An Individualized Web-Based Algebra Tutor Based on Dynamic Deep Model Tracing

1. An Individualized Web-Based Algebra Tutor Based on Dynamic Deep Model Tracing Dimitrios Sklavakis and Ioannis Refanidis dsklavakis@uom.gr, yrefranid@uom.gr Department of Applied Informatics Univercity of Macedonia Thessaloniki GREECE An Individualized Web-Based Algebra Tutor D.Sklavakis & I. Refanidis

2. Outline • The MATHESIS Project • Introduction: Cognitive Tutors • Motivation: Cognitive Tutors Successful Paradigm • Goals: Authoring Tools for Cognitive Tutors • Research approach: Bottom - Up • The MATHESIS Algebra Tutor • Web-based • Deep Cognitive Model Tracing • Broad Knowledge Monitoring • Related Work • Cognitive Tutor Authoring Tools (Carnegie Mellon) • Future Work • Ontology • Authoring Tools An Individualized Web-Based Algebra Tutor D.Sklavakis & I. Refanidis

3. The MATHESIS Project • Cognitive Tutors • Motivation • Goals • Research approach An Individualized Web-Based Algebra Tutor D.Sklavakis & I. Refanidis

4. The MATHESIS Project Cognitive Tutors • Model-tracing ITS build at Carnegie Mellon University • Learning by Doing: Problem-solving environment with interactive tools • Step by step tutorial guidance with feedback messages (correct, error, hints) • Can handle multiple solution paths • Adaptive problem selection and student pacing An Individualized Web-Based Algebra Tutor D.Sklavakis & I. Refanidis

5. The MATHESIS ProjectCognitive Tutors and the ACT-R theory • Adaptive Control of Thought-Rational: • Cognitive Theory of Learning and Performance • Learning by doing not by watching and listening • Cognitive Model Based on the ACT-R theory: • Problem solving knowledge is made of cognitive skills • A cognitive skill consists of: • Procedural knowledge: IF…THEN production rules • Declarative knowledge: Facts consisting of property-value pairs An Individualized Web-Based Algebra Tutor D.Sklavakis & I. Refanidis

6. Cognitive Tutor Technology:Use ACT-R theory to individualize instruction • Cognitive Model: A system that can solve problems in the various ways students can 3(2x - 5) = 9 If goal is solve a(bx+c) = d Then rewrite as abx + ac = d If goal is solve a(bx+c) = d Then rewrite as abx + c = d If goal is solve a(bx+c) = d Then rewrite as bx+c = d/a Hint: You must distribute a over bx and c Bug message: You must also multiply a by c Known = 85% Known =45% 6x - 15 = 9 2x - 5 = 3 6x - 5 = 9 • Model Tracing: The tutor matches the student’s steps against the solution produced by the cognitive model → context-sensitive instruction • Knowledge Tracing: The tutor records cognitive skill learning from problem to problem → individualized activity selection and pacing An Individualized Web-Based Algebra Tutor D.Sklavakis & I. Refanidis

7. The MATHESIS Project Motivation:Cognitive Tutors’ Real-world Success • Algebra Cognitive Tutor in over 2.000 schools in the USA, 300.000 students per year. • Geometry Cognitive Tutor in 350 schools • Approved by the U.S. Dept. of Education • Full year classroom experiments show significant efficiency gains: • 50-100% better on problem solving & representation use. • 15-25% better on standardized tests. An Individualized Web-Based Algebra Tutor D.Sklavakis & I. Refanidis

8. The MATHESIS Project Goal:Authoring Tools for Math Cognitive Tutors • Development costs of instructional technology are high • Approximately 300 development hours per hour of instruction for Computer Aided Instruction • Cognitive Tutors: • Approximately 200 development hours per hour of instruction • Requires PhD level cognitive scientists and AI programmers • Solution: Easy to use Cognitive Tutor Authoring Tools An Individualized Web-Based Algebra Tutor D.Sklavakis & I. Refanidis

9. The MATHESIS Project Approach:Bottom – Up Ontological Engineering The MATHESIS Authoring Tools: Guiding Tutor Authoring Through Searching in the Ontology The MATHESIS Ontology: Declarative description of the User Interface, Domain Model, Tutoring Model, Student Model and Authoring Model The MATHESIS Algebra/Math Tutor(s): Declarative and Procedural Knowledge hard-coded in a programming language Domain Experts’ Knowledge: Domain + Tutoring + Assessing + Programming An Individualized Web-Based Algebra Tutor D.Sklavakis & I. Refanidis

10. 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 An Individualized Web-Based Algebra Tutor D.Sklavakis & I. Refanidis

11. The MATHESIS Algebra Tutor • Tutoring model: deep cognitive model tracing through knowledge reuse When tutoring a cognitive skill, e.g. polynomial-multiplication the tutor traces the cognitive model for each one of the monomial-multiplications • Student model: broad knowledge monitoring • The tutor records and timestamps in a database the student’s performance for each skill that is tutored, giving a percentage assessment of cognitive skill learning over time • The tutor records in a database all the student’s interactions with the interface so that they can be re-traced at any time An Individualized Web-Based Algebra Tutor D.Sklavakis & I. Refanidis

12. MATHESIS Algebra Tutor Demo An Individualized Web-Based Algebra Tutor D.Sklavakis & I. Refanidis

13. Related WorkCMU Cognitive Tutor Authoring Tools • Example-tracing tutors: • Built through “programming by demonstration” • Authors create Examples of how the students should solve specific problems • For each solution step the author enters the answer • Cognitive Tutors • Built through Cognitive Task Analysis • Authors create Cognitive Models of how the students should solve a range of problems • For each solution step the author enters production rules • CTAT mainly supports Example-tracing Tutors An Individualized Web-Based Algebra Tutor D.Sklavakis & I. Refanidis

14. Future Work • Ontological Engineering • Build a declarative description of the Algebra Tutor’s knowledge (Interface, Domain, Tutoring and Student models) • Build an Authoring Model through Cognitive Task Analysis of the Algebra Tutor creation • Authoring Tools • Search, Select, Modify the existing Ontology → Re-create (part of ) the existing Algera Tutor • Extend the Ontology → Create new Tutors! An Individualized Web-Based Algebra Tutor D.Sklavakis & I. Refanidis