This book is one of the first to attempt a systematic in-depth analysis of assessment in mathematics education in most of its important aspects: it deals with assessment in mathematics education from historical, psychological, sociological, epistmological, ideological, and political perspectives. The book is based on work presented at an invited international ICMI seminar and includes chapters by a team of outstanding and prominent scholars in the field of mathematics education. Based on the observation of an increasing mismatch between the goals and accomplishments of mathematics education and prevalent assessment modes, the book assesses assessment in mathematics education and its effects. In so doing it pays particular attention to the need for and possibilities of assessing a much wider range of abilities than before, including understanding, problem solving and posing, modelling, and creativity. The book will be of particular interest to mathematics educators who are concerned with the role of assessment in mathematics education, especially as regards innovation, and to everybody working within the field of mathematics education and related areas: in R&D, curriculum planning, assessment institutions and agencies, teacher trainers, etc.

This book is one of the first to attempt a systematic in-depth analysis of assessment in mathematics education in most of its important aspects: it deals with assessment in mathematics education from historical, psychological, sociological, epistmological, ideological, and political perspectives. The book is based on work presented at an invited international ICMI seminar and includes chapters by a team of outstanding and prominent scholars in the field of mathematics education. Based on the observation of an increasing mismatch between the goals and accomplishments of mathematics education and prevalent assessment modes, the book assesses assessment in mathematics education and its effects. In so doing it pays particular attention to the need for and possibilities of assessing a much wider range of abilities than before, including understanding, problem solving and posing, modelling, and creativity. The book will be of particular interest to mathematics educators who are concerned with the role of assessment in mathematics education, especially as regards innovation, and to everybody working within the field of mathematics education and related areas: in R&D, curriculum planning, assessment institutions and agencies, teacher trainers, etc.

"It may be that I have stumbled upon an adequate description of life itself." These modest yet profound words trumpet an imminent paradigm shift in scientific, economic, and technological thinking. In the tradition of Schrödinger's classic What Is Life?, Kauffman's Investigations is a tour-de-force exploration of the very essence of life itself, with conclusions that radically undermine the scientific approaches on which modern science rests--the approaches of Newton, Boltzman, Bohr, and Einstein. Building on his pivotal ideas about order and evolution in complex life systems, Kauffman finds that classical science does not take into account that physical systems--such as people in a biosphere--effect their dynamic environments in addition to being affected by them. These systems act on their own behalf as autonomous agents, but what defines them as such? In other words, what is life? Kauffman supplies a novel answer that goes beyond traditional scientific thinking by defining and explaining autonomous agents and work in the contexts of thermodynamics and of information theory. Much of Investigations unpacks the progressively surprising implications of his definition. Significantly, he sets the stages for a technological revolution in the coming decades. Scientists and engineers may soon seek to create autonomous agents--both organic and mechanical--that can not only construct things and work, but also reproduce themselves! Kauffman also lays out a foundation for a new concept of organization, and explores the requirements for the emergence of a general biology that will transcend terrestrial biology to seek laws governing biospheres anywhere in the cosmos. Moreover, he presents four candidate laws to explain how autonomous agents co-create their biosphere and the startling idea of a "co-creating" cosmos. A showcase of Kauffman's most fundamental and significant ideas, Investigations presents a new way of thinking about the fundamentals of general biology that will change the way we understand life itself--on this planet and anywhere else in the cosmos.

Encourages teachers to explore play , imagination deep involvement and risk taking all I the mathematical context.

Investigations on topics such as the dangers of short term loans, interest, and other topics of financial literacy. Explore the math behind current topics such as ethanol and hybrid cars. Learn how math mistakes in the media have had significant consequences. These and other fascinating math investigations show the ability of mathematics to cut through deception and flawed thinking.

Funded by the National Science Foundation and successfully field-tested in a variety of settings, the materials presented give teachers the opportunity to grow as learners for the classes they teach.

Provides opportunities for engaging, differentiated, open-ended problem-solving experiences. Features more than two hundred tasks grouped by content standards that reflect the NCTM Standards and the NCTM Curriculum Focal Points.