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<!DOCTYPE html>
<html lang="en">
<head>
<title>Bayesian Knowledge Tracing</title>
<meta charset="utf-8">
<meta name="viewport" content="width=device-width,initial-scale=1,maximum-scale=1,user-scalable=no">
<meta http-equiv="X-UA-Compatible" content="IE=edge,chrome=1">
<meta name="HandheldFriendly" content="true">
<meta property="og:image" content="images/socimg.png" />
<link rel="icon" href="images/fav.png" type="image/png">
<link rel="stylesheet" type="text/css" href="style.css">
<link href="https://fonts.googleapis.com/css?family=Karla|Roboto&display=swap" rel="stylesheet">
<link rel="stylesheet" href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/4.7.0/css/font-awesome.min.css">
</head>
<body id="top" onresize="positionElements()">
<div class="intro">
<!-- mini balloons -->
<div class="mini">
<div class="balloon-box"><img class="mini-left" id="mini1" src="images/pink.png"
title="mini red balloon" alt="mini red balloon" ></div>
<div class="balloon-box"><img class="mini-left" id="mini2" src="images/yellow.png"
title="mini yellow balloon" alt="mini yellow balloon" ></div>
<div class="balloon-box"><img class="mini-right" id="mini3" src="images/green.png"
title="mini green balloon" alt="mini green balloon" ></div>
<div class="balloon-box"><img class="mini-right" id="mini4" src="images/blue.png"
title="mini blue balloon" alt="mini blue balloon" ></div>
</div>
<center>
<h1 id="mainTitle" style="font-size:40px;letter-spacing:4px">Predicting What Students Know</h1>
</center>
<center>
<h2 id="subtitle">An Introduction to Bayesian Knowledge Tracing</h2>
</center>
<center><div class="description">
<h4>
<b>Bayesian Knowledge Tracing</b>, or <b>BKT</b>, is an artificial intelligence
algorithm that lets us infer a student's current knowledge state to
predict if they have learned a skill.
<br /><br />
There are four parameters involved in BKT (each with a value between 0 and 1, inclusive):
<ul>
<li>
<b style="color:#A98666">P(known):</b>
the probability that the student already knew a skill.
</li>
<li>
<b style="color:#A57380">P(will learn):</b>
the probability that the student will learn a skill on the next practice opportunity.
</li>
<li>
<b style="color:#736C9B">P(slip):</b>
the probability that the student will answer incorrectly despite knowing a skill.
</li>
<li>
<b style="color:#7499AD">P(guess):</b>
the probability that the student will answer correctly despite not knowing a skill.
</li>
</ul>
Every time the student answers a question, our BKT algorithm calculates
<b>P(learned)</b>, the probability that the student has learned the skill
they are working on, using the values of these parameters.
The formula for <b>P(learned)</b> depends on whether their response was correct.
<input type="button" class="math" title="See the math" value="See the math" onclick="showMath(this, math)" />
<div class="extra" id="math">
<br />
First, we compute the conditional probability that the student
learned the skill previously (at time <i>n-1</i>), based on whether
they answered the current question (at time <i>n</i>) correctly or incorrectly.
<br />
<img class="formula" src="images/right-formula.png" title="p learned at time n-1 if correct"
alt="p learned at time n-1 if correct" >
<br />
<img class="formula" src="images/wrong-formula.png" title="p learned at time n-1 if wrong"
alt="p learned at time n-1 if wrong" >
<br /><br />
Then, we use the result of our first calculation to compute the
conditional probability that the student has learned the skill now
(at time <i>n</i>).
<img id="pL" class="formula" src="images/p-learned.png" title="p learned at time n given answer"
alt="p learned at time n given answer" style="width:820px;margin-bottom:-20px;">
</div>
<br /><br />
For the next question, we use <b>P(learned)</b> as the new value of <b>P(known)</b>.
Once <b>P(known)</b> ≥ 0.95, we say that the student has achieved
<b><i style="color:#A98666">m</i>
<i style="color:#A57380">a</i>
<i style="color:#736C9B">s</i>
<i style="color:#7499AD">t</i>
<i style="color:#736C9B">e</i>
<i style="color:#A57380">r</i>
<i style="color:#A98666">y</i></b>.
<br /><br />
Now that you’ve had a chance to learn about the four parameters,
here’s a tool that can help you visualize the relationships between them
and explore how each one influences the probability calculations underlying BKT.
We'll be modeling the system with a hot air balloon, using its height as a
measure of mastery.
</h4>
<br />
<h2>Let's begin!</h2>
<a href="#start">
<img class="arrow" src="images/down-arrow.png" title="start arrow" alt="start arrow" >
</a>
</div></center>
</div>
<div class="prompt-container" id="p-contain">
<div class="header" id="header">
<h1 style="margin-bottom:0;">BKT Balloon Simulator</h1>
<h4 style="margin-top:25px;font-size:17px;">
Drag/click the sliders on the right to adjust the parameters and help the balloon rise.
Explore on your own or use the following prompts as a guide.
</h4>
</div>
<div class="prompts" id="prompts">
<h4>
<ol>
<li>
Find two different parameter combinations that will result in mastery if the student
answers correctly. <i>Hint:</i> make <b>P(learned if correct)</b> ≥ 0.95
and press "answer correct" to verify your results.
</li>
<input type="button" title="More" class="more" value="More" onclick="showMore(this, more1)" />
<ul class="extra" id="more1">
<li>
Recall that <b>P(learned)</b> becomes the new value for <b>P(known)</b>.
</li>
<li>
Explore what adjustments you have to make depending on <b>P(known)</b>.
Try a higher <b>P(known)</b> and a lower <b>P(known)</b> and compare your results.
</li>
</ul>
<li>
What happens to <b>P(learned if correct)</b> and <b>P(learned if wrong)</b>
if <b>P(guess)</b> and/or <b>P(slip)</b> exceeds 0.5?
</li>
<input type="button" title="More" class="more second" value="More" onclick="showMore(this, more2)" />
<ul class="extra" id="more2">
<li>
<b>P(learned)</b> is higher if the user answers <i>incorrectly</i> vs. <i>correctly</i>.
This is why <b>P(guess)</b> is typically bounded at 0.3 and <b>P(slip)</b> at 0.1.
<a href="#cit3" style="color:#000">[3]</a>
</li>
<li>
Does it make sense why the balloon flips now?
</li>
</ul>
<li>
What happens to <b>P(learned)</b> if the student answers incorrectly?
<i>Hint:</i> compare <b>P(learned if wrong)</b> with <b>P(known)</b>
(aka. your previous <b>P(learned)</b>).
</li>
<input type="button" title="More" class="more third" value="More" onclick="showMore(this, more3)" />
<ul class="extra" id="more3">
<li>
Generally, <b>P(learned)</b> is always assumed to increase because BKT
considers every answer, wrong or right, as a learning opportunity that
brings you one step closer to mastery.
</li>
<li>
However, can you think of a situation where <b>P(learned)</b>
might decrease with a wrong answer? Feel free to try modeling
different scenarios with the sliders using your knowledge
of the BKT parameters.
</li>
</ul>
<li>
Keep exploring! Can you find any other flaws or interesting characteristics of BKT?
</li>
</ol>
</h4>
</div>
</div>
<!-- interactive begins -->
<div class="explain" id="start">
<!-- sliders -->
<div class="slidecontainer" id="slidecontain">
<input type="button" title="reset" class="reset" id="res" value="Reset" onclick="reset()" />
<!-- init -->
<div class="des" onmouseenter="displayInfo(iDes)" onmouseleave="hideInfo(iDes)"
style="width:140px">
<div class="info" id="iDes" style="top:0;padding-left:140px">
<h4>Controls the balloon's height.</h4>
</div>
<h3>P(known): <span id="demoI"></span></h3>
</div>
<input type="range" min="0.0" max="1.0" value="0.5" step="0.01" class="slider"
style="background-image: linear-gradient(to right, #f0c297, #fccfcf)" id="init"
oninput="updateI(this.value)" />
<!-- trans -->
<div class="des" onmouseenter="displayInfo(tDes)" onmouseleave="hideInfo(tDes)"
style="width:155px">
<div class="info" id="tDes" style="padding-left:160px;margin-top:-5px">
Changes the storminess and number of clouds to represent learning difficulty.
</div>
<h3>P(will learn): <span id="demoT"></span></h3>
</div>
<input type="range" min="0.0" max="1.0" value="0.5" step="0.01" class="slider"
style="background-image: linear-gradient(to right, #f2b3c3, #e0d1e8)" id="trans"
oninput="updateT(this.value)" />
<!-- slip -->
<div class="des" onmouseenter="displayInfo(sDes)" onmouseleave="hideInfo(sDes)"
style="width:115px">
<div class="info" id="sDes" style="padding-left:115px">
Certain values will flip the balloon.
</div>
<h3>P(slip): <span id="demoS"></span></h3>
</div>
<input type="range" min="0.0" max="1.0" value="0.5" step="0.01" class="slider"
style="background-image: linear-gradient(to right, #d3cef2, #c2dff0)" id="slip"
oninput="updateS(this.value)" />
<!-- guess -->
<div class="des" onmouseenter="displayInfo(gDes)" onmouseleave="hideInfo(gDes)">
<div class="info" id="gDes">
Certain values will flip the balloon.
</div>
<h3>P(guess): <span id="demoG"></span></h3>
</div>
<input type="range" min="0.0" max="1.0" value="0.5" step="0.01" class="slider" id="guess"
oninput="updateG(this.value)" style="margin-bottom:20px;" />
<!-- probabilities -->
<h4 style="margin-bottom:10px;font-size:17px">
Remember, <b>P(learned)</b> depends on whether the student answers correctly
and this probability becomes the new value for <b>P(known)</b>.
Simulate student responses by choosing an answer button below.
</h4>
<!-- P(learned if correct) -->
<div class="left">
<h3 style="margin-bottom:0;">P(learned if correct): <span id="correct"></span></h3>
<input type="button" title="answer correct" class="button" id="learned1" value="Answer Correct"
onclick="changeP(correct, init)" />
</div>
<!-- P(learned if wrong) -->
<div class="right">
<h3 style="margin-bottom:0">P(learned if wrong): <span id="wrong"></span></h3>
<input type="button" title="answer wrong" class="button" id="learned2" value="Answer Wrong"
onclick="changeP(wrong, init)" />
</div>
<h4 id="hint" style="padding-top:100px;position:absolute;font-style:italic">
<b>Hint:</b> hover over the parameters to see how they impact the simulator.
</h4>
</div>
</div>
<!-- game components -->
<div class="game" id="game">
<div class="clouds">
<div class="cloud" id="cloud1"></div>
<div class="cloud" id="cloud2" style="float:right;top:315px;"></div>
<div class="cloud" id="cloud3" style="top:500px"></div>
<div class="cloud" id="cloud4" style="float:right;top:-150px"></div>
</div>
<div class="balloon" id="balloon"></div>
<div class="lightwaves" id="lightwaves"></div>
<div class="darkwaves" id="darkwaves"></div>
</div>
<footer>
<center><div class="references" id="refs">
<h2 style="text-align:left">References</h2>
<h4>
<ol style="font-size:14px;">
<li>
<b>Knowledge Tracing: Modeling the Acquisition of Procedural Knowledge Tracing</b>
<a href="http://act-r.psy.cmu.edu/wordpress/wp-content/uploads/2012/12/893CorbettAnderson1995.pdf">[pdf]</a>
<br />
Corbett, A.T. & Anderson, J.R., 1995.
</li>
<li>
<b>Individualized Bayesian Knowledge Tracing Models</b>
<a href="https://www.cs.cmu.edu/~ggordon/yudelson-koedinger-gordon-individualized-bayesian-knowledge-tracing.pdf">[pdf]</a>
<br />
Yudelson, M.V., Koedinger, K.R. and Gordon, G.J., 2013.
</li>
<li id="cit3">
<b>More Accurate Student Modeling Through Contextual Estimation of Slip and Guess
Probabilities in Bayesian Knowledge Tracing</b>
<a href="http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.141.6617&rep=rep1&type=pdf">[pdf]</a>
<br />
d Baker, R.S., Corbett, A.T. and Aleven, V., 2008.
</li>
</ol>
<br />
<i style="font-size:14px;">Created by Catherine Yeh and Iris Howley, Williams College.
Funding for this research was provided by the IIS:Cyber-Human Systems program: NSF CISE award number 1849984.</i>
</h4>
<a id="back-to-top" href="#top">
Back to top
<i class="fa fa-angle-up" aria-hidden="true"></i>
</a>
</div></center>
</footer>
<script type="text/javascript" src="balloon.js"></script>
</body>
</html>