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
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