George Goguadze, Eric AndrèsUniversität des Saarlandes

Johan Jeuring, Bastiaan HeerenOpen Universiteit Nederland

Generation of Interactive Exercises using Domain Reasoners

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IntroductionOne of the crucial assets of ITS is interactive problem solving support:

constant assessment of student’s progress

training the mastery of concepts

Systems like Andes, PUMP Algebra Tutor are targeting problem solving

Complex learning environment (such as ActiveMath) need to support problem solving in multiple disciplines

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CTAT Example Tracing Tutors

The Solution graph is authored in a “Behavior Recorder”

Each possible correct answer has to be authored

Feedback and hints are authored

Can encode exercises in multiple domains

The Solution graph is generated

Feedback and hints are generated

Sequencing and types of feedback are fixed

Domain is fixed, but technology is applicable to other domains such as chemistry

ANDES

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ActiveMath Platform

Supports multiple math. disciplines

Relies on exercises for the student assessment

Needs different types of exercises for training domain skills

Adapts to students’ knowledge and other parameters

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ActiveMath Exercises

Well Done!

Well Done!

calculate (x^2)’+x’

calculate (x^2)’+x’

calculate (x^2)’+1

calculate (x^2)’+1

(x^2)’+1

calculate 2x+x’

calculate 2x+x’

2x+x’

2x+12x+1

2x+1

Correct!Correct!

IncorrectTry again

IncorrectTry again

Correct!Correct!

IncorrectTry again

IncorrectTry again

IncorrectTry again

IncorrectTry again

calculate (x^2)’+x’

calculate (x^2)’+x’

calculate (x^2)’+1

calculate (x^2)’+1

(x^2)’+1

calculate 2x+x’

calculate 2x+x’

2x+x’

2x+12x+1

2x+12x+1

2x+1 DomainResoner

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ActiveMath Exercises

Exercise is represented as a state graph

the structure is domain-independent

system knows how to “play” the exercise

External reasoners provide domain intelligence

domain related queries are sent to the reasoners

diagnosis, hints, solutions, feedback is generated

multiple reasoners can be adressed simultaneously

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Generic Query Format

A query to an external reasoning service consists of :

action of the query, e.g.’compare’, or ‘getUserSolutionPath’

(list of) input expressions

context of the query, e.g. ‘arith’

number of iterations (optional)

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query (compare, userInput, (x^2)’+x’, diff_arith, 2)

matching all possible correct answers

using queries reduces the solution space

(x^2)’+x’

(x^2)’+x’

(x^2)’+1(x^2)’+1

linear_rule

2x+x’2x+x’

2x+1

(x^2)’+x’

(x^2)’+x’

2x+12x+1

query(compare, userInput, 2x+1, diff_arith, 2)

power_rule

power_rulelinear_rule

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query (compare, userInput, (x^2)’+x’, diff_arith+buggy, 2)

x+x’x+x’

(x^2)’+x’

(x^2)’+x’

(x^2)’+1

(x^2)’+1

linear_rule

2x+x’2x+x’

power_rule

power_rulelinear_rule

2x+1

buggy_power1

x+1x+1

linear_rule

query(compare, (x^2)’+x’ ,x+1 , diff_arith) = false

query(compare, (x^2)’+x’, x+1 , diff_arith+buggy) = true

query(compare, x+x’ ,x+1 , diff_arith) = true

query(compare, (x^2)’+x’ ,x+1 , diff_arith) = false

query(compare, (x^2)’+x’, x+1 , diff_arith+buggy) = true

query(compare, x+x’ ,x+1 , diff_arith) = true

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Generation using Domain Reasoners

An exercise generator

produces general-purpose exercise

can use different tutorial strategies

keeps track of the student’s state

Diagnosis is generated by domain reasoner

queries: compare, getBuggyRules, getUserSolutionPaths, getNOfStepsLeft

Hint and Feedback generation:

basic correct/incorrect feedback (compare)

task related conceptual and procedural feedback (getConcepts)

product feedback (getNextStep, getExpertSolutionPath(s))

error feedback (getBuggyRules, getUserSolutionPath(s))

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Generation using Domain Reasoners

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Diagnosis and Feedback Generation

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Combining Domain Reasoners

Equation Solver Reasoner

Derivatives Reasoner

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Conclusion: Current State

DomainReasoner

Technology Domain(s)

IDEAS (1500 exercises)

Haskell

AlgebraArithmeticCalculusLinear AlgebraLogic

FractionDR YACAS Fraction Arithmetics

IntegralDR YACAS Integration

MathCoach PROLOG Differentiation

SLOPERT PROLOG Differentiation

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Conclusion/Future Work

Seemless Integration of different domain reasoners

most major mathematical subjects are covered

simultaneous access to multiple reasoners

Exercises with different tutorial behaviour possible

immediate or delayed feedback strategies possible

different types of feedback generated on request

Need to connect other domains (physics, computer science)

challenge: reuse domain reasoners of existing ITS

• Need more advanced interaction interfaces

• allow for more complex reasoning

• alternative graphical interaction

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Thank you!