Henry O. Pollak Chairman of the International Program Committee Bell Laboratories Murray Hill, New Jersey, USA The Fourth International Congress on Mathematics Education was held in Berkeley, California, USA, August 10-16, 1980. Previous Congresses were held in Lyons in 1969, Exeter in 1972, and Karlsruhe in 1976. Attendance at Berkeley was about 1800 full and 500 associate members from about 90 countries; at least half of these come from outside of North America. About 450 persons participated in the program either as speakers or as presiders; approximately 40 percent of these came from the U.S. or Canada. There were four plenary addresses; they were delivered by Hans Freudenthal on major problems of mathematics education, Hermina Sinclair on the relationship between the learning of language and of mathematics, Seymour Papert on the computer as carrier of mathematical culture, and Hua Loo-Keng on popularising and applying mathematical methods. Gearge Polya was the honorary president of the Congress; illness prevented his planned attendence but he sent a brief presentation entitled, "Mathematics Improves the Mind". There was a full program of speakers, panelists, debates, miniconferences, and meetings of working and study groups. In addition, 18 major projects from around the world were invited to make presentations, and various groups representing special areas of concern had the opportunity to meet and to plan their future activities.

Learning and Teaching explores major and current themes in the learning/teaching process—from an international and comparative perspective. The authors debate such issues as learning and cognitive processes, students in the classroom and teaching styles. Their views are based on either the findings of original research or observation as experienced teacher educators. Topics covered include learning enhancement, reflection in education, cognition, excellence in education, special schools, classroom interaction, discrimination, assessment and what makes a “good” teacher. Learning and Teaching offers a unique introduction to significant issues affecting the nature of learning and the quality of student/teacher interaction in the classroom.

No one disputes how important it is, in today's world, to prepare students to un derstand mathematics as well as to use and communicate mathematics in their future lives. That task is very difficult, however. Refocusing curricula on funda mental concepts, producing new teaching materials, and designing teaching units based on 'mathematicians' common sense' (or on logic) have not resulted in a better understanding of mathematics by more students. The failure of such efforts has raised questions suggesting that what was missing at the outset of these proposals, designs, and productions was a more profound knowledge of the phenomena of learning and teaching mathematics in socially established and culturally, politically, and economically justified institutions - namely, schools. Such knowledge cannot be built by mere juxtaposition of theories in disci plines such as psychology, sociology, and mathematics. Psychological theories focus on the individual learner. Theories of sociology of education look at the general laws of curriculum development, the specifics of pedagogic discourse as opposed to scientific discourse in general, the different possible pedagogic rela tions between the teacher and the taught, and other general problems in the inter face between education and society. Mathematics, aside from its theoretical contents, can be looked at from historical and epistemological points of view, clarifying the genetic development of its concepts, methods, and theories. This view can shed some light on the meaning of mathematical concepts and on the difficulties students have in teaching approaches that disregard the genetic development of these concepts.

Published to glowing praise in 1990, Science for All Americans defined the science-literate American--describing the knowledge, skills, and attitudes all students should retain from their learning experience--and offered a series of recommendations for reforming our system of education in science, mathematics, and technology. Benchmarks for Science Literacy takes this one step further. Created in close consultation with a cross-section of American teachers, administrators, and scientists, Benchmarks elaborates on the recommendations to provide guidelines for what all students should know and be able to do in science, mathematics, and technology by the end of grades 2, 5, 8, and 12. These grade levels offer reasonable checkpoints for student progress toward science literacy, but do not suggest a rigid formula for teaching. Benchmarks is not a proposed curriculum, nor is it a plan for one: it is a tool educators can use as they design curricula that fit their student's needs and meet the goals first outlined in Science for All Americans. Far from pressing for a single educational program, Project 2061 advocates a reform strategy that will lead to more curriculum diversity than is common today. IBenchmarks emerged from the work of six diverse school-district teams who were asked to rethink the K-12 curriculum and outline alternative ways of achieving science literacy for all students. These teams based their work on published research and the continuing advice of prominent educators, as well as their own teaching experience. Focusing on the understanding and interconnection of key concepts rather than rote memorization of terms and isolated facts, Benchmarks advocates building a lasting understanding of science and related fields. In a culture increasingly pervaded by science, mathematics, and technology, science literacy require habits of mind that will enable citizens to understand the world around them, make some sense of new technologies as they emerge and grow, and deal sensibly with problems that involve evidence, numbers, patterns, logical arguments, and technology--as well as the relationship of these disciplines to the arts, humanities, and vocational sciences--making science literacy relevant to all students, regardless of their career paths. If Americans are to participate in a world shaped by modern science and mathematics, a world where technological know-how will offer the keys to economic and political stability in the twenty-first century, education in these areas must become one of the nation's highest priorities. Together with Science for All Americans, Benchmarks for Science Literacy offers a bold new agenda for the future of science education in this country, one that is certain to prepare our children for life in the twenty-first century.

Solving non-routine problems is a key competence in a world full of changes, uncertainty and surprise where we strive to achieve so many ambitious goals. But the world is also full of solutions because of the extraordinary competences of humans who search for and find them.

This book is addressed to people with research interests in the nature of mathematical thinking at any level, topeople with an interest in "higher-order thinking skills" in any domain, and to all mathematics teachers. The focal point of the book is a framework for the analysis of complex problem-solving behavior. That framework is presented in Part One, which consists of Chapters 1 through 5. It describes four qualitatively different aspects of complex intellectual activity: cognitive resources, the body of facts and procedures at one's disposal; heuristics, "rules of thumb" for making progress in difficult situations; control, having to do with the efficiency with which individuals utilize the knowledge at their disposal; and belief systems, one's perspectives regarding the nature of a discipline and how one goes about working in it. Part Two of the book, consisting of Chapters 6 through 10, presents a series of empirical studies that flesh out the analytical framework. These studies document the ways that competent problem solvers make the most of the knowledge at their disposal. They include observations of students, indicating some typical roadblocks to success. Data taken from students before and after a series of intensive problem-solving courses document the kinds of learning that can result from carefully designed instruction. Finally, observations made in typical high school classrooms serve to indicate some of the sources of students' (often counterproductive) mathematical behavior.

Theoretical Foundations of Learning Environments provides students, faculty, and instructional designers with a clear, concise introduction to the major pedagogical and psychological theories and their implications for the design of new learning environments for schools, universities, or corporations. Leading experts describe the most important contemporary theories that form the foundation of the conception and design of student-centered learning environments and new applications of educational technologies. This book is well suited as a textbook for courses in instructional design, educational psychology, learning theory, curriculum theory and design, and related areas. The rise of constructivism and its associated theories represented a paradigm shift for educators and instructional designers to a view of learning as necessarily more social, conversational, and constructive than traditional transmissive views of learning. This bestselling book was the first to provide a manageable overview of the altered field, and the second edition has been fully updated to include expert introductions to Metacognition, Argumentation, and other key contemporary theories.

Theoretical Foundations of Learning Environments describes the most contemporary psychological and pedagogical theories that are foundations for the conception and design of open-ended learning environments and new applications of educational technologies. In the past decade, the cognitive revolution of the 60s and 70s has been replaced or restructured by constructivism and its associated theories, including situated, sociocultural, ecological, everyday, and distributed conceptions of cognition. These theories represent a paradigm shift for educators and instructional designers, to a view of learning as necessarily more social, conversational, and constructive than traditional transmissive views of learning. Never in the history of education have so many different theories said the same things about the nature of learning and the means for supporting it. At the same time, although there is a remarkable amount of consonance among these theories, each also provides a distinct perspective on how learning and sense making occur. This book provides students, faculty, and instructional designers with a clear, concise introduction to these theories and their implications for the design of new learning environments for schools, universities, and corporations. It is well-suited as a required or supplementary text for courses in instructional design and theory, educational psychology, learning, theory, curriculum theory and design, and related areas.