GraphLimit Flash Applet Sample Problem: Difference between revisions

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[http://hobbes.la.asu.edu/Holt/chaps-and-secs.html list of current chapter and section names] and a similar  
[http://hobbes.la.asu.edu/Holt/chaps-and-secs.html list of current chapter and section names] and a similar  
[http://hobbes.la.asu.edu/Holt/keywords.html list of keywords].  The list of keywords should be comma separated and quoted (e.g., KEYWORDS('calculus','derivatives')).
[http://hobbes.la.asu.edu/Holt/keywords.html list of keywords].  The list of keywords should be comma separated and quoted (e.g., KEYWORDS('calculus','derivatives')).
</p>
|- style=" background-color:#ddffdd;"
| <pre>
DOCUMENT();       
loadMacros(
  "PGstandard.pl",
  "AppletObjects.pl",
  "MathObjects.pl",
);
</pre>
| <p>
This is the <strong>initialization section</strong> of the problem.  The first executed line of the problem <strong>must</strong> be the <code>DOCUMENT();</code> command.  Note that every command <em>must end with a semicolon</em>.
</p>
<p>
The <code>loadMacros</code> command loads information that works behind the scenes.  For our purposes we can usually just load the macros shown here and not worry about things further.
</p>
|- style=" background-color:#ffffdd;"
| <pre>
# Set up problem
$qtype='limits';
$showHint = 0;
if(time>$dueDate){
  $showHint=1;
}
$x1=random(-8,-2,1);
$x2=$x1+random(2,4,1);
$x3=$x2+random(2,3,1);
$x4=random($x3+2,7,1);
</pre>
| <p>
The GraphLimits.swf applet will accept four different question types, specified with the <code>$qtype</code> variable.  These are: limits, continuity, first_derivative and second_derivative.  This sample problem is set to 'limits'.
</p>
<p>
The applet has solution/hint information embedded in it.  When <code>$hintState=0</code>, this information is not shown.  When <code>$hintState=1</code>, this information is revealed.  The <code>time</code> parameter tracks the current date and time.  The conditional compares that to the due date for the problem set (in the <code>$dueDate</code> scalar variable) and sets <code>$hintState</code> to 1 if the due date has passed and leaves <code>$hintState</code> set to 0 if the assignment is not yet due.
</p>
<p>
The four variables <code>$x1</code>, <code>$x2</code>, <code>$x3</code> and <code>$x4</code> are the x-coordinates of four points on the graph that the applet will set to be a removable discontinuity, a jump discontinuity or a cusp.  The order of these phenomena is random as are the y-values chosen.  The x-coordinates must be between -10 and 10.
</p>
|- style=" background-color:#ccffff;"
| <pre>
#######################################
#  How to use the Graph_Test applet.
#    Purpose:  The purpose of this
#      applet is to ask graphical
#      limit questions
#    Use of applet:  The applet
#      state consists of the
#      following fields:
#    qType - question type: limits,
#      continuity, first_derivative,
#      second_derivative
#    hintState - context sensitive
#      help is either on or off. 
#      Generally turned on after
#      dueDate
#    problemSeed - the seed sets
#      the random parameters that
#      control which graph is
#      chosen.  If the seed is
#      changed, the graph is
#      changed.
#######################################
#    qType = limits
#      right_limits - returns a
#        list of points (a,b)
#        such that
#        lim_{x\to a^-}f(x)=b,
#        but
#        lim_{x\to a^+}f(x)\= b
#      left_limits - returns a
#        list of points (a,b)
#        such that
#        lim_{x\to a^+}f(x)=b,
#        but
#        lim_{x\to a^-}f(x)\= b
#      neither_limits - returns
#        a list of points (a,b)
#        such that
#        lim_{x\to a^-}f(x)\=
#          lim_{x\to a^+}f(x)\=
#          f(a)=b
#      get_intervals returns a
#        list of intervals on
#        which f(x) is continuous.
#      get_f_of_x - given x value,
#        returns f(x). 
#        returns NaN for x notin
#        [-10,10].
#      getf_list - given x value
#        and string returns
#        "function" - returns f(x)
#        "leftlimit" - returns
#          lim_{x->a^-}f(x)
#        "rightlimit" - returns
#          lim_{x->a^+}f(x)
#        "limit" - returns
#          lim_{x->a}f(x) or "DNE"
#
#  What does the applet do?
#    The applet draws a graph
#    with jumps, a cusp and
#    discontinuities
#    When turned on, there is
#    context sensitive help.
################################
    ############################
    # Create  link to applet
    ############################
    $appletName = "Graph_Limit";
    $applet =  FlashApplet(
      codebase             
        => findAppletCodebase
        ("$appletName.swf"),
      appletName           
        => $appletName,
      appletId             
        => $appletName,
      setStateAlias       
        => 'setXML',
      getStateAlias       
        => 'getXML',
      setConfigAlias       
        => 'setConfig',
      maxInitializationAttempts
        => 10, 
      height               
        => '475',
      width               
        => '425',
      bgcolor             
        => '#e8e8e8',
      debugMode           
        =>  0,
      submitActionScript 
        =>    qq{
getQE("func").value=getApplet
  ("$appletName").getf_list($x1,"function");
getQE("rlimit").value=getApplet
  ("$appletName").getf_list($x2,"rightlimit");
getQE("llimit").value=getApplet
  ("$appletName").getf_list($x3,"leftlimit");
getQE("limit").value=getApplet
  ("$appletName").getf_list($x4,"limit");
  },
    );
###################################
# Configure applet
###################################
# configuration consists of
# hintState, question type, and
# random seed, and x-coordinates of
# four points where jumps,
# discontinuities or cusps
# occur.
$applet->configuration(qq{<xml>
<hintState>$hintState</hintState>
<qtype>limits</qtype>
<seed>$problemSeed</seed>
<xlist x1='$x1' x2='$x2'
x3='$x3' x4='$x4' /></xml>});
$applet->initialState(qq{<xml>
<hintState>$hintState</hintState>
<qtype>limits</qtype>
<seed>$problemSeed</seed>
<xlist x1='$x1' x2='$x2'
x3='$x3' x4='$x4' /></xml>});
TEXT( MODES(TeX=>'object code',
  HTML=>$applet->insertAll(
  debug=>0,
  includeAnswerBox=>0,
  )));
TEXT(MODES(TeX=>"", HTML=><<'END_TEXT'));
<input type="hidden"
  name="func" id="func" />
<input type="hidden"
  name="llimit" id="llimit" />
<input type="hidden"
  name="rlimit" id="rlimit" />
<input type="hidden"
  name="limit" id="limit" />
END_TEXT
$answerString1 =
$inputs_ref->{func};
my $correctAnswer1 =
Compute("$answerString1");
$answerString2 =
$inputs_ref->{rlimit};
my $correctAnswer2 =
Compute("$answerString2");
$answerString3 =
$inputs_ref->{llimit};
my $correctAnswer3 =
Compute("$answerString3");
$answerString4 =
$inputs_ref->{limit};
my $correctAnswer4 =
Compute("$answerString4");
</pre>
| <p>
This is the <strong>Applet link section</strong> of the problem. 
</p><br>
<p>
Those portions of the code that begin
the line with <code>#</code>
are comments and can be omitted or
replaced with comments appropriate
to your particular problem.
</p>
<p>You must include the section that
follows <code># Create  link to
applet</code>.  If you are embedding
a different applet, from the Graph_Limit
applet, put your applet name in place of
'Graph_Limit' in the line <code>$appletName =</code>
<code> "Graph_Limit";</code>. 
Enter the height of the applet
in the line <code>height => '475',</code>
in place of 475 and the width in the line 
<code>width => '425',</code> in place of 425.
</p><br>
<p>  The lines <code>$applet->configuration</code>
<code>(qq{<xml><hintState>$hintState</hintState></code>
<code><qtype>$qtype</qtype></code>
<code><seed>$problemSeed</seed></code>
<code><xlist x1='$x1' x2='$x2'</code>
<code> x3='$x3' x4='$x4' /></code>
<code></xml>});</code> and <code>$applet</code>
<code>->initialState</code><code>(qq{<xml></code>
<code><hintState>$hintState</hintState></code>
<code><qtype>$qtype</qtype></code><code><seed>$problemSeed</seed></code>
<code><xlist x1='$x1' x2='$x2'</code><code> x3='$x3' x4='$x4' /></code>
<code></xml>});</code> configure the applet. 
The configuration of the applet is done in xml. 
The hintState is set to the variable
<code>$hintState</code>, the question type is set to
<code>$qtype</code> and the problem seed is the
WeBWorK environmental variable <code>$problemSeed</code>. 
The variables <code>$x1</code>, <code>$x2</code>,
<code>$x3</code> and <code>$x4</code> are also
passed to the applet.
</p><br>
<p>The code <code>qq{ </code><code>
getQE("func").value=getApplet</code>
<code>("$appletName").getf_list($x1,"function");</code><code>
getQE("rlimit").value=getApplet</code>
<code>("$appletName").getf_list($x2,"rightlimit");</code><code>
getQE("llimit").value=getApplet</code>
<code>("$appletName").getf_list($x3,"leftlimit");</code><code>
getQE("limit").value=getApplet</code>
<code>("$appletName").getf_list($x4,"limit");</code><code>
  }</code>
is called when the 'Submit Answers'
button in the problem is pressed. 
There is an external interface function
designed inside the applet.  The function
name is 'getf_list'.  These lines of code
call the function with javascript. 
<code>getf_list</code>, takes two arguments: 
the x-coordinate of a point, and a string
value.  The string may be any of the
following four alternatives:  "function",
"rightlimit", "leftlimit", "limit". 
<code>getf_list</code> returns either
the value of the function at the x-coordinate,
or the specified limit.  The line <code>
getQE("func").value=getApplet</code>
<code>("$appletName").getf_list($x1,"function");</code>
gets the value of the function at <code>$x1</code>
and stores this value in the hidden javascript
form field named "func".</p>
<p>
The hidden form fields are created in the code block:
<code>
TEXT(MODES(TeX=>"", HTML=><<'END_TEXT'));
<input type="hidden"</code>
<code> name="func" id="func" /></code>
<code>
<input type="hidden"</code>
<code> name="llimit" id="llimit" /></code>
<code>
<input type="hidden"</code>
<code> name="rlimit" id="rlimit" /></code>
<code>
<input type="hidden"</code>
<code> name="limit" id="limit" /></code>
<code>
END_TEXT
</code>
The line <code>TEXT(MODES(TeX=>"", HTML=><<'END_TEXT'));</code>
prevents the hidden fields from becoming part of the hard copy.
</p><br>
<p>
The applet is configured in the code line:
<code>$applet->configuration</code>
<code>(qq{<xml></code>
<code><hintState>$hintState</hintState></code>
<code><qtype>limits</qtype></code><code>
<seed>$problemSeed</seed></code>
<code><xlist x1='$x1' x2='$x2' x3='$x3' x4='$x4' /></code>
<code></xml>});</code> and the similar line below it.
The variables $hintState, $problemSeed, and $x1, $x2,
$x3, and  $x4 are defined within WeBWorK and used
by the applet to set the problem up.
</p><br>
<p>
<code>TEXT( MODES(TeX=>'object code',</code>
<code> HTML=>$applet->insertAll(</code>
<code>
  debug=>0,</code>
<code>
  includeAnswerBox=>0,</code>
<code>
reinitialize_button=>$permissionLevel>=10,</code>
<code>
  )));</code> actually embeds the applet
in the WeBWorK problem.
</p><br>
<p>When the submit button is pressed, the
hidden form fields defined in this block are
filled with information from the applet.
</p>
<p>
The data from the hidden form fields is used
in these simple perl subroutines to define the
correct answers to the four questions that are
part of this WeBWorK problem.</p><br>
<p>The WeBWorK variable $answerString1 is the
content of the hidden form field "func". 
$correctAnswer1 is the solution to the first
question.  The solutions for the next two
questions are defined in a similar way. 
The final question also has 'DNE' as a possible
correct answer for the student to enter.  The
way that the applet is designed, the left and
right limits always exist.</p>
|- style=" background-color:#ffdddd;"
| <pre>
BEGIN_TEXT
$BR
The graph shown is for the
function \(f(x)\). 
$BR Compute the following
quantities:
$BR
a)
\(f($x1)=\)
\{ans_rule(35) \}
$BR
b)
\(\lim_{x\to {$x2}^+}f(x)=\)
\{ans_rule(35) \}
$BR
c)
\(\lim_{x\to {$x3}^-}f(x)=\)
\{ans_rule(35) \}
$BR
d)
\(\lim_{x\to {$x4}}f(x)=\)
\{ans_rule(35) \}
$BR
END_TEXT
Context()->normalStrings;
</pre>
| <p>
This is the <strong>text section</strong>
of the problem.  The
<code>TEXT(beginproblem());</code> line
displays a header for the problem, and
the <code>Context()-&gt;texStrings</code>
line sets how formulas are displayed in the
text, and we reset this after the text section. 
Everything between the <code>BEGIN_TEXT</code>
and <code>END_TEXT</code> lines (each of which
must appear alone on a line) is shown to the
student.
</p>
<p>
Mathematical equations are delimited by
<code class="tex2math_ignore">\( \)</code>
(for inline equations) or <code class="tex2math_ignore">\[ \]</code>
(for displayed equations); in these contexts inserted
text is assumed to be TeX code.
</p>
<p>
There are a number of variables that set
formatting: <code>$PAR</code> is a paragraph
break (like <code>\par</code> in TeX). 
[[FormatVariableList|This page]] gives a list
of variables like this.  Finally, <code>\{&nbsp;\}</code>
sets off <em>code that will be executed
in the problem text</em>.  Here, <code>ans_rule(35)</code>
is a function that inserts an answer blank 35
characters wide.
</p>
|- style=" background-color:#eeccff;"
| <pre>
#############################
#
#  Answers
#
## answer evaluators
ANS( $correctAnswer1->cmp() ); 
#checks AnSwEr00001
ANS( $correctAnswer2->cmp() ); 
#checks AnSwEr00002
ANS( $correctAnswer3->cmp() ); 
#checks AnSwEr00003
ANS(num_cmp($correctAnswer4,
strings=>['DNE'])); 
#checks AnSwEr00004
ENDDOCUMENT();   
</pre>
| <p>
This is the <strong>answer</strong>
section of the problem.  The problem answer
is set by the <code>ANS( $correctAnswer1->cmp() );</code>,
<code>ANS( $correctAnswer2->cmp() );</code>,
<code>ANS( $correctAnswer3->cmp() );</code>,
and <code>ANS(num_cmp</code>
<code>($correctAnswer4,</code>
<code>strings=>['DNE']));</code> lines. 
These compare the student's answer with the
answers returned from the applet.  Answers 1-3
follow the same basic structure.  The fourth
answer allows for either a numeric answer or
the string 'DNE' for limits that do not exist.
</p>
<p>
The solution is embedded in the applet and
becomes available when the due date has passed.
</p>
<p>
The <code>ENDDOCUMENT();</code> command is the
last command in the file.
</p>
</p>
|}
|}
[[Category:Sample Problems]]
[[Category:Applets]]
[[Category:Problem_Techniques]]
[[Category:Flash Applets]]

Revision as of 17:09, 9 August 2011

Flash Applets embedded in WeBWorK questions GraphLimit Example

Sample Problem with GraphLimit.swf embedded

This sample problem shows how to use this versatile applet.

A standard WeBWorK PG file with an embedded applet has six sections:

  1. A tagging and description section, that describes the problem for future users and authors,
  2. An initialization section, that loads required macros for the problem,
  3. A problem set-up section that sets variables specific to the problem,
  4. An Applet link section that inserts the applet and configures it, (this section is not present in WeBWorK problems without an embedded applet)
  5. A text section, that gives the text that is shown to the student, and
  6. An answer and solution section, that specifies how the answer(s) to the problem is(are) marked for correctness, and gives a solution that may be shown to the student after the problem set is complete.

The sample file attached to this page shows this; below the file is shown to the left, with a second column on its right that explains the different parts of the problem that are indicated above. A screenshot of the applet embedded in this WeBWorK problem is shown below:

There are other example problems using this applet:
GraphLimit Flash Applet Sample Problem 2
And other problems using applets:
Derivative Graph Matching Flash Applet Sample Problem
USub Applet Sample Problem
trigwidget Applet Sample Problem
solidsWW Flash Applet Sample Problem 1
solidsWW Flash Applet Sample Problem 2
solidsWW Flash Applet Sample Problem 3
Other useful links:
Flash Applets Tutorial
Things to consider in developing WeBWorK problems with embedded Flash applets

PG problem file Explanation 
##DESCRIPTION
##  Graphical limits
##    Sample problem to illustrate 
##    the use of the GraphLimit.swf 
##    Flash applet
##ENDDESCRIPTION

## KEYWORDS('limits')

## DBsubject('Calculus')
## DBchapter('Limits')
## DBsection('Graphical limits')
## Date('7/5/2011')
## Author('Barbara Margolius')
## Institution('Cleveland State University')
## TitleText1('')
## EditionText1('2011')
## AuthorText1('')
## Section1('')
## Problem1('')
###########################################
# This work is supported in part by 
# the National Science Foundation 
# under the grant DUE-0941388.
###########################################

This is the tagging and description section of the problem. Note that any line that begins with a "#" character is a comment for other authors who read the problem, and is not interpreted by WeBWorK.

The description is provided to give a quick summary of the problem so that someone reading it later knows what it does without having to read through all of the problem code.

All of the tagging information exists to allow the problem to be easily indexed. Because this is a sample problem there isn't a textbook per se, and we've used some default tagging values. There is an on-line list of current chapter and section names and a similar list of keywords. The list of keywords should be comma separated and quoted (e.g., KEYWORDS('calculus','derivatives')).

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