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<title>A framework for evaluating computer algebra systems for mathematics teaching and learning</title>
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<section id="sec-title-slide"><h1 class="title">A framework for evaluating computer algebra systems for mathematics teaching and learning</h1><h2 class="author">Alasdair McAndrew<br><br>College of Engineering and Science<br>Victoria University,<br>Melbourne, Australia</h2><h2 class="date">December, 2017</h2>
</section>
<section>
<section id="slide-org9b49ba4">
<div class="slide-header">Evaluating CAS for teaching & learning: Alasdair McAndrew, ATCM2017</div>
<h2 id="org9b49ba4">Some definitions</h2>
<ul>
<li class="fragment roll-in">A <i>computer algebra system</i> or CAS is a computer system which can perform
symmbolic, as well as numerical and graphical, operations</li>
<li class="fragment roll-in"><p>
they can be computer based or handheld
</p>
<p>
examples include: Mathematica, Maple, MuPAD (now Matlab Symbolic Toolbox),
Macsyma (reborn as GNU Maxima), Axiom, Sage, SymPy, TI-nspire CAS,
Casio ClassPad, HP Prime, lots of others
</p></li>
<li class="fragment roll-in">have been used in teaching since their inception</li>
<li class="fragment roll-in">there are two main schools of use:
<ul>
<li>students must not use a CAS until they have mastered the basics of algebra!</li>
<li>students should use CAS for experimentation right from the beginning, and
construct their own understandings</li>
</ul></li>
</ul>
</section>
</section>
<section>
<section id="slide-org15f8278">
<div class="slide-header">Evaluating CAS for teaching & learning: Alasdair McAndrew, ATCM2017</div>
<h2 id="org15f8278">Software evaluation: ISO9126</h2>
<p>
A generic framework:
</p>
<table border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
<colgroup>
<col class="org-left" />
<col class="org-left" />
</colgroup>
<thead>
<tr>
<th scope="col" class="org-left">Criterion</th>
<th scope="col" class="org-left">Meaning</th>
</tr>
</thead>
<tbody>
<tr>
<td class="org-left">Functionality</td>
<td class="org-left">how well the software performs its task</td>
</tr>
</tbody>
<tbody>
<tr>
<td class="org-left">Reliability</td>
<td class="org-left">fault tolerance and handling of errors);</td>
</tr>
</tbody>
<tbody>
<tr>
<td class="org-left">Usability</td>
<td class="org-left">how easy the software is to learn, user interface</td>
</tr>
</tbody>
<tbody>
<tr>
<td class="org-left">Efficiency</td>
<td class="org-left">response time and resource management</td>
</tr>
</tbody>
<tbody>
<tr>
<td class="org-left">Maintainability</td>
<td class="org-left">fault diagnosis, modifiability, testability</td>
</tr>
</tbody>
<tbody>
<tr>
<td class="org-left">Portability</td>
<td class="org-left">environmental flexibility, ease of installation</td>
</tr>
</tbody>
<tbody>
<tr>
<td class="org-left">Legal complaiance</td>
<td class="org-left">compliance with laws and regulations</td>
</tr>
</tbody>
</table>
</section>
</section>
<section>
<section id="slide-org7777540">
<div class="slide-header">Evaluating CAS for teaching & learning: Alasdair McAndrew, ATCM2017</div>
<h2 id="org7777540">Software evaluation: ACTIONS</h2>
<p>
Designed to evaluation software for distance learning:
</p>
<table border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
<colgroup>
<col class="org-left" />
<col class="org-left" />
</colgroup>
<thead>
<tr>
<th scope="col" class="org-left">Criterion</th>
<th scope="col" class="org-left">Meaning</th>
</tr>
</thead>
<tbody>
<tr>
<td class="org-left">Access</td>
<td class="org-left">all pretty self-explanatory</td>
</tr>
</tbody>
<tbody>
<tr>
<td class="org-left">Cost</td>
<td class="org-left"> </td>
</tr>
</tbody>
<tbody>
<tr>
<td class="org-left">Teaching & Learning</td>
<td class="org-left"> </td>
</tr>
</tbody>
<tbody>
<tr>
<td class="org-left">Interactivity and user-friendliness</td>
<td class="org-left"> </td>
</tr>
</tbody>
<tbody>
<tr>
<td class="org-left">Organizational issues</td>
<td class="org-left"> </td>
</tr>
</tbody>
<tbody>
<tr>
<td class="org-left">Novelty</td>
<td class="org-left"> </td>
</tr>
</tbody>
<tbody>
<tr>
<td class="org-left">Speed</td>
<td class="org-left"> </td>
</tr>
</tbody>
</table>
<p>
<b>Note:</b> because of huge variability, "teaching and learning is a weak
discriminator for selecting and using technologies"
</p>
</section>
</section>
<section>
<section id="slide-orged4f0d5">
<div class="slide-header">Evaluating CAS for teaching & learning: Alasdair McAndrew, ATCM2017</div>
<h2 id="orged4f0d5">Comparisons</h2>
<table border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
<colgroup>
<col class="org-left" />
<col class="org-left" />
</colgroup>
<thead>
<tr>
<th scope="col" class="org-left">ISO 9126</th>
<th scope="col" class="org-left">ACTIONS</th>
</tr>
</thead>
<tbody>
<tr>
<td class="org-left">Functionality</td>
<td class="org-left"> </td>
</tr>
</tbody>
<tbody>
<tr>
<td class="org-left">Reliability</td>
<td class="org-left"> </td>
</tr>
</tbody>
<tbody>
<tr>
<td class="org-left">Usability</td>
<td class="org-left">Interactivity & user-friendliness</td>
</tr>
</tbody>
<tbody>
<tr>
<td class="org-left">Efficieny</td>
<td class="org-left">Speed</td>
</tr>
</tbody>
<tbody>
<tr>
<td class="org-left">Maintainability</td>
<td class="org-left"> </td>
</tr>
</tbody>
<tbody>
<tr>
<td class="org-left">Portability</td>
<td class="org-left">Access & Cost</td>
</tr>
</tbody>
<tbody>
<tr>
<td class="org-left">Legal compliance</td>
<td class="org-left"> </td>
</tr>
</tbody>
<tbody>
<tr>
<td class="org-left"> </td>
<td class="org-left">Teaching & Learning</td>
</tr>
</tbody>
<tbody>
<tr>
<td class="org-left"> </td>
<td class="org-left">Organizational Issues</td>
</tr>
</tbody>
<tbody>
<tr>
<td class="org-left"> </td>
<td class="org-left">Novelty</td>
</tr>
</tbody>
</table>
</section>
</section>
<section>
<section id="slide-orga69892f">
<div class="slide-header">Evaluating CAS for teaching & learning: Alasdair McAndrew, ATCM2017</div>
<h2 id="orga69892f">A hybrid model: FACTIONS!</h2>
<table border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
<colgroup>
<col class="org-left" />
<col class="org-left" />
</colgroup>
<thead>
<tr>
<th scope="col" class="org-left">Criterion</th>
<th scope="col" class="org-left">Meaning</th>
</tr>
</thead>
<tbody>
<tr>
<td class="org-left">Functionality, or fitness for purpose</td>
<td class="org-left">Must manage all mathematics in the course</td>
</tr>
</tbody>
<tbody>
<tr>
<td class="org-left">Access</td>
<td class="org-left">by all students, at all times</td>
</tr>
</tbody>
<tbody>
<tr>
<td class="org-left">Cost</td>
<td class="org-left">initial purchase, deployment, upkeep, maintenance, licencing…</td>
</tr>
</tbody>
<tbody>
<tr>
<td class="org-left">Teaching & Learning</td>
<td class="org-left"> </td>
</tr>
</tbody>
<tbody>
<tr>
<td class="org-left">Interactivity and user-friendliness</td>
<td class="org-left">Must fit the needs of the <i>students</i> more than the <i>teacher</i></td>
</tr>
</tbody>
<tbody>
<tr>
<td class="org-left">Organizational issues</td>
<td class="org-left">Fit in with current policies and practices</td>
</tr>
</tbody>
<tbody>
<tr>
<td class="org-left">Novelty</td>
<td class="org-left">Should be seen as something new and exciting</td>
</tr>
</tbody>
<tbody>
<tr>
<td class="org-left">Students</td>
<td class="org-left">Different cohorts require difference approaches, and possibly different software</td>
</tr>
</tbody>
</table>
</section>
</section>
<section>
<section id="slide-orgacd4084">
<div class="slide-header">Evaluating CAS for teaching & learning: Alasdair McAndrew, ATCM2017</div>
<h2 id="orgacd4084">Case study 1: first year engineering mathematics</h2>
<table border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
<colgroup>
<col class="org-left" />
<col class="org-right" />
<col class="org-right" />
<col class="org-right" />
</colgroup>
<thead>
<tr>
<th scope="col" class="org-left">Criterion</th>
<th scope="col" class="org-right">Matlab</th>
<th scope="col" class="org-right">CAS Calculator</th>
<th scope="col" class="org-right">Maple</th>
</tr>
</thead>
<tbody>
<tr>
<td class="org-left">Functionality, or fitness for purpose</td>
<td class="org-right">2</td>
<td class="org-right">2</td>
<td class="org-right">2</td>
</tr>
</tbody>
<tbody>
<tr>
<td class="org-left">Access</td>
<td class="org-right">2</td>
<td class="org-right">1</td>
<td class="org-right">0</td>
</tr>
</tbody>
<tbody>
<tr>
<td class="org-left">Cost</td>
<td class="org-right">2</td>
<td class="org-right">1</td>
<td class="org-right">0</td>
</tr>
</tbody>
<tbody>
<tr>
<td class="org-left">Teaching & Learning</td>
<td class="org-right">1</td>
<td class="org-right">2</td>
<td class="org-right">1</td>
</tr>
</tbody>
<tbody>
<tr>
<td class="org-left">Interactivity and user-friendliness</td>
<td class="org-right">2</td>
<td class="org-right">2</td>
<td class="org-right">2</td>
</tr>
</tbody>
<tbody>
<tr>
<td class="org-left">Organizational issues</td>
<td class="org-right">2</td>
<td class="org-right">1</td>
<td class="org-right">0</td>
</tr>
</tbody>
<tbody>
<tr>
<td class="org-left">Novelty</td>
<td class="org-right">2</td>
<td class="org-right">1</td>
<td class="org-right">2</td>
</tr>
</tbody>
<tbody>
<tr>
<td class="org-left">Students</td>
<td class="org-right">2</td>
<td class="org-right">2</td>
<td class="org-right">2</td>
</tr>
</tbody>
<tbody>
<tr>
<td class="org-left"><b>Total</b></td>
<td class="org-right"><b>15</b></td>
<td class="org-right"><b>11</b></td>
<td class="org-right"><b>9</b></td>
</tr>
</tbody>
</table>
</section>
</section>
<section>
<section id="slide-org0b77096">
<div class="slide-header">Evaluating CAS for teaching & learning: Alasdair McAndrew, ATCM2017</div>
<h2 id="org0b77096">Case study 2: final year cryptography</h2>
<table border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
<colgroup>
<col class="org-left" />
<col class="org-center" />
<col class="org-center" />
<col class="org-center" />
<col class="org-center" />
<col class="org-center" />
</colgroup>
<thead>
<tr>
<th scope="col" class="org-left">Criterion</th>
<th scope="col" class="org-center">Mathematica</th>
<th scope="col" class="org-center">Maple</th>
<th scope="col" class="org-center">GNU Maxima</th>
<th scope="col" class="org-center">Axiom</th>
<th scope="col" class="org-center">Sage</th>
</tr>
</thead>
<tbody>
<tr>
<td class="org-left">Functionality, or fitness for purpose</td>
<td class="org-center">2</td>
<td class="org-center">1</td>
<td class="org-center">2</td>
<td class="org-center">2</td>
<td class="org-center">2</td>
</tr>
</tbody>
<tbody>
<tr>
<td class="org-left">Access</td>
<td class="org-center">0</td>
<td class="org-center">0</td>
<td class="org-center">2</td>
<td class="org-center">2</td>
<td class="org-center">2</td>
</tr>
</tbody>
<tbody>
<tr>
<td class="org-left">Cost</td>
<td class="org-center">0</td>
<td class="org-center">0</td>
<td class="org-center">2</td>
<td class="org-center">2</td>
<td class="org-center">2</td>
</tr>
</tbody>
<tbody>
<tr>
<td class="org-left">Teaching & Learning</td>
<td class="org-center">2</td>
<td class="org-center">2</td>
<td class="org-center">2</td>
<td class="org-center">2</td>
<td class="org-center">2</td>
</tr>
</tbody>
<tbody>
<tr>
<td class="org-left">Interactivity and user-friendliness</td>
<td class="org-center">2</td>
<td class="org-center">2</td>
<td class="org-center">2</td>
<td class="org-center">1</td>
<td class="org-center">2</td>
</tr>
</tbody>
<tbody>
<tr>
<td class="org-left">Organizational issues</td>
<td class="org-center">0</td>
<td class="org-center">0</td>
<td class="org-center">2</td>
<td class="org-center">2</td>
<td class="org-center">2</td>
</tr>
</tbody>
<tbody>
<tr>
<td class="org-left">Novelty</td>
<td class="org-center">2</td>
<td class="org-center">2</td>
<td class="org-center">2</td>
<td class="org-center">2</td>
<td class="org-center">2</td>
</tr>
</tbody>
<tbody>
<tr>
<td class="org-left">Students</td>
<td class="org-center">2</td>
<td class="org-center">2</td>
<td class="org-center">2</td>
<td class="org-center">2</td>
<td class="org-center">2</td>
</tr>
</tbody>
<tbody>
<tr>
<td class="org-left"><b>Total</b></td>
<td class="org-center"><b>10</b></td>
<td class="org-center"><b>9</b></td>
<td class="org-center"><b>16</b></td>
<td class="org-center"><b>15</b></td>
<td class="org-center"><b>16</b></td>
</tr>
</tbody>
</table>
</section>
</section>
<section>
<section id="slide-orgd283f0c">
<div class="slide-header">Evaluating CAS for teaching & learning: Alasdair McAndrew, ATCM2017</div>
<h2 id="orgd283f0c">Some final remarks</h2>
<ul>
<li class="fragment roll-in">These are not to be construed as definitive</li>
<li class="fragment roll-in">Your mileage may vary!</li>
<li class="fragment roll-in">This is offered as a method to help <b>you</b> decide what CAS would best suit
<b>your</b> course and <b>your</b> students</li>
<li class="fragment roll-in">Thank you all!</li>
</ul>
</section>
</section>
</div>
</div>
<p> Created by Alasdair </p>
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overview: true,
width: 1200,
minScale: 0.50,
theme: Reveal.getQueryHash().theme, // available themes are in /css/theme
transition: Reveal.getQueryHash().transition || 'None', // default/cube/page/concave/zoom/linear/fade/none
transitionSpeed: 'default',
multiplex: {
secret: '', // null if client
id: '', // id, obtained from socket.io server
url: '' // Location of socket.io server
},
// Optional libraries used to extend on reveal.js
dependencies: [
{ src: './plugin/highlight/highlight.js', async: true, callback: function() { hljs.initHighlightingOnLoad(); } },
{ src: './plugin/markdown/marked.js', condition: function() { return !!document.querySelector( '[data-markdown]' ); } },
{ src: './plugin/markdown/markdown.js', condition: function() { return !!document.querySelector( '[data-markdown]' ); } },
{ src: './plugin/notes/notes.js', async: true, condition: function() { return !!document.body.classList; } },
]
});
</script>
</body>
</html>