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 Inform

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

 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

The MATHESIS Project

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

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

Cognitive Tutor Technology:

Use ACT-R theory to individualize

instruction

3(2x - 5) = 9

6x - 15 = 9 2x - 5 = 3 6x - 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

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.

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

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 +

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

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

 4 3 * 5 2  x    x 

4*5, 4*  2 x , 3 *5, 3 *  x  x  2 x

MATHESIS Algebra Tutor

Demo

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

Future Work

Algebra Tutor’s knowledge (Interface,

Domain, Tutoring and Student models)

Task Analysis of the Algebra Tutor creation

 Authoring Tools

→ Re-create (part of ) the existing Algera

Tutor