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AIMSA2010, Sep 10th 2010 "Ontology-Based Authoring of Intelligent Math Tutors ", D.Sklavakis & I. Refanidis 1 Ontology-Based Authoring of Intelligent Model-Tracing.

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Presentation on theme: "AIMSA2010, Sep 10th 2010 "Ontology-Based Authoring of Intelligent Math Tutors ", D.Sklavakis & I. Refanidis 1 Ontology-Based Authoring of Intelligent Model-Tracing."— Presentation transcript:

1 AIMSA2010, Sep 10th 2010 "Ontology-Based Authoring of Intelligent Math Tutors ", D.Sklavakis & I. Refanidis 1 Ontology-Based Authoring of Intelligent Model-Tracing Math Tutors Dimitrios Sklavakis and Ioannis Refanidis dsklavakis@uom.grdsklavakis@uom.gr, yrefranid@uom.gryrefranid@uom.gr Department of Applied Informatics Univercity of Macedonia Thessaloniki GREECE

2 AIMSA2010, Sep 10th 2010 "Ontology-Based Authoring of Intelligent Math Tutors ", D.Sklavakis & I. Refanidis 2 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

3 AIMSA2010, Sep 10th 2010 "Ontology-Based Authoring of Intelligent Math Tutors ", D.Sklavakis & I. Refanidis 3 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

4 AIMSA2010, Sep 10th 2010 "Ontology-Based Authoring of Intelligent Math Tutors ", D.Sklavakis & I. Refanidis 4 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

5 AIMSA2010, Sep 10th 2010 "Ontology-Based Authoring of Intelligent Math Tutors ", D.Sklavakis & I. Refanidis 5 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

6 AIMSA2010, Sep 10th 2010 "Ontology-Based Authoring of Intelligent Math Tutors ", D.Sklavakis & I. Refanidis 6 The OWL-S Process Model: Ontological Representation of Procedural Knowledge Part of the OWL-S process model used by the MATHESIS ontology

7 AIMSA2010, Sep 10th 2010 "Ontology-Based Authoring of Intelligent Math Tutors ", D.Sklavakis & I. Refanidis 7 The OWL-S Process Model: Visual Representation of a Composite Process’ Structure A 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

8 AIMSA2010, Sep 10th 2010 "Ontology-Based Authoring of Intelligent Math Tutors ", D.Sklavakis & I. Refanidis 8 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.

9 Representing the Authoring Model: Part of the Composite Authoring Tasks Ontology AIMSA2010, Sep 10th 2010 "Ontology-Based Authoring of Intelligent Math Tutors ", D.Sklavakis & I. Refanidis 9

10 Representing the Authoring Model: Part of the Atomic Authoring Statements Ontology AIMSA2010, Sep 10th 2010 "Ontology-Based Authoring of Intelligent Math Tutors ", D.Sklavakis & I. Refanidis 10

11 AIMSA2010, Sep 10th 2010 "Ontology-Based Authoring of Intelligent Math Tutors ", D.Sklavakis & I. Refanidis 11 Representing the Authoring Model: “Interpreting” the authoring processes For each tutoring task… There is a correspon- ding authoring process… …which can be further refined.

12 AIMSA2010, Sep 10th 2010 "Ontology-Based Authoring of Intelligent Math Tutors ", D.Sklavakis & I. Refanidis 12 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

13 AIMSA2010, Sep 10th 2010 "Ontology-Based Authoring of Intelligent Math Tutors ", D.Sklavakis & I. Refanidis 13 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

14 AIMSA2010, Sep 10th 2010 "Ontology-Based Authoring of Intelligent Math Tutors ", D.Sklavakis & I. Refanidis 14 The Low-Level Ontology: Interface Representation

15 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 201015 "Ontology-Based Authoring of Intelligent Math Tutors ", D.Sklavakis & I. Refanidis

16 AIMSA2010, Sep 10th 2010 "Ontology-Based Authoring of Intelligent Math Tutors ", D.Sklavakis & I. Refanidis 16 The MATHESIS Ontology Further 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)

17 AIMSA2010, Sep 10th 2010 "Ontology-Based Authoring of Intelligent Math Tutors ", D.Sklavakis & I. Refanidis 17 The MATHESIS Ontology Discussion 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

18 AIMSA2010, Sep 10th 2010 "Ontology-Based Authoring of Intelligent Math Tutors ", D.Sklavakis & I. Refanidis 18 Thank you! You May Find More About The MATHESIS Project at http://users.uom.gr/~dsklavakis Interactive Event at 7pm

19 AIMSA2010, Sep 10th 2010 "Ontology-Based Authoring of Intelligent Math Tutors ", D.Sklavakis & I. Refanidis 19 Representing the Authoring Model: The define_data_structures_for_knowledge_components authoring task process

20 AIMSA2010, Sep 10th 2010 "Ontology-Based Authoring of Intelligent Math Tutors ", D.Sklavakis & I. Refanidis 20 Representing the Authoring Model: The Task_Execution_By_Expert authoring task process

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