1. An Individualized Web-Based Algebra Tutor D.Sklavakis & I. Refanidis 1 An Individualized Web-Based Algebra Tutor Based on Dynamic Deep Model Tracing 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. 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

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

4. 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

5. An Individualized Web-Based Algebra Tutor D.Sklavakis & I. Refanidis 5 The MATHESIS Project Cognitive 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

6. An Individualized Web-Based Algebra Tutor D.Sklavakis & I. Refanidis 6 Cognitive Tutor Technology: Use ACT-R theory to individualize instruction 3(2x - 5) = 9 6x - 15 = 92x - 5 = 36x - 5 = 9 Cognitive Model: A system that can solve problems in the various ways students can 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 Model Tracing: The tutor matches the student’s steps against the solution produced by the cognitive model → context-sensitive instruction Known = 85% Known =45% Bug message: You must also multiply a by c Hint: You must distribute a over bx and c Knowledge Tracing: The tutor records cognitive skill learning from problem to problem → individualized activity selection and pacing

7. 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.

8. 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

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

10. 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

11. 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

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

13. An Individualized Web-Based Algebra Tutor D.Sklavakis & I. Refanidis 13 Related Work CMU 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

14. 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!