Math-Bridge Edit Authoring

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

2. 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

3. 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

4. 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

5. 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

6. 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

7. 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

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

9. 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.

10. 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

11. Layers of Learning Objects
Concept Layer
Satellite Layer
Definition Axiom Assertion Proof
OmtextExerciseExample
FOR
Abstract Layer Symbol
FOR

12. Pyramid of Learning Objects
Symbols
Concepts
Satellites

13. Hands-On
• Find symbols and corresponding for-relations

14. 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

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

16. Summary (i)
• Saw learning objects:
Content Layer
Satellite Layer
Definition Axiom Assertion Proof
OmtextExerciseExample
Abstract Layer Symbol

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

18. 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

19. 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>

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

21. Hands-On
• Write as XML

22. 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

23. 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

24. 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

25. 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>

26. 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>

27. 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>

28. 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>

29. 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 $X^2+Y^3=0$.

30. 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.

31. 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

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

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

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