Ontology-Based Authoring of Intelligent Model-Tracing Math Tutors

AIMSA2010, Sep 10th 2010

"Ontology-Based Authoring of Intelligent Math Tutors ",

D.Sklavakis & I. Refanidis 1

Ontology-Based Authoring ofIntelligent Model-Tracing Math

Tutors

Dimitrios Sklavakis and Ioannis [email protected], [email protected]

Department of Applied InformaticsUnivercity of Macedonia

ThessalonikiGREECE




Overview The MATHESIS Project

Bottom-up approach The MATHESIS Algebra Tutor

Tutor Representation in MATHESIS Ontology The OWL-S process model The Tutoring model The Authoring model The Program code model The Interface model

Further Work Discussion




The MATHESIS Project Approach:

Bottom – Up Ontological Engineering

The MATHESIS Algebra/Math Tutor(s):

Declarative and Procedural Knowledge hard-coded in HTML and JavaScript

The MATHESIS Ontology:

Declarative description of the User Interface, Domain Model, Tutoring Model, Student Model and Authoring Model( OWL and

OWL-S)

The MATHESIS Authoring Tools:

Guiding Tutor Authoring Through Searching in the Ontology and “Interpreting” the Authoring Model (OWL-S Processes)

Domain Experts’ Knowledge: Domain + Tutoring + Assessing + Programming




The MATHESIS Algebra Tutor

Web-based User Interface: HTML + JavaScript Specialized math editing applets: WebEq by Design

Science Declarative Knowledge: JavaScript variables and

Objects Procedural Knowledge: JavaScript functions Domain cognitive model

Top-level skills (20) : algebraic operations (7), identities (5) , factoring (8)

Detailed cognitive task analysis gives a total of 104 cognitive (sub)skills

Detailed hint and error messages for all of the above




MATHESIS Algebra Tutor Screenshot

Help, Hint and Error Messages Area

WebEq Input Control for the Algebraic Expression being Rewriten

WebEq Input Control for Student Answers

WebEq Input Control for Intermediate Results




The OWL-S Process Model:Ontological Representation of Procedural

Knowledge Part of the

OWL-S process model

used by the

MATHESIS

ontology


"Ontology-Based Authoring of Intelligent Math Tutors ", D.Sklavakis

& I. Refanidis 7

The OWL-S Process Model:Visual Representation of a Composite

Process’ StructureA composite process is a tree whose non-terminal nodes are control constructs

Leaf nodes are invocations of other processes, composite or simple (Perform constructs)

In MATHESIS Ontology, procedural knowledge is represented as composite processes




Representing the Tutoring Model:

The Model-Tracing Process(KVL variation)

Being procedural knowledge…

…the model-tracing algorithm is represented as a composite porcess…

…calling other composite processes for each tutoring task.

Representing the Authoring Model:

Part of the Composite Authoring Tasks Ontology





Part of the Atomic Authoring Statements Ontology








“Interpreting” the authoring processes

For each tutoring task…

There is a correspon-ding authoring process…

…which can be further refined.




From processes to code: monomial multiplication

var pos;var i;var vars1 = parsedMonomials[0].variables;var vars2 = parsedMonomials[1].variables.concat([]);var n1 = vars1.length;var n2 = vars2.length;var exps1 = parsedMonomials[0].exponents;var exps2 = parsedMonomials[1].exponents;for(i=0; i < n1 ; i++) {

parsedMonomials[2].variables.push(vars1[i]); pos = getVariablePosition(vars1[i],vars2); if(pos == -1) { parsedMonomials[2].exponents.push(exps1[i]); var sum = exps1[i]; } else { var sum = parseInt(exps1[i]) + parseInt(exps2[pos]); parsedMonomials[2].exponents.push(sum); vars2[pos] = ""; } for(var j=0; j < n2; j++) { if(vars2[j] != "") { parsedMonomials[2].variables.push(vars2[j]); parsedMonomials[2].exponents.push(exps2[j]); } }

Part of the model-tracing process adapted to monomial multiplication

The monomial_multiplication_execution process

Atomic processes are JavaScriptStatement individuals

JavaScript program lines are JavaScriptProgramLine

individuals

hasJavaScriptCode

hasJavaScriptStatement




The Low-Level Ontology:JavaScript Code Representation

JavaScript code is represented as a special kind of atomic process, the JavaScriptStatement

Every JavaScriptStatement has a corresponding JavaScript_ProgramLine…

…which holds the actual JavaScript code




The Low-Level Ontology:Interface Representation

Interface Representation

…which defines corresponding HTMLObject(s).

Every line of HTML code is represented as an HTML_ProgramLine…

HTMLObject(s) are connected via their hasFirstChild and hasNextSibling properties to represent the DOM

AIMSA2010, Sep 10th 2010 15


D.Sklavakis & I. Refanidis




The MATHESIS OntologyFurther Work

Extend, Refine, Formalise the Ontology Represent the Algebra Tutor in the Ontology Create Authoring Tools:

Parsers HTML ↔ MATHESIS Interface model Parsers JavaScript ↔ JavaScriptStatements Interpreter (“tracer”) for the OWL-S processes Visualisation Tools for the authoring processes

and the authored tutor parts (tutoring, domain, student models, interface and program code)


"Ontology-Based Authoring of Intelligent Math Tutors ", D.Sklavakis

& I. Refanidis 17

The MATHESIS OntologyDiscussion

Being an Ontology, it has all known advantages and disadvantages of ontologies

New approach: ontological representation of procedural knowledge (rules) through OWL-S processes.

Both authoring and authored knowledge share the same representation and lie in the same place

Newly authored tutors become new knowledge to be used for the next ones

Maximum knowledge reuse anticipated




Thank you!You May Find More About The

MATHESIS Project at http://users.uom.gr/~dsklavakis

Interactive Event at 7pm

Documents

Ontology-Based Authoring of Intelligent Model-Tracing Math Tutors