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SQS: A Pedagogy for Computational Science

SQS: A Pedagogy for Computational Science. D. E. (Steve) Stevenson and friends Partial support from NSDL DUE-0435187 and STEP program DUE-0525474. Changing the Status Quo?. If work paradigm changes, education paradigm changes.

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SQS: A Pedagogy for Computational Science

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  1. SQS: A Pedagogy for Computational Science D. E. (Steve) Stevenson and friends Partial support from NSDL DUE-0435187 and STEP program DUE-0525474. ICCSE - Rochester

  2. Changing the Status Quo? • If work paradigm changes, education paradigm changes. • You never change something by fighting the existing reality. To change something, build a new model that makes the existing model obsolete Buckminster Fuller ICCSE - Rochester

  3. Before We Begin • This talk is most effective If you have a problem you want to solve. • Think of a student or colleague that you have tried to work with who just didn’t get a model and its simulation. ICCSE - Rochester

  4. Science is About SQS • Definitions of Systems, • Questions about those systems, and • Solutions to questions interpreted on these systems ICCSE - Rochester

  5. SQS Examples • (system, question) - engineering fare. • (systems, solutions) - debugging • (questions, solutions) - synthesize one or more systems with given capabilities. • (solutions) ``To an engineer with a hammer, the whole world looks like a nail.'' ICCSE - Rochester

  6. CS as Explanation of Systems • Modeling and simulation aids researcher explain systems. • The knowledge structure of CS follows the Knowledge Vee. • M&S knowledge warranted by verification and validation. ICCSE - Rochester

  7. Initial Observations • CS applications are interdisciplinary. • CS problems are defined on systems. • Switching systems requires significant learning effort. • Computational scientists must be efficient learners. ICCSE - Rochester

  8. The A3 Paradigm ICCSE - Rochester

  9. Four Tenets • University education mirrors professional practice to build expertise. • General systems theory is theoretical paradigm. • Knowledge Vee is organizer and V&V is knowledge warrantor. • Systems-Questions-Solutions is the pedagogical principle. ICCSE - Rochester

  10. World View Epistemology Theory Principles Constructs Concepts Knowledge Claims Transformations Records Knowledge Vee for Systems • Focus Questions and Observations • Objects, Events, and Observations. ICCSE - Rochester

  11. SQS Concepts

  12. The Challenge Students must learn how to learn • professional methods, • principles, and • values from multiple disciplines and how to apply these concepts to a broad range of problems. ICCSE - Rochester

  13. How People Learn • Deep factual knowledge (facts) of the subject, • Deep knowledge of pragmatic issues (schemata), and • Meta-cognitive control and evaluation ICCSE - Rochester

  14. Inquiry-Based Learning • PBL learners learn best when presented with a realistic problem to focus on. • CBM use collaborative analysis leading to judgments when there is no single, correct answer. ICCSE - Rochester

  15. Goal is Expertise • Experts readily grasp what is problematic in a situation • Experts decompose problems in novel ways, ask novel questions, and to develop novel solutions. • Propositional knowledge is not enough. ICCSE - Rochester

  16. Knowledge Comprehension Application Analysis Synthesis Evaluation Meta-cognition Novice Intermediate Expert Bloom’s Taxonomy ICCSE - Rochester

  17. Experts Hold Knowledge in Schemata • Triggers and Patterns • Constraints and Criteria • Planning • Implementation ICCSE - Rochester

  18. Examples • Physical principles are schemata. If the word energy occurs in a problem (pattern match), then the Law of Conservation of Energy must be involved. • Data structures are schemata. Functional languages provide superior facilities. ICCSE - Rochester

  19. Meaningful Problem Solving • Finding a mapping from the semantics of the problem to the semantics of the solution. • Once worked out, semantics of computation is written syntactically. • The semantics-semantics link is provided by schemata. ICCSE - Rochester

  20. SQS Outline • Linguistics Phase • Semantic Map Down • Semantics Map Up • Syntactic Write-up ICCSE - Rochester

  21. Verification and Validation

  22. Epistemology as Verification and Validation • Verification: Did we construct the specified system correctly? • Validation: Did we specify and construct the correct system? ICCSE - Rochester

  23. Verification and Validation of Models and Simulations • In discipline-centric world, models accepted based on successful experience. • Interdisciplinarians should not accept on face value. ICCSE - Rochester

  24. Standards • Verification and validation references: • Defense Modeling and Simulation Agency, • the American Institute of Aeronautics and • Astronautics, and the American Society of Mechanical Engineers. ICCSE - Rochester

  25. Verification is … • the demonstration that the model is logically correct and follows from the physical and mathematical laws used. • For a computer simulation, verification shows that the specifications are fulfilled. ICCSE - Rochester

  26. Verification • Verification shows M&S is “correct” by demonstration or evidence. The use of “correct” is problematic because we need to know what “correct” means. • In mathematics, we are speaking of the proof. • In computer science we are generally speaking of testing. ICCSE - Rochester

  27. Verification Attributes • The four characteristics we consider are • consistency, • justification, • lawfulness, and • reasoned. ICCSE - Rochester

  28. Validation is … • the demonstration that the model correctly predicts the phenomena modeled. This can be a lengthy and expensive process particularly if new experiments are conducted. ICCSE - Rochester

  29. Validation Attributes • Coherent • Credible • Organized • Relevant ICCSE - Rochester

  30. One Possible Module ICCSE - Rochester

  31. Conclusion • Incorporates PBL/CBM principles. • SQS is based on general systems concepts. • Meaningful problem solving approach expands the SQS paradigm to specific problems. • Suitable for university students and professionals. ICCSE - Rochester

  32. Conclusions II • Addresses the issue of semantics-to-semantics relationships. • Has been used in my classes. • Is natural extension of disciplinary practice. • Emphasizes the correctness. ICCSE - Rochester

  33. The End … of the Beginning ICCSE - Rochester

  34. Systems • A system is any object with behaviors and recursively • Standard schemata • States and transitions, • components and couplings • time-invariant functions and relations. ICCSE - Rochester

  35. Bloom’s Taxonomy • Knowledge: Recall data or information • Comprehension: Understand the meaning, translation, interpolation, and interpretation of instructions and problems. State a problem in one's own words. • Application: Use a concept in a new situation or unprompted use of an abstraction. Applies what was learned in the classroom into novel situations in the work place. ICCSE - Rochester

  36. Bloom’s Taxonomy (cont) • Analysis: Separates material or concepts into component parts so that its organizational structure may be understood. Distinguishes between facts and inferences. • Synthesis: Builds a structure or pattern from diverse elements. Put parts together to form a whole, with emphasis on creating a new meaning or structure. • Evaluation: Make judgments about the value of ideas or materials. select the most effective solution. ICCSE - Rochester

  37. Triggers and Patterns • Pattern matching triggers. • The setting of values, recognition of keywords, or recognition of patterns triggers the schemata. ICCSE - Rochester

  38. Constraints and Criteria • Constraints and criteria are logical criteria and performance constraints that must be met. • A schema may be triggered and then ignored if the criteria or constraints fail to hold. • Criteria could be theorems or physical laws. ICCSE - Rochester

  39. Planning • Planning is the organization of a computation or perhaps putting other schemata in play. • Complex systems often have very large and complex decompositions that must be planned out, activating other schemata. ICCSE - Rochester

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

  41. The SQS Procedure-Problem Semantics • Linguistic Phase. A problem is received as words and images in the problem poser's vocabulary and context. • Concept Map Phase. During the concept map phase, the SQS-specific context is established through the lexicon, vocabulary, and concept maps ICCSE - Rochester

  42. Semantic Map • Schematic Map Phase. The issues are understood semantically. The system-question-solution classification takes place. Schemata relevant to the missing information are accessed. The initial SQS elements are formulated. • Initial mapping phase. The semantics of the problem are mapped to the computational semantics, which are primarily data ICCSE - Rochester

  43. First Code • Representation and algorithm ``snippets'' that will be used later in planning to suggest other coding schemata. • Completion. In order to produce a program, the semantics of the program from above are converted to programming language syntax. ICCSE - Rochester

  44. Modification and Judgment • Judgment in constraints and criteria. • Design decisions are often based on what can be safely ignored or approximated. • Many judgment calls on algorithm complexity. ICCSE - Rochester

  45. VVA Detail Slides

  46. Consistency. Outside the strict mathematical meaning, consistency means ``freedom from contradiction.'' ICCSE - Rochester

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

  48. Consistency • Outside the strict mathematical meaning, consistency means ``freedom from contradiction.'' ICCSE - Rochester

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

  50. Law-like • Development and reasoning must use established laws. ICCSE - Rochester

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