Math-Bridge Edit Authoring

Joint Math-Bridge Training
Program
Michael Dietrich (DFKI)
Source Based Authoring Basics
10.07.2015 Saarbrücken

Learning Objects
• In Math-Bridge: Atomic units of knowledge
• Reusable
– Adressable
– Authors have to keep reusablity in mind
• Can be structured
– Table Of Contents (Authors/Users)
– Theories and Collections (Authors)
• Are typed

Different Learning Objects (i)
• Axiom: statement on elements of a theory
• Definition: A statement, defining the meaning
of some elements of a theory
• Assertion: A statement on elements of a
theory. Different types available “theorem”,
“lemma”, etc.
• Proof: Proof of an assertion

Different Learning Objects (ii)
• Example: an Example
• Exercise: an exercise training some
competencies of a LO
• Omtext: different types of text elements i.e.
“introduction”, “conclusion”, “motivation” …
• Ppmethod: Special type for mathematical
methods . Rarely used

Hands-On
• Example content on straight lines
• Annotate example content
– Decompose in learning objects
– Specify type of learning objects
• Types:
– Axiom, Definition, Assertion, Proof, Example,
Exercise, Omtext

Relations between learning Objects
• Obviously there are relations between
learning objects like example for an axiom.
• Modelling by relations.
• The for-relation is an important one.
• It represents that one LO is supporting
another
Example 1+1 Definition TermFOR

Differentiation Of Learning Objects
• For-relation partitions learning objects
– Learning objects, which can occur “standalone”
• Axiom, Definition, …
• Terminology: Concepts
– Learning objects, which support other LOs:
• Example, Exercise, …
• Terminology: Satellites
• Often we have:
Satellite ConceptFOR

Hands-On
• Identify for-relations in example content
• Content is separated in two layers
Content layer
Satellite layer
Definition Axiom Assertion Proof
OmtextExerciseExample
FOR

Problem: Abstract Concepts
• Some (mathematical) concepts can be defined
in different ways
• Logarithm ln(x)…
– …as primitive of x-1
– …as Inverse of ex
• Solution: Symbol Learning Object
• Symbols represents abstract concepts.

Symbols
• Symbol learning object that represents an
atomic (mathematical) concept being part of a
formal theory
• Example:
• New layer of learning objects
Ln(x)
Defined using x-1 Defined using ex

Layers of Learning Objects
Concept Layer
Satellite Layer
FOR
Abstract Layer Symbol
FOR

Pyramid of Learning Objects
Symbols
Concepts
Satellites

Hands-On
• Find symbols and corresponding for-relations

One More Relation
• We cannot say currently:
– Addition is prerequisite for multiplication
• Solution: New relation domain-prerequisite
• Used to specify prerequisites
• Used in MathBridge:
– Search
– Tutorial Component (Course Generation)
– User model

Hands-On
• Find all domain-prerequisite relations in
example content

Summary (i)
• Saw learning objects:
Content Layer
Satellite Layer
Abstract Layer Symbol

Summary (ii)
• Saw two most important Math-Bridge
relations:
– For
• Learning object is supporting another
– domain-prerequisite
• Learning object is prerequisite of another

Representation of Learning Objects
• Knowledge Representation – Discipline of AI
• In our case – a lot of markup
• Format must be reuseable
• Format should separate content from
presentation
• Different output formats should be possible
– XML is very suitable here

Using XML for Representation
• Can store and annotate data in a structured
way
– <adresse art=“postanschrift”>
• <strasse>Stuhlsatzenhausweg</strasse>
• <hausnummer>3</hausnummer>
• <plz>66123</plz>
• <ort>Saarbrücken</ort>
– </adresse>

XML language Elements
• Tags
– ‘Markup’
– Provide structure to documents
– <adresse> … </adresse>
• Attributes
– Used inside tags
– <adresse art=‘…’>…
• Disadvantage : is unreadable fast

Differences
• Hands-on shows: Rules are needed
• Can define language using DTD, RNG, XSD
• Many projects for mathematical markup
• Have different goals
• Use different technologies

Representation of Mathematics
• Syntactic:
– LaTeX, MathML Presentation
• Semantic:
– OpenMath, MathML Content
• Formal:
– HELM, TPTP
• OMDoc is a language basing on OpenMath
• Extended for Math-Bridge

OMDoc – Learning objects
• Representing Learning Objects using OMDoc:
<definition id="def_interval”>
<CMP>Eine Teilmenge der reellen Zahlen heißt
Intervall.</CMP>
</definition>
• All learning object types have a similar
structure in OMDoc

OMDoc: for
• For-relation can be given as an attribute:
<definition id="def_interval”
for=“sym_interval”>
<CMP>Eine Teilmenge der reellen Zahlen heißt
Intervall.</CMP>
</definition>

OMDoc: domain-prerequisite
<definition id="def_interval” for=“sym_interval”>
<metadata>
<extradata>
<relation type=“domain-prerequisite”>
<ref xref=“sym_reals”/>
</relation>
</extradata>
</metadata>
<CMP>Eine Teilmenge der reellen Zahlen heißt Intervall.</CMP>
</definition>

Formulæ in OMDoc (forecast)
• OMDoc: Extension of OpenMath
• Formulæ coded using OMDoc
• 1+1 in OpenMath:
<OMOBJ>
<OMA>
<OMS cd="arith1" name="plus”/>
<OMI>1</OMI>
<OMI>1</OMI>
</OMA>
</OMOBJ>

Polynomial in OMDoc
<OMOBJ>
<OMA>
<OMS cd="relation1" name="eq" />
<OMA>
<OMS name="plus" cd="arith1" />
<OMA>
<OMS name="power" cd="arith1" /><OMV name="X" /><OMI>2</OMI>
</OMA>
<OMA>
<OMS cd="arith1" name="power" /><OMV name="Y" /><OMI>3</OMI>
</OMA>
</OMA>
<OMI>0</OMI>
</OMA>
</OMOBJ>

QMath
• Produces OMDoc from text files
• Instead
– <OMOBJ><OMA><OMS cd="arith1”
name="plus”/><OMI>1</OMI><OMI>1</OMI></OMA></OMOBJ>
– 1+1
• Polynomial from previous slide is: X^2+Y^3=0
• Formulæ in text:
– Find solutions of $X^2+Y^3=0$.

Structuring Of Learning Objects
• Constructs for structuring LOs:
– Theory
• Set of strongly related learning objects
• Like ‘Add fraction’, ‘Multiply fractions’
– Collection
• Set of Theories, with strong relations
• Example: ‘Fractions Arithmetics’
• OMGroup used to present Los in a structured
way.

Tools for Omdoc+QMath
• Main Development-tool: JEditOQMath
– Basing on Jedit an open source editor by Slava
Pestov
• Contains many useful plugins
• Controls QMath functionalities
– Templates for learning objects
– Communikation with Math-Bridge-server
– Integrates Qmath
– Direct feedback on errors

Get jEdit
• Copy jEdit.zip to HDD
• Unpack
• Start by
– java –Xmx512M –jar jedit.jar& (*nix, Mac)
– Doubleclick jedit.jar

jEdit Config
• Configure OQMath Plugin
• Set Math-Bridge URL
– Plugins – Plugin Options...
– OQMath Jedit
– Enter URL
• Specify Math-Bridge location
– analogue

jEdit Test
• OQMath – Start a collection
• Provide a name
• Let the magic happen
• Restart Math-Bridge
• Visit new collection with browser

Math-Bridge Edit Authoring

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