1 / 59

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.

elmer
Download Presentation

SQS: A Pedagogy for Computational Science

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  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

More Related