submissions, we set $showHint = 5; and tell the students in the problem text that they will see a hint after 5 attempts. We include a general answer hint in the block of text between the commands BEGIN_HINT (which is HINT(EV3(<<'END_HINT')); in older versions of WeBWorK) and END_HINT, which must be on their own lines and at the start of a line. The hint will automatically generate the word HINT: before the block of text that is the hint, so you don't need to add it manually. The modification of the context from texStrings and back to normalStrings ensures that MathObjects (formulas, etc.) will be beautifully typset. No special macros are needed for hints inside of BEGIN_HINT and END_HINT text blocks.

$showPartialCorrectAnswers = 1; ANS($answer->cmp()->withPostFilter(AnswerHints(
Formula("6 t") => "Are you using the correct variable?",
Formula("6 u") => "Good work!",
)));


Answer Evaluation: To generate specific, customized answer hints for particular answers, we use the AnswerHints postfilter provided by answerHints.pl. The answer hints should be provided by a particular answer, followed by the hash table association operator =>, followed by a string that will show up in the messages portion of the answer preview and feedback box when students submit their answers. You may include as many answer and hint pairs as you like, and even use subroutines in them (see answerHints.pl for more on this).

If the same error message should be given for several different answers, you should make a square bracketed list of those answers. For example, if the variables x, t, and u were all in the context, we could use

ANS($answer->cmp()->withPostFilter(AnswerHints( [Compute("6 t"),Compute("6 x")] => "Are you using the correct variable?", )));  If the MathObjects answer evaluator normally generates a message, the default is not to change a message that is already in place. To override a message generated by a MathObjects answer evaluator, you should set replaceMessage=>1 as below. ANS($answer->cmp()->withPostFilter(AnswerHints(
Compute("6 u") => ["Good work!",replaceMessage=>1],
)));