10 Aug 06ICCSE - Rochester1 SQS: A Pedagogy for Computational Science D. E. (Steve) Stevenson and...

10 Aug 0610 Aug 06 ICCSE - RochesterICCSE - Rochester 11

SQS: A Pedagogy for SQS: A Pedagogy for Computational ScienceComputational Science

D. E. (Steve) Stevenson and friendsD. E. (Steve) Stevenson and friends

Partial support from NSDL DUE-0435187 Partial support from NSDL DUE-0435187 and STEP program DUE-0525474.and STEP program DUE-0525474.


Changing the Status Quo?Changing the Status Quo?

If work paradigm changes, education If work paradigm changes, education paradigm changes. paradigm changes.

You never change something by fighting You never change something by fighting the existing reality. To change something, the existing reality. To change something, build a new model that makes the existing build a new model that makes the existing model obsoletemodel obsolete

Buckminster FullerBuckminster Fuller


Before We BeginBefore We Begin

This talk is most effective If you have a This talk is most effective If you have a problem you want to solve.problem you want to solve.

Think of a student or colleague that you Think of a student or colleague that you have tried to work with who just didn’t get have tried to work with who just didn’t get a model and its simulation.a model and its simulation.


Science is About SQSScience is About SQS

Definitions of Systems, Definitions of Systems,

Questions about those systems, and Questions about those systems, and

Solutions to questions interpreted on Solutions to questions interpreted on these systemsthese systems


SQS ExamplesSQS Examples

(system, question) - engineering fare. (system, question) - engineering fare.

(systems, solutions) - debugging (systems, solutions) - debugging

(questions, solutions) - synthesize one or (questions, solutions) - synthesize one or more systems with given capabilities. more systems with given capabilities.

(solutions) ``To an engineer with a (solutions) ``To an engineer with a hammer, the whole world looks like a nail.'' hammer, the whole world looks like a nail.''


CS as Explanation of SystemsCS as Explanation of Systems

Modeling and simulation aids researcher Modeling and simulation aids researcher explain systems.explain systems.

The knowledge structure of CS follows the The knowledge structure of CS follows the Knowledge Vee.Knowledge Vee.

M&S knowledge warranted by verification M&S knowledge warranted by verification and validation.and validation.


Initial ObservationsInitial Observations

CS applications are interdisciplinary. CS applications are interdisciplinary.

CS problems are defined on systems. CS problems are defined on systems.

Switching systems requires significant Switching systems requires significant learning effort.learning effort.

Computational scientists must be efficient Computational scientists must be efficient learners.learners.


The AThe A33 Paradigm Paradigm


Four TenetsFour Tenets

University education mirrors professional University education mirrors professional practice to build expertise. practice to build expertise.

General systems theory is theoretical General systems theory is theoretical paradigm. paradigm.

Knowledge Vee is organizer and V&V is Knowledge Vee is organizer and V&V is knowledge warrantor.knowledge warrantor.

Systems-Questions-Solutions is the Systems-Questions-Solutions is the pedagogical principle. pedagogical principle.


Knowledge Vee for Knowledge Vee for SystemsSystems

World ViewWorld View EpistemologyEpistemology TheoryTheory PrinciplesPrinciples ConstructsConstructs ConceptsConcepts

Knowledge ClaimsKnowledge Claims TransformationsTransformations RecordsRecords

•Focus Questions and Observations

• Objects, Events, and Observations.

SQS ConceptsSQS Concepts


The ChallengeThe Challenge

Students must learn how to learn Students must learn how to learn professional methods, professional methods, principles, and principles, and valuesvalues

from multiple disciplines and how to apply from multiple disciplines and how to apply these concepts to a broad range of these concepts to a broad range of problems.problems.


How People LearnHow People Learn

Deep factual knowledge (facts) of the Deep factual knowledge (facts) of the subject, subject,

Deep knowledge of pragmatic issues Deep knowledge of pragmatic issues (schemata), and (schemata), and

Meta-cognitive control and evaluationMeta-cognitive control and evaluation


Inquiry-Based LearningInquiry-Based Learning

PBL learners learn best when presented PBL learners learn best when presented with a realistic problem to focus on. with a realistic problem to focus on.

CBM use collaborative analysis leading to CBM use collaborative analysis leading to judgments when there is no single, correct judgments when there is no single, correct answer. answer.


Goal is ExpertiseGoal is Expertise

Experts readily grasp what is problematic Experts readily grasp what is problematic in a situationin a situation

Experts decompose problems in novel Experts decompose problems in novel ways, ask novel questions, and to develop ways, ask novel questions, and to develop novel solutions.novel solutions.

Propositional knowledge is not enough. Propositional knowledge is not enough.


Bloom’s TaxonomyBloom’s Taxonomy

KnowledgeKnowledge ComprehensionComprehension ApplicationApplication AnalysisAnalysis SynthesisSynthesis EvaluationEvaluation Meta-cognitionMeta-cognition

NoviceNovice

IntermediateIntermediate

ExpertExpert


Experts Hold Knowledge in Experts Hold Knowledge in SchemataSchemata

Triggers and PatternsTriggers and Patterns

Constraints and CriteriaConstraints and Criteria

PlanningPlanning

ImplementationImplementation


ExamplesExamples

Physical principles are schemata. If the Physical principles are schemata. If the word energy occurs in a problem (pattern word energy occurs in a problem (pattern match), then the Law of Conservation of match), then the Law of Conservation of Energy must be involved.Energy must be involved.

Data structures are schemata. Functional Data structures are schemata. Functional languages provide superior facilities.languages provide superior facilities.


Meaningful Problem SolvingMeaningful Problem Solving

Finding a mapping from the semantics of Finding a mapping from the semantics of the problem to the semantics of the the problem to the semantics of the solution.solution.

Once worked out, semantics of Once worked out, semantics of computation is written syntactically.computation is written syntactically.

The semantics-semantics link is provided The semantics-semantics link is provided by schemata. by schemata.


SQS OutlineSQS Outline

Linguistics PhaseLinguistics Phase Semantic Map DownSemantic Map Down Semantics Map UpSemantics Map Up Syntactic Write-upSyntactic Write-up

Verification and Verification and ValidationValidation


Epistemology as Verification Epistemology as Verification and Validationand Validation

Verification: Did we construct the specified Verification: Did we construct the specified system correctly?system correctly?

Validation: Did we specify and construct Validation: Did we specify and construct the correct system?the correct system?


Verification and Validation of Verification and Validation of Models and SimulationsModels and Simulations

In discipline-centric world, models In discipline-centric world, models accepted based on successful experience. accepted based on successful experience.

Interdisciplinarians should not accept on Interdisciplinarians should not accept on face value. face value.


StandardsStandards

Verification and validation references: Verification and validation references: Defense Modeling and Simulation Agency, Defense Modeling and Simulation Agency, the American Institute of Aeronautics and the American Institute of Aeronautics and Astronautics, and the American Society of Astronautics, and the American Society of

Mechanical Engineers.Mechanical Engineers.


Verification is …Verification is …

the demonstration that the model is the demonstration that the model is logically correct and follows from the logically correct and follows from the physical and mathematical laws used. physical and mathematical laws used.

For a computer simulation, verification For a computer simulation, verification shows that the specifications are fulfilled.shows that the specifications are fulfilled.


Verification Verification

Verification shows M&S is “correct” by Verification shows M&S is “correct” by demonstration or evidence. The use of demonstration or evidence. The use of “correct” is problematic because we need “correct” is problematic because we need to know what “correct” means. to know what “correct” means.

In mathematics, we are speaking of the In mathematics, we are speaking of the proof.proof.

In computer science we are generally In computer science we are generally speaking of testing. speaking of testing.


Verification AttributesVerification Attributes

The four characteristics we consider areThe four characteristics we consider are consistency, consistency, justification, justification, lawfulness, and lawfulness, and reasoned.reasoned.


Validation is …Validation is …

the demonstration that the model correctly the demonstration that the model correctly predicts the phenomena modeled. This predicts the phenomena modeled. This can be a lengthy and expensive process can be a lengthy and expensive process particularly if new experiments are particularly if new experiments are conducted.conducted.


Validation AttributesValidation Attributes

CoherentCoherent CredibleCredible Organized Organized RelevantRelevant


One Possible ModuleOne Possible Module


ConclusionConclusion

Incorporates PBL/CBM principles. Incorporates PBL/CBM principles. SQS is based on general systems SQS is based on general systems

concepts. concepts. Meaningful problem solving approach Meaningful problem solving approach

expands the SQS paradigm to specific expands the SQS paradigm to specific problems. problems.

Suitable for university students and Suitable for university students and professionals.professionals.


Conclusions IIConclusions II

Addresses the issue of semantics-to-Addresses the issue of semantics-to-semantics relationships. semantics relationships.

Has been used in my classes.Has been used in my classes.

Is natural extension of disciplinary Is natural extension of disciplinary practice.practice.

Emphasizes the correctness.Emphasizes the correctness.


The End … of the BeginningThe End … of the Beginning


SystemsSystems

A system is any object with behaviors and A system is any object with behaviors and recursivelyrecursively

Standard schemata Standard schemata States and transitions, States and transitions,

components and couplingscomponents and couplings

time-invariant functions and relations. time-invariant functions and relations.


Bloom’s TaxonomyBloom’s Taxonomy

Knowledge: Recall data or information Knowledge: Recall data or information Comprehension: Understand the meaning, Comprehension: Understand the meaning,

translation, interpolation, and interpretation of translation, interpolation, and interpretation of instructions and problems. State a problem in instructions and problems. State a problem in one's own words. one's own words.

Application: Use a concept in a new situation or Application: Use a concept in a new situation or unprompted use of an abstraction. Applies what unprompted use of an abstraction. Applies what was learned in the classroom into novel was learned in the classroom into novel situations in the work place.situations in the work place.


Bloom’s Taxonomy (cont)Bloom’s Taxonomy (cont)

Analysis: Separates material or concepts into Analysis: Separates material or concepts into component parts so that its organizational component parts so that its organizational structure may be understood. Distinguishes structure may be understood. Distinguishes between facts and inferences.between facts and inferences.

Synthesis: Builds a structure or pattern from Synthesis: Builds a structure or pattern from diverse elements. Put parts together to form a diverse elements. Put parts together to form a whole, with emphasis on creating a new whole, with emphasis on creating a new meaning or structure.meaning or structure.

Evaluation: Make judgments about the value of Evaluation: Make judgments about the value of ideas or materials. select the most effective ideas or materials. select the most effective solution.solution.


Triggers and PatternsTriggers and Patterns

Pattern matching triggers.Pattern matching triggers.

The setting of values, recognition of The setting of values, recognition of keywords, or recognition of patterns keywords, or recognition of patterns triggers the schemata.triggers the schemata.


Constraints and CriteriaConstraints and Criteria

Constraints and criteria are logical criteria Constraints and criteria are logical criteria and performance constraints that must be and performance constraints that must be met. met.

A schema may be triggered and then A schema may be triggered and then ignored if the criteria or constraints fail to ignored if the criteria or constraints fail to hold. hold.

Criteria could be theorems or physical Criteria could be theorems or physical laws.laws.


PlanningPlanning

Planning is the organization of a Planning is the organization of a computation or perhaps putting other computation or perhaps putting other schemata in play. schemata in play.

Complex systems often have very large Complex systems often have very large and complex decompositions that must be and complex decompositions that must be planned out, activating other schemata.planned out, activating other schemata.


ImplementationImplementation

This is the computation of ``the answer.'' This is the computation of ``the answer.'' Even with all the available information, the Even with all the available information, the ``answer'' may still be non-computable.``answer'' may still be non-computable.


The SQS Procedure-Problem The SQS Procedure-Problem SemanticsSemantics

Linguistic Phase. A problem is received as Linguistic Phase. A problem is received as words and images in the problem poser's words and images in the problem poser's vocabulary and context. vocabulary and context.

Concept Map Phase. During the concept Concept Map Phase. During the concept map phase, the SQS-specific context is map phase, the SQS-specific context is established through the lexicon, established through the lexicon, vocabulary, and concept maps vocabulary, and concept maps


Semantic MapSemantic Map

Schematic Map Phase. The issues are Schematic Map Phase. The issues are understood semantically. The system-question-understood semantically. The system-question-solution classification takes place. Schemata solution classification takes place. Schemata relevant to the missing information are relevant to the missing information are accessed. The initial SQS elements are accessed. The initial SQS elements are formulated.formulated.

Initial mapping phase. The semantics of the Initial mapping phase. The semantics of the problem are mapped to the computational problem are mapped to the computational semantics, which are primarily datasemantics, which are primarily data


First CodeFirst Code

Representation and algorithm ``snippets'' Representation and algorithm ``snippets'' that will be used later in planning to that will be used later in planning to suggest other coding schemata.suggest other coding schemata.

Completion. In order to produce a Completion. In order to produce a program, the semantics of the program program, the semantics of the program from above are converted to programming from above are converted to programming language syntax.language syntax.


Modification and JudgmentModification and Judgment

Judgment in constraints and criteria. Judgment in constraints and criteria.

Design decisions are often based on what Design decisions are often based on what can be safely ignored or approximated. can be safely ignored or approximated.

Many judgment calls on algorithm Many judgment calls on algorithm complexity.complexity.

VVA Detail SlidesVVA Detail Slides


Consistency. Outside the Consistency. Outside the strict mathematical meaning, strict mathematical meaning, consistency means ``freedom consistency means ``freedom

from contradiction.''from contradiction.''


Justification. According to the Justification. According to the Routledge Dictionary of Routledge Dictionary of

Philosophy, the term Philosophy, the term ``justification'' belongs to a ``justification'' belongs to a

set of terms that also includes set of terms that also includes ``rational'', ``reasonable'' and ``rational'', ``reasonable'' and ``warranted'' that do not have ``warranted'' that do not have

a commonly agreed a commonly agreed definitions or relationships.definitions or relationships.


ConsistencyConsistency

Outside the strict mathematical meaning, Outside the strict mathematical meaning, consistency means ``freedom from consistency means ``freedom from contradiction.''contradiction.''


JustificationJustification

According to the Routledge Dictionary of According to the Routledge Dictionary of Philosophy, the term ``justification'' Philosophy, the term ``justification'' belongs to a set of terms that also includes belongs to a set of terms that also includes ``rational'', ``reasonable'' and ``warranted'' ``rational'', ``reasonable'' and ``warranted'' that do not have a commonly agreed that do not have a commonly agreed definitions or relationships.definitions or relationships.


Law-like Law-like

Development and reasoning must use Development and reasoning must use established laws.established laws.


ReasonedReasoned

Reasons are propositions that meet Reasons are propositions that meet certain conditions such as ``being believed certain conditions such as ``being believed by someone.'' Suppose we have a by someone.'' Suppose we have a proposition P and we also have a proposition P and we also have a statement ``If P then Q'' then we have statement ``If P then Q'' then we have some ``reason'' to believe Q$. But we some ``reason'' to believe Q$. But we need an external reason to believe P. So need an external reason to believe P. So for someone to actually believe Q, that for someone to actually believe Q, that someone must believe P as a reason to someone must believe P as a reason to believe Q.believe Q.


Validation Validation

Whereas verification is concerned about Whereas verification is concerned about rules, validation is concerned with the rules, validation is concerned with the agreement between the model or agreement between the model or simulation and the evidence produced simulation and the evidence produced from observations. from observations.


Coherent Coherent

Areas of knowledge are coherent if all the Areas of knowledge are coherent if all the elements ``fit'' together. This is a central elements ``fit'' together. This is a central tenet of modern science.tenet of modern science.


Credible. Credible.

Scientific observation has an epistemic Scientific observation has an epistemic side, with sufficient meaning and credibility side, with sufficient meaning and credibility to contribute to knowledge.to contribute to knowledge.


Organized. Organized.

Each science has an agreed-upon Each science has an agreed-upon standard arrangement of ideas. Models standard arrangement of ideas. Models and simulations should make use of this and simulations should make use of this structure.structure.


Relevant. Relevant.

Relevance is the ability to retrieve material Relevance is the ability to retrieve material that satisfies the needs of the user. There that satisfies the needs of the user. There are many examples of people focusing on are many examples of people focusing on irrelevant things when attempting to irrelevant things when attempting to validate.validate.


Law-like. Law-like.

Development and reasoning must use Development and reasoning must use established laws.established laws.


ReasonedReasoned

Suppose we have a proposition P and a Suppose we have a proposition P and a statement ``If P then Q'' then we have statement ``If P then Q'' then we have some ``reason'' to believe Q. some ``reason'' to believe Q.

But we need an external reason to believe But we need an external reason to believe P. P.

So for someone to actually believe Q, that So for someone to actually believe Q, that someone must believe P as a reason to someone must believe P as a reason to believe Q.believe Q.


NotesNotes

APA survey - rubin quoted.APA survey - rubin quoted.

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