What is distinctive in (our views about) models and modelling perspectives on mathematics problem solving, learning, and teaching?

Abstract

What is the nature of typical problem-solving situations where elementary-butpowerfiil mathematical constructs and conceptual systems are needed for success beyond school in a technology-based age of information? What kind of "mathematical thinking" is emphasized in these situations? What does it mean to "understand" the most important ideas and abilities that are needed in the preceding situations? How do these competencies develop? What can be done to facilitate development? How can we document and assess the most important achievements that are needed: (i) for informed citizenship, or (ii) for successful participation in the increasingly wide range of professions that are becoming heavy users of mathematics, science, and technology?