Domain Knowledge, Structural Learning Theory

1



Domain Knowledge,

Structural Learning Theory


& Role in Building Teaching and Learning Systems


April 10, 2006


Symposium on Knowledge Representation

TICL SIG

Joseph M. Scandura, Ph.D.

Chairman, Board Scientific Advisors, MERGE Research Institute

Emeritus and Adjunct Professor, University of Pennsylvania

Visiting Research Professor, College of Information Science and Technology, Drexel University


www. scandura.com

It’s hard to believe 36 years have gone by since I first introduced the SLT at
the 1970 SL Conference in Philadelphia, repeated a couple days later here.
A lot has gone on since then, but the focus has always been on
understanding fundamentals
–

on four basic questions.

2

Research Motivated by

Four Basic Questions

Content
: What does it mean to know something?
Specifically, how can competence (content knowledge)
be represented so it is executable & has direct
behavioral relevance?


Assessing Behavior
: How can one determine individual
knowledge? What does an individual know and not
know about any given content?


Cognition
: Why can some people solve problems
whereas others cannot? What are the basic
mechanisms & constraints governing how learners use
and acquire knowledge?


Instruction
: How does knowledge change over time as
a result of interacting with an external environment?

3

Cognitive Models in

Teaching & Learning (TICL)

Top
-
down
: Cognitive Models in TICL provide
motivation & guidelines for TICL systems

Bottom
-
up
: Extend AI &/or Learning Theories to
support TICL

Goal of
Structural Learning Theory (SLT)
: Fill Gap
between high level conceptualization & executable
systems


Like most cognitive models, SLT started at the top (like
cognitive models but with deterministic assumptions)


Continuing refinement & extension has made SLT fully
executable for the first time (like AI & biologically inspired
models & theories but with behavior/observable emphasis)


4

Overview of Structural Learning Theory

w/ Authoring & Delivery Systems Needed for Automation


I
-
A. Content Knowledge
Representation

tasks/problems

lower & higher order SLT rules

TutorIT


I
-
A. Content knowledge w/

III. UCM, capacity/speed

IV. Full diagnostic & tutorial
expertise;

fully configurable

Learner


III. U Control Mechanism,

capacity/speed

IV. Individual knowledge


II. Structural Analysis
via

AuthorIT


AutoBuilder


Blackboard Editor


TutorIT Options


I
-
B. Blackboard Interface

TutorIT displays & Learner responses

copyright scandura 2001
-
5
-
56

Major
components &
relationships in
SLT


5

I. Structural Learning Theory

Representing Observable Behavior & Knowledge

I
-
A.
Content Knowledge
Representation

tasks/problems

lower & higher order SLT rules

TutorIT


I
-
A. Content knowledge w/

III. UCM, capacity/speed

IV. Full diagnostic & tutorial
expertise;

fully configurable

Learner


III. U Control Mechanism,

capacity/speed

IV. Individual knowledge


II. Structural Analysis
via

AuthorIT


AutoBuilder


Blackboard Editor


TutorIT Options


I
-
B.
Blackboard Interface

TutorIT displays & Learner responses

copyright scandura 2001
-
5
-
56

SKIP

6


I. Representing Observables &
Knowledge as SLT Rules

•
I
-
A. Content Knowledge (Competence) Represented at
Multiple Levels of Abstraction as SLT Content Rules

•
SLT Rules include both Structural & Procedural Abstract
Syntax Trees (ASTs)

•
Structural/Declarative ASTs of SLT Rules

•
Represent Domain & Range Data Structures

•
Correspond to Perceptual/Automated Knowledge

•
Procedural ASTs of SLT Rules

•
Represent Hierarchies of Behaviorally Equivalent Processes

•
Correspond to Procedural Knowledge


•
I
-
B. Observable Behavior Represented as Problem
ASTs

•
Represent Observables (e.g., problems)

•
Via which Learners & Tutors Interact


7

Sample Problem AST for






hundreds

Top

= 7

Given AST


(Initialized Nodes Domain AST)

Goal AST

tens

ones

difference

Bottom

= 5

borrow digit

Bottom

= 2

difference

borrow digit

borrow digit

difference

Top

= 5

Top

= 0

Bottom
= 9


705

-
529


problem

8

Abstract Syntax Tree (AST)

Definition of SLT Rules



category



Domain
-
Range AST

Procedure

AST

SLT Rule

component

dynamic

loop

condition

sequence

SLT Rule

Domain

prototype

operation

IF..THEN

Range

Procedure

refinement types

…

component

SLT Rule

SKIP

Dynamic &
Interaction
refinements

9

component

Abstract Syntax Tree (AST)


SLT Higher Order Rule for

Column Subtraction











Domain
-
Range AST

Procedure

AST

prototype

category

dynamic

SLT Rule

loop

condition

sequence

SLT Rule

Domain

subtract

(top, bottom: ;

difference
)

IF..THEN

Range

Procedure

refinement types

…

component

…

SLT Rule

draw difference
digit
–
e.g., 5

10

component

Abstract Syntax Tree (AST)


SLT Higher Order Rule for

Docking Space Station











Domain
-
Range AST

Procedure

AST

prototype

category

dynamic

SLT Rule

loop

condition

sequence

SLT Rule

Domain


fire_rocket


(start, end, time: ;

movement
)




IF..THEN

Range

Procedure

refinement types

…

component

…

SLT Rule

fire_rocket

(start, end,
time:..;distance)

BRIEF

11

Structural Knowledge

Input
-
Output Data Structure AST defining Column Subtraction










12

Procedural Knowledge

Procedure AST Generating Specified Input and Output Behavior









13

ALL Content Knowledge represented by

Sets of SLT Content Rules


•
Behavior

is represented as
Problems
;
Knowledge

as SLT Content Rules

(domain dependent & independent; declarative & procedural; h.o. &l.o.)

SLT Content Rule

= AST structure & procedure, representing multiple levels
of equivalent knowledge;
Behavior

associated with various levels is
equivalent but not identical

Individual SLT Rule

= slice (single level) in an SLT Content Rule*


individual differences in mastery level
:
represented by specific levels of
abstraction in ASTs defining Individual SLT rules


declarative knowledge
:

Procedure is simple (e.g., top
-
level); Structure is
correspondingly complex.*


procedural knowledge
:

Structure is simple (e.g., top
-
level); Procedure is
correspondingly complex.


*Note: Multiple gradations between declarative & procedural knowledge


higher order knowledge/meta
-
knowledge/heuristics/deduction:
Structure of SLT (h.o.) Rule includes other SLT Rules. H.O. rules
generate new SLT rules


conflict resolution/rule selection/design alternatives:
H.O. rules select
from alternative rules (e.g., design)


automation
:
h.o. SLT chunking rules mapping lower level
Individual SLT
Rules

to behaviorally equivalent higher level SLT Rules


SUMMARY

14

II. Structural Learning Theory

Structural Analysis: A Systematic Method for
Constructing AST Rule Knowledge

Representations


I
-
A. Content Knowledge
Representation

tasks/problems

lower & higher order SLT rules

TutorIT


I
-
A. Content knowledge w/

III. UCM, capacity/speed

IV. Full diagnostic & tutorial
expertise;

fully configurable

Learner


III. U Control Mechanism,

capacity/speed

IV. Individual knowledge


II.
Structural Analysis
via

AuthorIT


AutoBuilder


Blackboard Editor


TutorIT Options


I
-
B. Blackboard Interface

TutorIT displays & Learner responses

copyright scandura 2001
-
5
-
56

15


Structural (Content) Analysis (SA):

Summary & Benefits I

•
Early Research* Showed that Identifying
Expected Behavior & What Must be
Learned made Empirical Research Largely
Redundant


•
Result Motivated Development of a
Systematic (now Patented) Process for
Knowledge Representation associated
with any Given Domain


Roughead, W.G. & Scandura, J.M. “What is learned” in mathematical
discovery.
Jr. Educational Psychology
, 1968,

59
, 283
-
298.


16

II. Structural Analysis (SA):

A Cognitive Meta
-
Theory



A Systematic, Extensible & Patented Method for
Subject Matter Experts (SME) to Represent
Observable Behavior & Knowledge as AST
-
based
Problems & SLT Content Rules


1.
Start with Informally Defined Problem Domain:
Select
&
Systematically Define R
epresentative Sample of Prototypic
Problems in Domain & Represent in Terms of ASTs


2.
Systematically Construct SLT Rules for Solving Prototypic
Problems


3.
Convert SLT Rules into Higher Order Problems


4.
Construct Higher Order SLT Rules for Solving H.O. Problems


5.
Optionally Eliminate Redundant SLT Rules


6.
Repeat Process Until Desired Level of Domain Coverage Is
Attained


17

Analyzing Simple
Well
-
Defined

Domains
(
Problem Types

Exhaust Domain*)





1.
SME Selects & Represents Well
-
Defined Problems

as
Hierarchical ASTs




Whole Number
Arithmetic













___




4027


324


324

37 | 285




-

2535



256

x 37





+

37


Domain of Bedrooms to be Cleaned



Bedroom <presentable, unpresentable>




Bed <made, unmade>




Carpeting <clean, dirty>





Rug1 <clean, messy, messy
-
dirty>





Rug2 <clean, messy, messy
-
dirty>





Rug3 <clean, messy, messy
-
dirty>


One SLT Solution Rule Sufficient to Solve each Problem Type


SLT solution rules also can be represented with any desired degree of
precision (because ASTs may be refined arbitrarily)







18

Problem Structure (AST)


Problem Layout



Node Attributes


1.
Sample Problem in AuthorIT


Input
-
Output ASTs for Mixed Fractions

ANOTHER
EXAMPLE

19

2. Systematically Construct Structure AST of
Clean Room SLT Solution (Content) Rule


20

2. Systematically Construct Procedure AST
for Clean Room SLT Solution (Content) Rule

21



2.

Full Hierarchical

(AST) Representation

of procedure for

SLT Column

Subtraction rule


NOTE: “Atomic”
Digits (e.g.,
Difference) may be
further refined as
new SLT rules

22

Analyzing Simple
Ill
-
Defined

Domains


(emphasis on identifying SLT rules & h.o. rules)








1.
SME Selects Prototypic Problems


Examples

Measure conversion


Example 1:


A.
3 yd

--

?in

; B.
2 gallons

--

?pints

Number series


Example 2:


1 + 3 + 5 + … + 99


--

?sum




2 + 5 + 8 + … + 32

--

?sum





3 + 5 + 5 + … + 23


--

?sum


Proofs in High School Trigonometry


Examples:

sin
2

A + cos
2

A = 1


--

?proof




a
2

+ b
2

= c
2


--

? proof




tan
2

A + 1 = sec
2

A


--

? proof






Key is for SME to select only representative problems


i.e., intuitively different problems
–

problems requiring different
kinds of representations &/or solution methods


SME can represent problems with any desired degree of
precision

23




Simple
Ill
-
Defined

Domains


(
emphasis on identifying SLT rules & h.o. rules)


2. Construct Solution Rules for Prototypic Problems








Domain of measure conversion problems


Example 1A:


yd




㌶彴業_s

†

楮



Example 1B:


gallons



8_瑩浥s



灩湴n


Domain of number series problems*


Example 2A:


1 + 3 + 5 + … + 99


㔰砵5

†


†
㈵〰2


Example 2B:


1 + 3 + 5 + … + 99


㔰砨x⬹㤩⼲




†
㈵〰



Example 2C:


1 + 3 + 5 + … + 99


獵s捥獳楶i 慤摩瑩tn


㈵〰


Proofs in High School Trigonometry


Example 3:



sin
2

A + cos
2

A = 1



獴s牴rw楴i a
2

+ b
2

= c
2
, divide by c, substitute sin, cos definitions

†

偲潯映楳⁲ 獵汴s湧 獴s灳

_____

* For early research on this subject see:

Scandura, J.M., Woodward, E., & Lee, F. Rule generality and consistency in mathematics
learning.
American Educational Research Journal
, 1967, 4, 303
-
319.

Scandura, J.M.
Learning verbal and symbolic statements of mathematical rules.
Journal of
Educational Psychology
, 1967, 58, 356
-
364.


24

Simple
Ill
-
Defined

Domains

3. Convert SLT Rule to Higher Order Problem


(
Construct
Goal

&
Given

of Higher Order Problem)







A. Replace semantic
-
specific nodes in Solution Rule with abstractions.
B. Select given rules from which Solution Rule can be constructed.

Example 1

Problem:


3 yd


--

?in



Solution Rule:


yd



㌶彴業敳

†

楮



Higher Order Problem
:


Givens:

yd




n
1
_
times



硸x



硸砠



n
2
_
times



楮



Goal:


blug



湟瑩浥n



捬畧





i)
blug & clug =
units of measurement




ii)

n
is a specific number




iii) variations include substituting
“op”
for
“times”




25

Simple
Ill
-
Defined

Domains

3. Convert SLT Rule to Higher Order Problem


(
Construct
Goal

&
Given

of Higher Order Problem)







A. Replace semantic
-
specific nodes in Solution Rule with abstractions.
B. Select given rules from which Solution Rule can be constructed.

Example 2


Example 2A:

1 + 3 + 5




㍸3

†††
㤠




1 + 3 + 5 + … + 2n
-
1

湸n

†††
卵S






Example 2B:

1 + 3 + 5





㍸⠱⬵3⼲


†††
㈵〰






a + a+d + a+2d + … + 1

n x (a + l)/2

†
卵S



Example 2C:

1 + 3 + 5


獵捣s獳楶攠慤摩瑩潮


†
㈵〰




a
1

+ a
2

+ a
3

+ … + a
n
-
1



獵捣s獳楶攠慤摩瑩潮



卵S









n
= no. terms



a/l/d
= first/last term/common difference



a
i
= arbitrary term in arithmetic series


26

Simple
Ill
-
Defined

Domains

3. Convert SLT Rule to Higher Order Problem


(
Construct
Goal

&
Given

of Higher Order Problem)







A. Replace semantic
-
specific nodes in Solution Rule with abstractions.
B. Select given rules from which Solution Rule can be constructed.


Example 3


sin
2

A + cos
2

A = 1




獴慲琠w楴栠a
2

+ b
2

= c
2
, divide by c, substitute sin, cos definitions




Proof is resulting steps





trig identity





start with a
2

+ b
2

= c
2
, divide by side, substitute trig definitions








Proof is resulting steps





27

4. Construct SLT Higher Order Rule to
Solve Higher Order
Composition

Problems







Domain/Range Structure of Higher Order
Rule is un
-
initialized (general) version of
Higher Order Problem



DOMAIN*:

blug

[n_
times
] xxx




xxx [n_tim
es
]) clug

RANGE:

blug (n_times)
clug



Construct Procedure for H.O. SLT Rule



PROCEDURE:
compose rules so






output of first matches





input to second



*
Domain

is
un
-
initialized version of problem Givens

28

4. Alternative SLT Higher Order Rules to
Solve Higher Order
Generalization

Problem






•
Higher Order SLT Rules*



Example 2A:



1 + 3 + 5

㍸3


†


9



a
1

+ a
2

+ a
3

+ … + a
n
-
1


湸n


†


卵S




replace three terms by n


Example 2B:





1 + 3 + 5



㍸⠱⬵⤯2

†


㤠




1 + 3 + 5 + … + 2n
-
1

渠砠⡡x⬠氩⼲

† †

卵S





replace 1 by a, 5 by l &/or three terms by n


Example 2C:





1 + 3 + 5





ㄫ㌫3


††


9




a + a+d + a+2d + … + 1

successive addition

†
S畭




replace each term by a variable, three terms by n

________

* In these examples, “1 + 3 + 5” may be ANY specific arithmetic series

Given

Goal

Procedure

Given

Goal

Procedure

Given

Goal

Procedure

29

4.
Different examples result in

Different generalizations with

Different domains of applicability*









replace number of terms by n & multiple n x n



[very efficient but works only with arithmetic series





beginning with 1 with a common difference of 2]





replace number of terms by n, first by a, last by l and


compute n (a+l)/2


[efficient; works with ALL arithmetic series]


replace each term by a variable & add successively

[very
in
efficient but works with ALL series, arithmetic or otherwise]







___________

*Scandura, J.M., Woodward, E., & Lee, F. Rule generality and consistency in

mathematics learning.
American Educational Research Journal
, 1967,



4, 303
-
319.

Scandura, J.M.
Learning verbal and symbolic statements of mathematical

rules.
Journal of Educational Psychology
, 1967, 58, 356
-
364.


30

5
-
6.
Eliminate Redundant
Solution Rules







5.

Higher order rule may generate solutions for
any number of problems of similar type

•
Kernel of truth truth behind typologies (cf. Polya, 1962; Scandura,
M:CBF, 1971; Jonassen, Spector & others in Y2K)

•
New conversion rules generated as needed from basic rules; Basic
rules can be added at will

•
e.g., 12 ft. = 12 in., 4 qt. = 1 gal., etc.

•
Hence, Original solution rules become redundant

•
i.e.,derived as needed via higher & lower order rules




6. Process can be continued indefinitely

•
Convert new rules to still higher order problems, etc.

•
Procedures in enhanced rule set become simpler but generating
power goes up dramatically expanding coverage in original domain

31

4
-
5
-
6.
Higher Order
Selection
Rules

(a/k/a Conflict Resolution)*









1 + 3 + 5



㍸3

†††
㤠



1 + 3 + 5 + … + 2n
-
1

湸n

† ††
卵S



replace three terms by n






1 + 3 + 5





㍸3ㄫ㔩⼲


†††
㈵〰




a + a+d + a+2d + … + 1


渠砠n愠⬠氩⼲

†
卵S




replace 1 by a, 5 by l &/or three terms by n




1 + 3 + 5

獵捣敳獩癥⁡摤楴楯i


†
㈵〰



†
a
1

+ a
2

+ a
3

+ … + a
n
-
1


獵捣敳獩癥⁡摤楴楯i


†††
卵S




replace each term by a variable, three terms by n



One Higher Order Selection Rule:


Case Type
-
of
-
Series:

a)
starts with 1 with a common difference of 2, select rule N x N

b)
common difference, select rule N x (A+D)/2

c)
else select successive addition


A more General but Error
-
prone Selection Rule:


Choose the simplest rule

_____

*Importance of selection rules becomes clear In discussion of associated SLT theory.

Conflicting Rules

32

Kinds of Higher Order SLT rules:

Schematics

Composition:

A
--
> B, B
--
> C

==>









A
--
> B
--
> C

Analogy:


A1
--
> B


==>

A2
--
> B

Generalization:

A
0

--
> B
0



==>

A
--
> B

Selection:

A
--
> B, B
--
> C

==>

A
--
> B or







B
--
> C

Automation:

A1, A2
--
> B1, B2

==>

A
--
> B

where

A = parent of A1, A2



B = parent of B1, B2


Retrieval

Others

Combinations

33



Structural Analysis (SA):

Summary & Benefits


•
SA Systematic
: Method of SA is highly systematic

•
SA partially automated with much of remainder automatable

•
SA Indefinitely Precise
: Advance in AST (hierarchical)
representation makes level of detail arbitrary

•
High level conceptualization thru atomic representation possible

•
SA can be continued indefinitely as desired

•
Domain of applicability is automatically specified by AST structures


(in SLT content rules)

•
SA Universally Applicable
: Applicable to arbitrarily
complex domains

•
Domain coverage indefinitely extendable

•
New higher (& lower) order rules automatically introduced as needed

•
SA cumulative
–

builds on prior SA

•
Generating Power increases monotonically

•
SLT rules tend to become simpler as SA continues

•
(breadth of) coverage & collective generating power goes up qualitatively



34

Structural (Content) Analysis (SA)

What is Learned?


Bad News

SA of Content

requires work


Good News


Experience shows SA
adds precision

&
minimizes need for empirical research


Preliminary SA is helpful


Further SA is better


Atomic SA is best

SA is
cumulative


one can build on preliminary SA without loss

35

Structural Analysis

Foundation for Structural Learning Theory (SLT)

Structure

of a KR
alone

is sufficient to

guide T &L


SLT builds on structural (content analysis) to
:


assess lower & higher order knowledge


predict behavior


specify needed instruction

with
arbitrary degrees of precision

SLT
–

a general & precise
infrastructure

for
automated learning & tutoring systems


36

Cognitive Theory:

Transitions from

Naive to Neophyte to Master

Why is it that some people can solve
problems that others cannot?

And, how is it that initially naïve learners
acquire new competence?

And, gradually come to acquire mastery
associated with experts?




(Quote from Scandura, 1981, Educational
Psychologist, p. 139)

37

III. Structural Learning Theory

SLT
-

Cognitive Theory: Universal Control Mechanism,
Processing Capacity, Processing Speed

I
-
A. Content Knowledge
Representation

tasks/problems

lower & higher order SLT rules

TutorIT


I
-
A. Content knowledge w/

III.
UCM, capacity/speed

IV. Full diagnostic & tutorial
expertise;

fully configurable

Learner


III.
U Control Mechanism,

capacity/speed

IV. Individual knowledge


II. Structural Analysis
via

AuthorIT


AutoBuilder


Blackboard Editor


TutorIT Options


I
-
B. Blackboard Interface

TutorIT displays & Learner responses

copyright scandura 2001
-
5
-
56

38

III. SLT
as Cognitive Theory:
Characterizing the Learner (& Tutor)


•
Learner is a Goal Directed Problem Solver

•
Well
-
defined or otherwise

•
Individual Knowledge Consists of Lower & Higher
Order (Individual) SLT Rules (at specific levels of
abstraction)

•
Universal Control Mechanism (UCM)

•
Controls use of SLT Rules with respect to Problems

•
All Processing under Control of UCM: Problem Solving,
Learning, Conflict Resolution, Retrieval from Memory, etc.

•
Fixed Capacity for Each Individual

•
Empirical Support Extends Miller’s Classic Research

•
Characteristic Processing Speed for Each Individual

•
Hypothetical
–

based on common observation




39

Problem Solver / Learner

Architecture





External Agent

Problem Solver

External Interface

Universal Control Mechanism


Working Memory

(problems, structures, SLT rules)



Long Term Memory:

SLT Problem(s) & Set(s) of

Higher & Lower Order Rules

(new problems, rules, etc.)

40

Transitions

Local
: Transitions from Naïve to
Neophyte to Master (within given
domains)


Global
: Transitions from One
Developmental Stage to the Next
(mastered rules in one domain
providing goals for the next)

41

Local Transitions


Learning German


[Idea: know little German]
--
> <Proper Phrase>



Naïve Knowledge Base:



“ich”, “Deutch”, “ein wenig”, “leider”, “sprechen”, “kann”,
“bin”, “nur”, <put things in the order: subject, initial verb,
adjectives and objects, other verbs>

Neophyte Knowledge Base:




““Leider, Ich kann nur ein wenig Deutsch sprechen”

Master Knowledge Base:

““leider, Ich kann nur ein wenig Deutsch sprechen”,

“Ich bin im Deutschen ein Anfanger”, ...


42

Global Transitions:

Mastered Rules Provide Goals for New Problems


Only after mastery (SLT rule becomes automatic)
can new problems be defined

Example 1


Mastery of reading & writing numerals (e.g., assembling
line segments to write “5”, “7”, etc.) is prerequisite to
learning arithmetic algorithms)


Example 2


Piagetian developmental stages are similar
--

e.g., only
after mastery of 1
-
1 comparisons does conservation of
number become possible*


____

* Scandura, J.M. & Scandura, A.
Structural Leaning & Concrete
Operations
. Praeger, 1980.)

43

Universal Control Mechanism (UCM)
How Rules are Used & New Ones Generated


(A Least Common Denominator with Minimal Assumptions)

Overview of a Patented Method*

•
Check available rules to see which AST structures match the
given problem

•
Unless
exactly one

SLT Rule matches,
control goes to a deeper
level looking for rules whose ranges contain structures that
match

the given problem (a recursive process)

•
Once
exactly one

rule is found, that rule is applied & new rule
generated

•
Control reverts to previous level & process continues with
checking at previous level of embedding

•
Eventually, process halts because problem is solved or
processing capacity is exceeded (alternatively a predetermined
recursion limit may be set in automated systems)



* See Figs. 27
-
27A in U.S. Patent 6,275,976

44

bedroom {presentable}


bed {made}


carpet {clean}


Example of UCM in Action:

Initial Problem and Partial SLT Rule Set

--
?

Initial Problem

bedroom {not
-
presentable} Component


bed {unmade}


carpet {dirty}

Original SLT Rule set

make


bed (DOMAIN)


make (bed) (PROCEDURE)


bed (RANGE)

vacuum


carpet (DOMAIN)


vacuum (rug) (PROCEDURE)


carpet (RANGE)

_____

No Lower Order SLT rule i
n Rule Set

matches problem.

Hence, control seeks rules whose range includes rules that do match

Lower Order SLT Rules in (Partial) Rule Set

?

45

Example of UCM in Action:

Higher Order SLT Rule


Apply SLT
-
rule1 and SLT
-
rule2 in parallel

{parallel refinement}





SLT
-
rule1 (par1)



SLT
-
rule2 (par2)




SLT
-
rule (par)


{compnt refnmnt}




SLT
-
rule1 (par1)




SLT
-
rule2 (par2)

_____

1.
Range Structure

of Higher Order Rule matches
Problem Structure

2. Control seeks to match H.O. Rule Domain against set of


available SLT rules

3. Domain of higher order rule satisfied by lower order SLT rules in rule set

Range of Higher Order

Conjunction Rule

Domain of Higher Order

Conjunction Rule

Procedure of Higher Order

Conjunction Rule

46

Example of UCM in Action:

Higher Order SLT Rule Generates New Solution Rule


Result:



1. Higher Order

SLT (
Conjunction)
Rule
is applied to
make

&
vacuum
SLT rules in Rule Set.


2. Newly generated
solution rule
clean

is added to set of
available rules


3. Control checks


original problem against


rule set enhanced w/
clean


4. Control reverts to previous level
where newly generated rule,
clean
, matches, is applied &
solves original problem

clean (bedroom)


make (bed)


vacuum (carpet)

Newly Generated Solution Rule


47

Importance of

Universal Control Mechanism (UCM)?


•
Empirical Research

Supports UCM & Processing
Constraints

•
UCM Available from Earliest Ages (e.g., JEP, Sam)

•
Fixed Processing capacity (Voorhies)

•
Processing Speed (observation)

•
Emphasizes Observable Behavior Not Brain Physiology


•
Applicability

to both Human Behavior & Automated
Intelligence



•
Supports
Incremental Development

of Knowledge Base

•
Continuing SA introduces new SLT rules as needed



Ability to Add

Learning, Conflict Resolution & Chunking
SLT rules
without change to UCM


Supports ill
-
defined problem solving, design (selection) &
automatization without change

48

IV. Structural Learning Theory

Diagnostic and Instructional Logic

I
-
A. Content Knowledge
Representation

tasks/problems

lower & higher order SLT rules

TutorIT


I
-
A. Content knowledge w/

III. UCM, capacity/speed

IV.
Full diagnostic & tutorial
expertise;

fully configurable

Learner


III. U Control Mechanism,

capacity/speed

IV.
Individual knowledge



II. Structural Analysis
via

AuthorIT


AutoBuilder


Blackboard Editor


TutorIT Options


I
-
B. Blackboard Interface

TutorIT displays & Learner responses

copyright scandura 2001
-
5
-
56

49

IV. Making SLT Operational/Testable

Diagnostic and Tutorial Mechanisms

Assessing

What SLT (Individual) Rule
a Learner Does & Does Not Know


External Observer/Tutor/Co
-
Learner can Only
Infer Knowledge from Observable Behavior


Influencing

What a Learner Knows


Tutor Compares What is to be Known & What
Tutor Infers that Learner Already Knows

50






Assessing Behavior Potential:

Sub
-
problems defined by Nodes in Procedural ASTs







Node Defining


Borrowing



51

Assessing Behavior Potential

Problem Template & Diagnostic Sub
-
Problems






3

6

2

9

3

5

_____

7

1

/

-

3

6

2

9

3

5

_____

-

Problem Template

Diagnostic Sub
-
Problems

Adding “ing”

Problem Templates

Diagnostic Sub
-
Problems

xxxe

xxx<consonant>

running

run

--
>

date

dating

--
>

3

6

2

9

3

5

_____

7

-

--
>

3

6

2

9

3

5

_____

7

-

3

6

2

9

3

5

-

--
>

_____

Column Subtraction

52

Diagnosis = Assessing Behavior Potential

Determining Known & Unknown Parts of SLT Rules


Examples: subtract with borrowing (but not with zeros
in top); adding ‘ing’ to verbs with silent ‘e’ (but not when
verb ends in consonant)


Given a problem, patented processes show how an SLT
solution rule implicitly & automatically defines a set of
diagnostic sub
-
problems


These sub
-
problems correspond to nodes (at various
levels) in the defining procedural AST


Assuming Sufficient Precision (i.e., atomic refinement)
Research shows that a Single Test Item under Atomicity
conditions is Sufficient to Determine Whether the
Learner Knows the corresponding Node


Learner’s Current State of Knowledge wrt SLT rule is
Represented by Assigning +,
-
, ? to Nodes


Probabilities or multiple test items may be used when
analyses are incomplete

53

Assessing Behavior Potential

Distinguishing Knowledge Representations

Alternative Accounts of the Same Behavior





Example: Determining “Best Fit” Between Borrowing &
Equal Additions


Alternative SLT rules Accommodate ALL Relevant
Behavior


Requires Test Items in Intersection / for all Nodes in all
SLT rules (e.g., Durnin & Scandura,
Jr. Educ. Psy.

1973)











4 3


4 3





-
2 7

-
2 7






6


6


Predicating (not assessing) Which Alternative
Account will be Used


Requires identification of Higher Order Selection rules

/

/

3

3

1

1

54

Assessing Behavior Potential


Distinguishing Expertise

Distinguishing Atomicity Level in SLT
Rule Hierarchies


higher levels in hierarchy have less detailed processes & more
complex structures: top level corresponds to atomic rules
equivalent to declarative knowledge (faster execution)



Procedural Steps at a Lower Level in AST Hierarchy



4 3




4 3


4 3


4 3


4 3

-
2 7


-
2 7


-
2 7

-
2 7

-
2 7







6


1 6


Procedural Steps at the Top Level in AST Hierarchy


4 3




4 3

-
2 7


-
2 7


(e.g., working problem in head)





1 6



/

1

3





1

/

1

3







1

/

3

55

Assessing Behavior Potential

Higher Order Knowledge*

Assessing Higher Order SLT rules Requires
Problems in which Givens and/or Goals include
Processes (other SLT rules)






A B, B C ==> A B C



In Complex Domains: It is Sufficient to Assess
Behavior on Rules and Higher Order Rule
Individually


Universal Control Mechanism makes it Possible to
Predict Behavior on Complex Problems whose Solution
Requires both Higher and Lower Order SLT rules


* Scandura, J.M. Role of higher order rules in problem solving.
Journal of Experimental Psychology
, 1974,

120
, 984
-
991.









56

T
utoring

Influencing What a Learner Knows


Deciding What to Teach and When to Teach: Based
Entirely

on the Structure of SLT Rules to be Learned



Learner’s
Current State of Knowledge

wrt SLT rule is
Represented by Assigning +,
-
, ? to Nodes



Standard Pedagogy
: If Learner’s Status on Node is



Undetermined (?)

Test


Unknown (
-
)


Teach if Prerequisite Nodes is Mastered


Known (+)



Select Next Node in Execution or


Mastery (+ w/ latency)



add time constraints



Other Pedagogies


Range from making Larger (or smaller) Leaps (e.g., teaching when when
prerequisites undetermined and/or selecting nodes from top
-
down) to fully
Learner Controlled







57

Quick Summary of SLT

Structural (Content) Analysis
: systematically identify desired
behavior & what must be learned:


prototypic problems represented hierarchically as AST
-
structures with
Givens & Goals


knowledge represented hierarchically via AST
-
based SLT content rules


higher order & selection rules systematically identified;


play a key role in ill
-
defined & design problem solving

Cognition
: SLT rules & higher order rules plus control & processing
universals

Diagnosis & Instruction
:


diagnostic sub
-
problems & instruction associated with AST nodes of SLT
rules


individual knowledge & needed instruction based on performance on sub
-
problems defined by AST nodes


current state of individual’s SLT rule knowledge & pedagogical logic
determine instruction at each point in time


h.o. rules used to assess extra
-
domain problem solving, rule
selection/motivation & mastery


transition from naïve to neophyte to master, with mastery opening
possibilities for new levels of learning

58

SLT Problem(s) & Set(s) of

Higher & Lower Order Rules

Extension to Multiple Learners

AST Knowledge Representation, Human Interface &
Problem Solver / Learner












Blackboard Interface

Tutor


Learner 1


Planned:

Learner n


&



…


Learner n


Learner 2

AutoBuilder

Blackboard
Editor

Core Flexform AST Machinery

SoftBuilder

Consistent
SLT Rule
ASTs

Problem
ASTs with

Layout

Higher Order &
Custom SLT Rule &
Problem ASTs