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Ontology-Based Authoring of Intelligent Model-Tracing Math Tutors

Ontology-Based Authoring of Intelligent Model-Tracing Math Tutors. Dimitrios Sklavakis and Ioannis Refanidis dsklavakis@uom.gr , yrefranid@uom.gr Department of Applied Informatics Univercity of Macedonia Thessaloniki GREECE. Overview. The MATHESIS Project Bottom-up approach

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Ontology-Based Authoring of Intelligent Model-Tracing Math Tutors

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

  3. The MATHESIS Project Approach:Bottom – Up Ontological Engineering The MATHESIS Authoring Tools: Guiding Tutor Authoring Through Searching in the Ontology and “Interpreting” the Authoring Model (OWL-S Processes) The MATHESIS Ontology: Declarative description of the User Interface, Domain Model, Tutoring Model, Student Model and Authoring Model( OWL and OWL-S) The MATHESIS Algebra/Math Tutor(s): Declarative and Procedural Knowledge hard-coded in HTML and JavaScript Domain Experts’ Knowledge: Domain + Tutoring + Assessing + Programming "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 "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 Student Answers WebEq Input Control for the Algebraic Expression being Rewriten WebEq Input Control for Intermediate Results "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 "Ontology-Based Authoring of Intelligent Math Tutors ", D.Sklavakis & I. Refanidis

  7. The OWL-S Process Model:VisualRepresentation 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 "Ontology-Based Authoring of Intelligent Math Tutors ", D.Sklavakis & I. Refanidis

  8. Representing the Tutoring Model:The Model-Tracing Process(KVL variation) …calling other composite processes for each tutoring task. Being procedural knowledge… …the model-tracing algorithm is represented as a composite porcess… "Ontology-Based Authoring of Intelligent Math Tutors ", D.Sklavakis & I. Refanidis

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

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

  12. From processes to code: monomial multiplication Part of the model-tracing process adapted to monomial multiplication The monomial_multiplication_execution process 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]); } } Atomic processes are JavaScriptStatement individuals hasJavaScriptCode hasJavaScriptStatement JavaScript program lines are JavaScriptProgramLine individuals "Ontology-Based Authoring of Intelligent Math Tutors ", D.Sklavakis & I. Refanidis

  13. The Low-Level Ontology:JavaScript Code Representation Every JavaScriptStatement has a corresponding JavaScript_ProgramLine… JavaScript code is represented as a special kind of atomic process, the JavaScriptStatement …which holds the actual JavaScript code "Ontology-Based Authoring of Intelligent Math Tutors ", D.Sklavakis & I. Refanidis

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

  15. Every line of HTML code is represented as an HTML_ProgramLine… …which defines corresponding HTMLObject(s). HTMLObject(s) are connected via their hasFirstChild and hasNextSibling properties to represent the DOM Interface Representation "Ontology-Based Authoring of Intelligent Math Tutors ", D.Sklavakis & I. Refanidis

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

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