1. SWEL09, July 7th 2009 "The MATHESIS Ontology", D.Sklavakis & I. Refanidis 1 The MATHESIS Ontology: Reusable Authoring Knowledge for Reusable Intelligent 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. SWEL09, July 7th 2009 "The MATHESIS Ontology", 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. SWEL09, July 7th 2009 "The MATHESIS Ontology", 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. SWEL09, July 7th 2009 "The MATHESIS Ontology", 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. SWEL09, July 7th 2009 "The MATHESIS Ontology", 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. SWEL09, July 7th 2009 "The MATHESIS Ontology", D.Sklavakis & I. Refanidis 6 The OWL-S Process Model: Ontological Representation of Procedural Knowledge 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

7. SWEL09, July 7th 2009 "The MATHESIS Ontology", D.Sklavakis & I. Refanidis 7 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.

8. SWEL09, July 7th 2009 "The MATHESIS Ontology", D.Sklavakis & I. Refanidis 8 Representing the Authoring Model: “Interpreting” the authoring processes The Model-Tracing process The Execute_Task_By_Expert authoring process The define_data_structures_for_knowledge_components authoring process For each tutoring task… There is an authoring process… …which can be further refined.

9. SWEL09, July 7th 2009 "The MATHESIS Ontology", D.Sklavakis & I. Refanidis 9 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

10. SWEL09, July 7th 2009 "The MATHESIS Ontology", D.Sklavakis & I. Refanidis 10 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

11. SWEL09, July 7th 2009 "The MATHESIS Ontology", D.Sklavakis & I. Refanidis 11 The Low-Level Ontology: Interface Representation

12. 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

13. SWEL09, July 7th 2009 "The MATHESIS Ontology", D.Sklavakis & I. Refanidis 13 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)

14. SWEL09, July 7th 2009 "The MATHESIS Ontology", D.Sklavakis & I. Refanidis 14 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

15. SWEL09, July 7th 2009 "The MATHESIS Ontology", D.Sklavakis & I. Refanidis 15 Thank you! You May Visit The MATHESIS Algebra Tutor Interactive Event at 7pm

16. SWEL09, July 7th 2009 "The MATHESIS Ontology", D.Sklavakis & I. Refanidis 16 Representing the Authoring Model: The define_data_structures_for_knowledge_components authoring task process

17. SWEL09, July 7th 2009 "The MATHESIS Ontology", D.Sklavakis & I. Refanidis 17 Representing the Authoring Model: The Task_Execution_By_Expert authoring task process