The Cardiff Maths e-Learning Project

CaMEL The Cardiﬀ Maths eLearning Project Dafydd Evans Cardiff School
of Mathematics DjangoCon Europe 1st June 2015

DjangoCon Europe 2015 Contents 1 Motivation 3 2 Typesetting 4
3 The Cardiﬀ Maths eLearning Project 9 4 Next steps 14 D Evans Cardiff School of Mathematics 2

DjangoCon Europe 2015 1 Motivation Writing mathematics requires speciﬁc layouts
and fonts. (1) Learning materials. • Teachers produce high-quality PDF documents using L A TEX. • PDF documents lack interactive capabilities. (2) Homework submission and feedback. • Students submit handwritten solutions to homework questions. • Teachers marks and returns the scripts Can L A TEX documents be used as the basis of an e-learning system for mathematics? D Evans Cardiff School of Mathematics 3

DjangoCon Europe 2015 2 Typesetting • Basic building blocks are
letters, numerals and symbols. These are collectively known as glyphs. • Groups of glyphs are called fonts. • Groups of fonts sharing particular design fea- tures are called typefaces. • Computer Modern typefaces for mathematics created by Donald Knuth for TEX (1978) • TEX extended to L A TEX by Leslie Lamport (1984). • L A TEX is the de-facto standard for typesetting mathematical articles and books. D Evans Cardiff School of Mathematics 4

DjangoCon Europe 2015 2.1 Mark-up Languages LaTeX -> PDF HTML
-> Web \documentclass{book} \title{My Book} \begin{document} %comment \maketitle \chapter{Introduction} Hello world. \begin{equation}\label{eq:gauss} \int_{- \infty }^{+ \infty} e^{-x^2}dx = \sqrt{\pi}. \end{equation} \end{document} <html > <head > <title >My Book </title > </head> <body >  <h1>Introduction </h1> Hello world! <equation id="eq:gauss"> oops! </equation > </body> </html > • Mark-up used to deﬁne structure, styles, cross-references and citations. • L A TEX documents are not “well-formed”. D Evans Cardiff School of Mathematics 5

DjangoCon Europe 2015 2.2 L A TEX Structural mark-up \chapter,\section,...
\begin{equation}...\end{equation} Stylistic mark-up \textbf,\textit,... \alpha,\pi,\partial,... Cross-references and citations \label,\ref,\cite. Extensible \begin{homework}...\end{homework} \question \documentclass{camel} \title{Lecture Notes} \begin{document} \maketitle \chapter{Introduction}\label{ch:intro} Hello world. \begin{equation}\label{eq:gauss} \int_{-\infty }^{+ \infty} e^{-x^2}dx = \sqrt{\pi}. \end{equation} \chapter{Background} In Chapter~\ref{ch:intro} we saw ... \begin{homework} \begin{questions} \question Area of a circle? \begin{answer} $A = \pi r^2$ \end{answer} \end{questions} \end{homework} \end{document} D Evans Cardiff School of Mathematics 6

DjangoCon Europe 2015 2.3 Yet Another L A TEX Parser
• Implemented in python. • Source ﬁle processed using regular expressions and a stack (pushdown automaton). • Output is a so-called materialized path tree. • Numbering implemented using class variables. • Mathmode environments/commands left for MathJax to handle. latex_node_types = { level : ( book , chapter , section , subsection ), theorem : ( definition , theorem , lemma , remark , example , exercise ), mathmode : ( equation , eqnarray , array , align , cases ), list : ( itemize , enumerate , questions , parts , subparts , choices ), item : ( item , question , part , subpart , choice , correctchoice ), float : ( table , figure , subtable , subfigure ), box : ( proof , solution , answer , hint ), assignment : ( homework , mctest ), content : ( jax , image , reference , citation ), } D Evans Cardiff School of Mathematics 7

DjangoCon Europe 2015 <book > <chapter label="ch:intro" number="1" title="Introduction"> <jax>Hello
world. \begin{equation} \int_{-\infty }^{+\ infty} e^{-x^2}dx = \sqrt {\pi}. \end{equation}</jax> </chapter > <chapter number="2" title="Background"> <jax>In Chapter </jax> <ref target="ch:intro">1</ref> <jax>we saw ...</jax> <homework number="1"> <questions number="1"> <question number="1"> <jax>Area of a circle?</jax> <answer > <jax>$A = \pi r^2$</jax> </answer > </question > </questions > </homework > </chapter > </book > D Evans Cardiff School of Mathematics 8

DjangoCon Europe 2015 3 The CaMEL project pdf xml latex
doctree models database views templates web Models • BookNode: node_type, number, title, content, mpath • Label: label_text, target_mpath • Answer: user, question, text • Submission: user, assignment http://github.com/dimbyd/camel/ D Evans Cardiff School of Mathematics 9

DjangoCon Europe 2015 3.1 django-mptt Modified Preorder Tree Traversal (MPTT)
is a technique for storing and accessing hierarchical data in a database. • Retrieval operations are efficient. • Inserts, moves and deletions are comparatively expensive. The django-mptt app makes it very easy to use MPTT with Django models. • Models are defined as subclasses of mptt.models.MPTTModel. • Tree updated automatically when model instances are inserted/moved/deleted. • Instance methods: get_ancestors(), get_children(), etc. • Custom form fields provided by the mptt.forms package. • Template tags and filters for rendering trees recursively. http://github.com/django-mptt/django-mptt/ D Evans Cardiff School of Mathematics 10

DjangoCon Europe 2015 models.py c l a s s BookNode(
M P T T M o d e l ): parent = T r e e F o r e i g n K e y ( s e l f , null=True , related_name= children ) node_type = models. C h a r F i e l d (max_length =10) number = P o s i t i v e S m a l l I n t e g e r F i e l d (null=True) title = C h a r F i e l d (max_length =100, null=True , blank=False) content = T e x t F i e l d (null=True) mpath = C h a r F i e l d (max_length =100, null=True) views.py context[ chapter ] = BookNode.objects.get( pk=pk ) context[ subtree ] = context[ chapter ]. get_descendants(include_ s e l f =True) template.html {% load mptt_tags %} {% recursetree subtree %} {% if node.node_type == "chapter" %} <div class="chapter"> <h1 class="chapter">{{ node.number }}. {{ node.title }}</h1> {{ children }} </div> {% elif %} ... D Evans Cardiff School of Mathematics 11

DjangoCon Europe 2015 3.2 Custom L A TEX environments for
interaction The following were inspired by exam.cls (written by Phil Hirschhorn, MIT). Free-text answers \begin{homework} \begin{questions} \question First Question. \begin{solution} Solution of First Question. \end{solution} \question Second Question. \begin{solution} Solution of Second Question. \end{solution} \end{questions} \end{homework} Multiple-choice answers \begin{mctest} \begin{questions} \question Which is the odd one out? \begin{choices} \choice John \choice Paul \choice George \correctchoice Dingo \end{choices} \end{questions} \end{mctest} D Evans Cardiff School of Mathematics 12

DjangoCon Europe 2015 3.3 Database schema student module book submission
homework answer question D Evans Cardiff School of Mathematics 13

DjangoCon Europe 2015 4 Next steps Django • Admin pages
• Teacher pages • Visualisation • Partial updates using labels • PDFs of homework submissions • Beautify URLs Python • GitHub • Exception handling • Unit tests • Logging • DocBook and MathML schemas. D Evans Cardiff School of Mathematics 14

The Cardiff Maths e-Learning Project

The Cardiff Maths e-Learning Project

Dafydd Evans

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CaMEL The Cardiﬀ Maths eLearning Project Dafydd Evans Cardiff School

DjangoCon Europe 2015 Contents 1 Motivation 3 2 Typesetting 4

DjangoCon Europe 2015 1 Motivation Writing mathematics requires speciﬁc layouts

DjangoCon Europe 2015 2 Typesetting • Basic building blocks are

DjangoCon Europe 2015 2.1 Mark-up Languages LaTeX -> PDF HTML

DjangoCon Europe 2015 2.2 L A TEX Structural mark-up \chapter,\section,...

DjangoCon Europe 2015 2.3 Yet Another L A TEX Parser

DjangoCon Europe 2015 <book > <chapter label="ch:intro" number="1" title="Introduction"> <jax>Hello

DjangoCon Europe 2015 3 The CaMEL project pdf xml latex

DjangoCon Europe 2015 3.1 django-mptt Modiﬁed Preorder Tree Traversal (MPTT)

DjangoCon Europe 2015 models.py c l a s s BookNode(

DjangoCon Europe 2015 3.2 Custom L A TEX environments for

DjangoCon Europe 2015 3.3 Database schema student module book submission

DjangoCon Europe 2015 4 Next steps Django • Admin pages