An Individualized WebBased Algebra Tutor Based on Dynamic Deep Model Tracing

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-Base Outline  The MATHESIS Project      The MATHESIS Algebra Tutor     Web-based Deep Cognitive Model Tracing Broad Knowledge Monitoring Related Work   Introduction: Cognitive Tutors Motivation: Cognitive Tutors Successful Paradigm Goals: Authoring Tools for Cognitive Tutors Research approach: Bottom - Up Cognitive Tutor Authoring Tools (Carnegie Mellon) Future Work   Ontology Authoring Tools An Individualized Web-Base The MATHESIS Project  Cognitive Tutors  Motivation  Goals  Research approach An Individualized Web-Base 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-Base 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 propertyvalue pairs An Individualized Web-Base 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) = If goal is solve a(bx+c) =d Then rewrite as abx +If goal is solve Hint: ac = dYou must a(bx+c) = d distribute a over bx Then rewrite as bx+c and c = d/a Known = 85% Known =45% 6x - 15 =  2x - = If goal is solve a(bx+c) = d Then rewrite as abx + c = d Bug message: You must also multiply a by c 6x - = 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-Base 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-Base The MATHESIS Project Goal: Authoring Tools for Math Cognitive  Development costs of Tutors 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-Base 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-Base 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-Base 10 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 x) *( − 2x) ( − 3of one the monomial-multiplications *5, * ( −2 x ) , − x *5, − x * ( −2 x )  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-Base 11 MATHESIS Algebra Tutor Demo An Individualized Web-Base 12 Related Work  CMU Cognitive Tutor Authoring Tools Example-tracing tutors:     Cognitive 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 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-Base 13 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-Base 14 ...   The MATHESIS Algebra Tutor     Web -based Deep Cognitive Model Tracing Broad Knowledge Monitoring Related Work   Introduction: Cognitive Tutors Motivation: Cognitive Tutors Successful... 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... Detailed hint and error messages for all of the above An Individualized Web-Base 10 The MATHESIS Algebra Tutor  Tutoring model: deep cognitive model tracing through knowledge reuse When tutoring