SimStudent: A computational model of learning for Intelligent Authoring and beyond

SimStudent:A computational model of learning for Intelligent Authoring and beyond

Noboru Matsuda

Human-Computer Interaction Institute

Carnegie Mellon University

Sim

Stu

den

t Pro

ject

PSLC Summer School 2010 :: SimStudent Demo :: Noboru Matsuda (CMU) 2

CTAT: Cognitive Tutor Authoring Tools

• Example-Tracing Tutor

– Zero programming

– A cognitive model specific to a particular problem

– Limited generalization by editing a behavior graph

• Model-Tracing Tutor

– Requires a cognitive model– Cognitive task analysis is hard– Writing production rules is even more challenging

• Performing a task is much easier…

Sim

Stu

den

t Pro

ject


Next Generation AuthoringBuild a tutor GUI

Teaching a solution

SimSt. learning

Rule simplify-LHS:

IF is-equation( Eq ),

is-lhs( Eq, Lhs ),

polynomial( Lhs ),

all-var-terms( Lhs )

Then simplify( Lhs, S-lhs ),

enter( S-lhs )

Production Rules

Rule simplify-LHS:


is-lhs( Eq, Lhs ),

polynomial( Lhs ),



enter( S-lhs )

Rule simplify-LHS:


is-lhs( Eq, Lhs ),

polynomial( Lhs ),



enter( S-lhs )

Sim

Stu

den

t Pro

ject


SimStudent

• Machine learning agent

– Learns problem-solving steps by …

– Observes model solutions / solving problems, and …

– Outputs a set of production rules

• Fundamental technology

– Programming by Demonstration

– Inductive Logic Programming

Lau & Weld (1998). Blessing (1997).

Sim

Stu

den

t Pro

ject

PSLC Summer School 2010 :: SimStudent Demo :: Noboru Matsuda (CMU)

Authoring Strategies

• Authoring by demonstration– Demonstrate whole solutions

– Learning from worked-out examples• Demonstrated solutions as positive examples

• Authoring by tutoring– Interactively tutor with immediate feedback and hint

– Learning by tutored problem-solving• Learning by generalizing hint with taking feedback into

account

5

Sim

Stu

den

t Pro

ject


Demo!

6

Authoring by Tutoring

Sim

Stu

den

t Pro

ject


Learning Production Rules in 3 parts: What-When-How

If

among this and that GUI elements

such and such constraints hold

Then

do actions with the GUI elements

When

What

How

Sim

Stu

den

t Pro

ject


Production Rule in JESS

(defrule trans-lr-lhs

?problem <- (problem (interface-elements ?table1 ? ? ?))?table1 <- (table (columns ?column1))?column1 <- (column (cells $?m1 ?cell0 $?))?cell0 <- (cell (value ?val0&~nil))

?problem <- (problem (interface-elements ? ?table2 ? ?))?table2 <- (table (columns ?column2))?column2 <- (column (cells $?m2 ?cell1 $?))?cell1 <- (cell (value ?val1&~nil))

?column1 <- (column (cells $?m3 ?cell2 $?))?cell2 <- (cell (name ?selection) (value ?input))

(test (consecutive-row ?cell0 ?cell2))(test (same-column ?cell0 ?cell2))(test (distinctive ?cell0 ?cell2))(test (consecutive-row ?cell1 ?cell2))(test (same-column ?cell1 ?cell2))(test (distinctive ?cell1 ?cell2))

(test (polynomial ?val0))(test (not (has-var-term ?val1)))

=>

(bind ?input (first-var-term ?val0))(modify ?cell2 (value ?input)) )

LHS

RHS

WME path

Topologicalconstraints

Featureconstraints

WMEconditions

Working Memory Element (WME)(defrule trans-lr-lhs

?problem <- (problem (interface-elements ?table1 ? ? ?))?table1 <- (table (columns ?column1))?column1 <- (column (cells $?m1 ?cell0 $?))?cell0 <- (cell (value ?val0&~nil))

?problem <- (problem (interface-elements ? ?table2 ? ?))?table2 <- (table (columns ?column2))?column2 <- (column (cells $?m2 ?cell1 $?))?cell1 <- (cell (value ?val1&~nil))

?column1 <- (column (cells $?m3 ?cell2 $?))?cell2 <- (cell (name ?selection) (value ?input))

(test (consecutive-row ?cell0 ?cell2))(test (same-column ?cell0 ?cell2))(test (distinctive ?cell0 ?cell2))(test (consecutive-row ?cell1 ?cell2))(test (same-column ?cell1 ?cell2))(test (distinctive ?cell1 ?cell2))

(test (polynomial ?val0))(test (not (has-var-term ?val1)))

=>

(bind ?input (first-var-term ?val0))(modify ?cell2 (value ?input)) )

LHS

RHS

WME path

Topologicalconstraints

Featureconstraints

WMEconditions

Working Memory Element (WME) GUI elements

Constraints

Actions

Sim

Stu

den

t Pro

ject


Background Knowledge

• Domain concepts to “explain” demonstrations– Operators

– Feature predicates

• External Jess function written in Java

(defrule multi-lhs…?var22140 <- (column (cells ? ? ?var22143 ? ? ? ? ?))?var22143 <- (cell (value ?val0&~nil))

(test (fraction-term ?val0 )) =>

(bind ?val2 (denominator ?val0))(bind ?input (mul-term-by ?val0 ?val2))…

)

Sim

Stu

den

t Pro

ject


Example ： Algebra domain•16 Feature predicates & 28 operators

Feature Predicates for LHS conditions Operators for RHS actions

HasCoefficient

HasConstTerm

HasVarTerm

Homogeneous

IsFractionTerm

IsConstant

IsDenominatorOf

IsNumeratorOf

IsPolynomial

Monomial

NotNull

VarTerm

IsSkillAdd

IsSkillSubtract

IsSkillDivide

IsSkillMultiply

AddTerm

AddTermBy

Coefficient

CopyTerm

Denominator

DivTerm

DivTermBy

EvalArithmetic

FirstTerm

FirstVarTerm

GetOperand

InverseTerm

LastConstTerm

LastTerm

LastVarTerm

MulTerm

MulTermBy

Numerator

ReverseSign

RipCoefficient

SkillAdd

SkillClt

SkillDivide

SkillMultiply

SkillRf

SkillMt

SkillSubtract

VarName

Sim

Stu

den

t Pro

ject


Learning Results

€

StepScore =0, if C = 0

C

C + I

⎧ ⎨ ⎪

⎩ ⎪

# of training tasks

% C

orr

ect

rule

firi

ng

s (

10

test

tasks) Authoring by

tutoring

Authoring by demonstration

Betterthan

Sim

Stu

den

t Pro

ject


Authoring TimeAuthoring by Tutoring

Authoring by Demonstration

• Authoring by tutoring took 86 minutes

• Authoring by demonstration took 238 minutes

• A 2.8x speed-up!

Sim

Stu

den

t Pro

ject


Example: Stoichiometry Tutor

Approximate Time Distribution (hours)

55

30

15

40

Operator generation

Feature predicate generation

Debugging

Testing

Sim

Stu

den

t Pro

ject


SimStudent Projects

• Intelligent Authoring– Building a Cognitive Tutor as a CTAT Plug-in

• Student Modeling and Simulation– Controlled educational studies

– Error formation study

– Prerequisite conceptual knowledge study

• Teachable Peer Learner– Learning by teaching

14

Sim

Stu

den

t Pro

ject


SimStudent Projects






15

Sim

Stu

den

t Pro

ject


Model of Incorrect Learning

• Identify errors students commonly make

• Weaken SimStudent’s background knowledge

• Let SimStudent make an induction error

16

Sim

Stu

den

t Pro

ject


Weak Prior Knowledge Hypothesis

• Multiple ways to make sense of examples

17

3x=5 “divide by 3”3x=5 “divide by 3”

Get a coefficient and divideGet a coefficient and divide

Get a number and divideGet a number and divide

Get a denominator and multiplyGet a denominator and multiply

4/x=5

strong prior knowledge

weak prior knowledge

“divide by 4”

“multiply by x”

Sim

Stu

den

t Pro

ject


Target Common Errors

18

€

ax − b = c → "subtract b"

€

ax = b → "multiply by a"€

ax + b = c → "add b"

€

x

a= b → "divide by a"

Sim

Stu

den

t Pro

ject


Results: Learning Rate

Steps Score = 0 (if there is no rule applicable)# correct rule applications / # all rule applications

# training problems

Step Score

Sim

Stu

den

t Pro

ject


SimStudent Projects






20

Sim

Stu

den

t Pro

ject


Learning by Teaching SimStudent

Sim

Stu

den

t Pro

ject


Demo!

22

Learning by Teaching

Sim

Stu

den

t Pro

ject


Learn more about SimStudents

• Project Web– www.SimStudent.org

• Download & Tutorial– http://ctat.pact.cs.cmu.edu (linked from project web)

• Contact us!– [email protected]

23

SimStudent: A computational model of learning for Intelligent Authoring and beyond

Documents

lhs eq

polynomial lhs

slhs rule

simstudent demo

javadefrule multilhs

slhs production rulesrule

noboru matsuda cmudemo

ifisequation eq