Transcript PPT
An Individualized Web-Based Algebra Tutor Based on Dynamic Deep Model Tracing
Dimitrios Sklavakis and Ioannis Refanidis [email protected]
Department of Applied Informatics Univercity of Macedonia Thessaloniki GREECE An Individualized Web-Based Algebra Tutor D.Sklavakis & I. Refanidis 1
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 2
The MATHESIS Project
Cognitive Tutors Motivation Goals Research approach An Individualized Web-Based Algebra Tutor D.Sklavakis & I. Refanidis 3
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 4
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 An Individualized Web-Based Algebra Tutor D.Sklavakis & I. Refanidis 5
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 Hint: You must distribute a over bx and c If goal is solve a(bx+c) = d Then rewrite as bx+c = d/a Known = 85% 6x - 15 = 9 Known =45% 2x - 5 = 3 If goal is solve a(bx+c) = d Then rewrite as abx + c = d Bug message: You must also multiply a by c 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 6
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.
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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 8
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 9
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 10
The MATHESIS Algebra Tutor
Tutoring model: deep cognitive model tracing through knowledge reuse When tutoring a cognitive skill, e.g. polynomial-multiplication
x
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the tutor traces the cognitive model for each one of 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-Based Algebra Tutor D.Sklavakis & I. Refanidis 11
MATHESIS Algebra Tutor Demo
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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 An Individualized Web-Based Algebra Tutor D.Sklavakis & I. Refanidis 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-Based Algebra Tutor D.Sklavakis & I. Refanidis 14