PATTERNS. The Pattern of Two Loci. The Cartesian Pattern. Recursion. Superposition. TOWARD A GENERAL METHOD. Problems. Widening the Scope. Solutions. Appendix. Bibliography. Index.

This study shows that top-down decomposition is problematic in the early stages of design. Instead, an opportunistic decomposition is better suited to handle the ill-structuredness of design problems. Designers are observed interleaving decisions at various levels of abstraction in the solution decomposition. The verbal protocols of three professionals designing a software system of realistic complexity are analyzed to determine the frequency and causes of opportunistic decompositions. The sudden discovery of new requirements and partial solutions triggered by data-driven rules and associations, the immediate development of solutions for newly discovered requirements, and drifting through partial solutions are shown to be important causes of opportunistic design. A top-down decomposition appears to be a special case for well-structured problems when the designer already knows the correct decomposition. Two cognitive models are briefly discussed in relation to opportunistic design. Finally, implications for training, methods, and computational environments to support the early stages of design are outlined.

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Mathematical discovery;: On understanding, learning, and teaching problem solving

Designing the design process: exploiting opportunistic thoughts

1. Paradigms and pragmatism: comparative politics during the past decade Mark I. Lichbach and Alan S. Zuckerman 2. Thinking and working: discovery, explanation, and evidence in comparative politics Mark Irving Lichbach 3. Advancing explanation in comparative politics: social mechanisms, endogenous processes, and empirical rigor Alan S. Zuckerman 4. Strong theory, complex history: structure and configuration in comparative politics revisited Ira Katznelson 5. Reconsiderations of rational choice in comparative and historical analysis Margaret Levi 6. Culture in comparative political analysis Marc Ross 7. Researching the state Joel S. Migdal 8. An approach to comparative analysis, or a sub-field within a sub-field? Political economy Mark Blyth 9. The global context of comparative politics Etel Solingen 10. Comparative perspectives on contentious politics Doug McAdam, Sidney Tarrow and Charles Tilly 11. Citizenship in democratic politics: density dependence and the micro-macro divide Robert Huckfeldt 12. Macropolitics and microbehavior in comparative politics Christopher J. Anderson 13. Back to the future: endogenous institutions and comparative politics Jonathan Rodden 14. The comparative political economy of the welfare state Isabela Mares 15. Making causal claims about the effect of 'ethnicity' Kanchan Chandra.

Comparative Politics: Rationality, Culture, and Structure

Chapter 9: Classrooms as Learning Environments for Teachers and Researchers

Many researchers and curriculum frameworks recommend that the concept of proof and the corresponding activity of proving become part of students' mathematical experiences throughout the grades. Yet it is still unclear what "proof" means in school mathematics, especially in the elementary grades, and what role the teacher has in cultivating proof and proving among their students. In this article, I propose a conceptualization of the meaning of proof in school mathematics and use classroom episodes from third grade to elaborate elements of this conceptualization and to illustrate its applicability even in the early elementary grades. Furthermore, I use the conceptualization to develop a tool to analyze the classroom episodes and to examine aspects of the teachers' role in managing their students? proving activity. This analysis supports the development of a framework about instructional practices for cultivating proof and proving in school mathematics.

Proof and Proving in School Mathematics

Paper 17: David H. Bailey and Jonathan M. Borwein, “Pi and its friends,” and “Normality: A stubborn question,” from Mathematics by Experiment: Plausible Reasoning in the 21st Century, A. K. Peters, Natick, MA, 2nd edition, 2008. Reproduced with permission of AK Peters.

/pdf/mathematics-by-experiment-plausible-reasoning-in-the-21st-4oo6eoy636.pdf

Mathematical discovery;: On understanding, learning, and teaching problem solving

Citations

Designing the design process: exploiting opportunistic thoughts

Comparative Politics: Rationality, Culture, and Structure

Chapter 9: Classrooms as Learning Environments for Teachers and Researchers

Proof and Proving in School Mathematics

Mathematics by experiment : plausible reasoning in the 21st century

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