1. Domain Knowledge, Structural Learning Theory & Role in Building Teaching and Learning Systems April 10, 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
II. Structural Analysis via
AuthorIT
AutoBuilder
Blackboard Editor
TutorIT Options
I-A. Content Knowledge Representation
tasks/problems
lower & higher order SLT rules
I-B. Blackboard Interface
TutorIT displays & Learner responses
Major components & relationships in SLT
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
copyright scandura

5. SKIP I. Structural Learning Theory
Representing Observable Behavior & Knowledge
II. Structural Analysis via
AuthorIT
AutoBuilder
Blackboard Editor
TutorIT Options
I-A. Content Knowledge Representation
tasks/problems
lower & higher order SLT rules
I-B. Blackboard Interface
TutorIT displays & Learner responses
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
copyright scandura

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. (Initialized Nodes Domain AST)
705
-529
Sample Problem AST for
Given AST
(Initialized Nodes Domain AST)
Goal AST
problem
hundreds
tens
ones
Top
= 7
Bottom
= 5
borrow digit
difference
Top
= 0
Bottom
= 2
borrow digit
difference
Top
= 5
Bottom= 9
difference
borrow digit

8. Abstract Syntax Tree (AST) Definition of SLT Rules
SKIP
Abstract Syntax Tree (AST) Definition of SLT Rules
SLT Rule
Domain-Range AST
Procedure AST
prototype
loop
refinement types
component
component
condition
sequence
category
dynamic
IF..THEN …
operation
SLT Rule
Domain
Range
Dynamic & Interaction refinements
Procedure
SLT Rule

9. draw difference digit –e.g., 5
Abstract Syntax Tree (AST) SLT Higher Order Rule for Column Subtraction
SLT Rule
Domain-Range AST
Procedure AST
prototype
loop
refinement types
component
component
condition
sequence
category …
dynamic
IF..THEN …
subtract
(top, bottom: ;
difference)
SLT Rule
Domain
Range
draw difference digit –e.g., 5
Procedure
SLT Rule

10. (start, end, time:..;distance)
BRIEF
Abstract Syntax Tree (AST) SLT Higher Order Rule for Docking Space Station
SLT Rule
Domain-Range AST
Procedure AST
prototype
loop
refinement types
component
component
condition
sequence
category …
dynamic
IF..THEN …
fire_rocket
(start, end, time: ;
movement)
SLT Rule
Domain
Range
fire_rocket
(start, end, time:..;distance)
Procedure
SLT Rule

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
SUMMARY
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

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
II. Structural Analysis via
AuthorIT
AutoBuilder
Blackboard Editor
TutorIT Options
I-B. Blackboard Interface
TutorIT displays & Learner responses
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
copyright scandura

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,

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
Start with Informally Defined Problem Domain: Select & Systematically Define Representative Sample of Prototypic Problems in Domain & Represent in Terms of ASTs
Systematically Construct SLT Rules for Solving Prototypic Problems
Convert SLT Rules into Higher Order Problems
Construct Higher Order SLT Rules for Solving H.O. Problems
Optionally Eliminate Redundant SLT Rules
Repeat Process Until Desired Level of Domain Coverage Is Attained

17. Analyzing Simple Well-Defined Domains (Problem Types Exhaust Domain*)
SME Selects & Represents Well-Defined Problems as Hierarchical ASTs
Whole Number Arithmetic ___
| 285
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. Sample Problem in AuthorIT Input-Output ASTs for Mixed Fractions
ANOTHER EXAMPLE
Sample Problem in AuthorIT
Input-Output ASTs for Mixed Fractions
Problem Structure (AST) Problem Layout Node Attributes

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. 1. SME Selects Prototypic Problems
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: … ?sum
… ?sum
… ?sum
Proofs in High School Trigonometry
Examples: sin2 A + cos2 A = ?proof
a2 + b2 = c ? proof
tan2 A + 1 = sec2 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. Proof is resulting steps
Domain of measure conversion problems
Example 1A: yd 36_times in
Example 1B: gallons 8_times pints
Domain of number series problems*
Example 2A: … + 99 50x50
Example 2B: … + 99 50x(1+99)/2
Example 2C: … + 99 successive addition 2500
Proofs in High School Trigonometry
Example 3:
sin2 A + cos2 A = 1
start with a2 + b2 = c2, divide by c, substitute sin, cos definitions
Proof is resulting steps
_____
* 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,
Scandura, J.M. Learning verbal and symbolic statements of mathematical rules. Journal of Educational Psychology, 1967, 58,
Simple Ill-Defined Domains (emphasis on identifying SLT rules & h.o. rules) 2. Construct Solution Rules for Prototypic Problems

24. Simple Ill-Defined Domains 3
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 36_times in
Higher Order Problem:
Givens: yd n1_times xxx
xxx n2_times in
Goal: blug n_times clug
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
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: 3x3
… + 2n nxn Sum
Example 2B: 3x(1+5)/2
a + a+d + a+2d + … n x (a + l)/2 Sum
Example 2C: successive addition
a1 + a2 + a3 + … + an-1 successive addition Sum
n = no. terms
a/l/d = first/last term/common difference
ai = arbitrary term in arithmetic series

26. Proof is resulting steps
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
sin2 A + cos2 A = 1
start with a2 + b2 = c2, divide by c, substitute sin, cos definitions
Proof is resulting steps
trig identity
start with a2 + b2 = c2, 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_times]) 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. Higher Order SLT Rules*
4. Alternative SLT Higher Order Rules to Solve Higher Order Generalization Problem
Higher Order SLT Rules*
Example 2A:
3x3 9
a1 + a2 + a3 + … + an-1 nxn Sum
replace three terms by n
Example 2B:
3x(1+5)/2
… + 2n n x (a + l)/2 Sum
replace 1 by a, 5 by l &/or three terms by n
Example 2C:
1+3+5
a + a+d + a+2d + … successive addition Sum
replace each term by a variable, three terms by n
________
* In these examples, “ ” 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 inefficient 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,
Scandura, J.M. Learning verbal and symbolic statements of mathematical rules. Journal of Educational Psychology, 1967, 58,

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)*
3x3
… + 2n nxn Sum
replace three terms by n
3x(1+5)/2
a + a+d + a+2d + … n x (a + l)/2 Sum
replace 1 by a, 5 by l &/or three terms by n
successive addition
a1 + a2 + a3 + … + an-1 successive addition Sum
replace each term by a variable, three terms by n
One Higher Order Selection Rule:
Case Type-of-Series:
starts with 1 with a common difference of 2, select rule N x N
common difference, select rule N x (A+D)/2
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: A0 --> B0 ==> 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
II. Structural Analysis via
AuthorIT
AutoBuilder
Blackboard Editor
TutorIT Options
I-A. Content Knowledge Representation
tasks/problems
lower & higher order SLT rules
I-B. Blackboard Interface
TutorIT displays & Learner responses
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
copyright scandura

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 Interface
Problem Solver
External Agent
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 A in U.S. Patent 6,275,976

44. Example of UCM in Action: Initial Problem and Partial SLT Rule Set
bedroom {not-presentable} Component
bed {unmade}
carpet {dirty} ?
bedroom {presentable}
bed {made}
carpet {clean}
--?
Lower Order SLT Rules in (Partial) Rule Set
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 in Rule Set matches problem.
Hence, control seeks rules whose range includes rules that do match

45. Example of UCM in Action:
Higher Order SLT Rule
Domain of Higher Order
Conjunction Rule
Range of Higher Order
Conjunction Rule
SLT-rule1 (par1)
SLT-rule2 (par2)
SLT-rule (par) {compnt refnmnt}
SLT-rule1 (par1)
SLT-rule2 (par2)
Procedure of Higher Order
Conjunction Rule
Apply SLT-rule1 and SLT-rule2 in parallel {parallel refinement}
_____
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

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
Newly Generated Solution Rule
clean (bedroom)
make (bed)
vacuum (carpet)

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
II. Structural Analysis via
AuthorIT
AutoBuilder
Blackboard Editor
TutorIT Options
I-A. Content Knowledge Representation
tasks/problems
lower & higher order SLT rules
I-B. Blackboard Interface
TutorIT displays & Learner responses
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
copyright scandura

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. xxx<consonant> Diagnostic Sub-Problems Diagnostic Sub-Problems
Assessing Behavior Potential Problem Template & Diagnostic Sub-Problems
Column Subtraction
Adding “ing”
Problem Templates
Problem Template 5 3 9
xxxe
_____ - 3 6 2
xxx<consonant>
Diagnostic Sub-Problems
Diagnostic Sub-Problems 1 5 3 9
_____ 5 / 3 9
-->
date
dating
--> -
_____ 3 6 2 - 3 6 2 7 7
running
run
--> 5 3 9 5 3 9
-->
_____ - 3 6 2 -
_____ 3 6 2 7

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)
Predicating (not assessing) Which Alternative Account will be Used
Requires identification of Higher Order Selection rules 3 1 1 / 3 /

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
6 1 6
Procedural Steps at the Top Level in AST Hierarchy
(e.g., working problem in head)
1 6 1 3 1 3 1 3 1 / / /     

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,    

56. Tutoring 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. Extension to Multiple Learners AST Knowledge Representation, Human Interface & Problem Solver / Learner
SoftBuilder
Tutor
Core Flexform AST Machinery
SLT Problem(s) & Set(s) of
Higher & Lower Order Rules
Blackboard Editor
AutoBuilder
Blackboard Interface
Problem ASTs with
Layout
Consistent SLT Rule ASTs
Learner 1
Higher Order & Custom SLT Rule & Problem ASTs
Learner 2 …
Learner n
Planned: Learner n
&