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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 Its 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.

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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?

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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)

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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

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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

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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

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

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

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9 component Abstract Syntax Tree (AST) SLT Higher Order Rule for Column Subtraction Domain-Range ASTProcedure 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

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10 component Abstract Syntax Tree (AST) SLT Higher Order Rule for Docking Space Station Domain-Range ASTProcedure 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

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11 Structural Knowledge Input-Output Data Structure AST defining Column Subtraction

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12 Procedural Knowledge Procedure AST Generating Specified Input and Output Behavior

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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

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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

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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.

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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 Representative 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

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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 32437 | 285 - 2535 256x 37 + 37 Domain of Bedrooms to be Cleaned Bedroom Bed Carpeting Rug1 Rug2 Rug3 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)

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18 Problem Structure (AST) Problem LayoutNode Attributes 1.Sample Problem in AuthorIT Input-Output ASTs for Mixed Fractions ANOTHER EXAMPLE

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

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

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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

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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

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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 36_times in Example 1B: gallons 8_times pints Domain of number series problems* Example 2A: 1 + 3 + 5 + … + 99 50x50 2500 Example 2B: 1 + 3 + 5 + … + 99 50x(1+99)/2 2500 Example 2C: 1 + 3 + 5 + … + 99 successive addition 2500 Proofs in High School Trigonometry Example 3: sin 2 A + cos 2 A = 1 start with a 2 + b 2 = c 2, 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, 303-319. Scandura, J.M. Learning verbal and symbolic statements of mathematical rules. Journal of Educational Psychology, 1967, 58, 356-364.

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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 36_times in Higher Order Problem : Givens: yd n 1 _times xxx xxx n 2 _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

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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 3x3 9 1 + 3 + 5 + … + 2n-1 nxn Sum Example 2B:1 + 3 + 5 3x(1+5)/2 2500 a + a+d + a+2d + … + 1 n x (a + l)/2 Sum Example 2C:1 + 3 + 5 successive addition 2500 a 1 + a 2 + a 3 + … + a n-1 successive addition Sum n = no. terms a/l/d = first/last term/common difference a i = arbitrary term in arithmetic series

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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 start with 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

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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

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28 4. Alternative SLT Higher Order Rules to Solve Higher Order Generalization Problem Higher Order SLT Rules* Example 2A: 1 + 3 + 5 3x3 9 a 1 + a 2 + a 3 + … + a n-1 nxn Sum replace three terms by n Example 2B: 1 + 3 + 5 3x(1+5)/2 9 1 + 3 + 5 + … + 2n-1 n x (a + l)/2 Sum replace 1 by a, 5 by l &/or three terms by n Example 2C: 1 + 3 + 5 1+3+5 9 a + a+d + a+2d + … + 1 successive addition Sum 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

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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, 303-319. Scandura, J.M. Learning verbal and symbolic statements of mathematical rules. Journal of Educational Psychology, 1967, 58, 356-364.

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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

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31 4-5-6. Higher Order Selection Rules (a/k/a Conflict Resolution)* 1 + 3 + 5 3x3 9 1 + 3 + 5 + … + 2n-1 nxn Sum replace three terms by n 1 + 3 + 5 3x(1+5)/2 2500 a + a+d + a+2d + … + 1 n x (a + l)/2 Sum replace 1 by a, 5 by l &/or three terms by n 1 + 3 + 5 successive addition 2500 a 1 + a 2 + a 3 + … + a n-1 successive addition Sum 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

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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

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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

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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

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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

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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)

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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

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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 Millers Classic Research Characteristic Processing Speed for Each Individual Hypothetical – based on common observation

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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.)

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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)

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41 Local Transitions Learning German [Idea: know little German] --> Naïve Knowledge Base: ich, Deutch, ein wenig, leider, sprechen, kann, bin, nur, 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,...

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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.)

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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

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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 in Rule Set matches problem. Hence, control seeks rules whose range includes rules that do match Lower Order SLT Rules in (Partial) Rule Set ?

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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

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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

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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

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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

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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

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50 Assessing Behavior Potential: Sub-problems defined by Nodes in Procedural ASTs Node Defining Borrowing

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51 Assessing Behavior Potential Problem Template & Diagnostic Sub-Problems 362 935 _____ 7 1 / - 362 935 - Problem Template Diagnostic Sub-Problems Adding ing Problem Templates Diagnostic Sub-Problems xxxe xxx running run --> date dating --> 362 935 _____ 7 - --> 362 935 _____ 7 - 362 935 - --> _____ Column Subtraction

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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 Learners 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

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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 -2 7-2 7 6 Predicating (not assessing) Which Alternative Account will be Used Requires identification of Higher Order Selection rules / / 3 3 1 1

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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

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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.

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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 Learners Current State of Knowledge wrt SLT rule is Represented by Assigning +, -, ? to Nodes Standard Pedagogy: If Learners 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

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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 individuals 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

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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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