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Mathematics as a discipline has a long history, emerging from many cultures, with a truly universal character. Mathematicians throughout the world have a fundamentally common understanding of the nature of mathematics and of its central problems and methods. Research mathematicians in any part of the world are part of a cohesive intellectual community that communicates fluently. Among organizations devoted to mathematics education, The International Commission on Mathematical Instruction (ICMI) is distinctive because of its close ties to the mathematics community. The great challenges now facing mathematics education around the world demand a deeper and more sensitive involvement of disciplinary mathematicians than we now have, both in the work of educational improvements and in research on the nature of teaching and learning.
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.
This book addresses the need of professional development leaders and policymakers for scholarly knowledge about influencing teachers to modify mathematical instruction to bring it more in alignment with the recommendations of the current reform movement initiated by the National Council of Teachers of Mathematics. The book presents: * theoretical perspectives for studying, analyzing, and understanding teacher change; * descriptions of contextual variables to be considered as one studies and attempts to understand teacher change; and * descriptions of professional development programs that resulted in teacher change. One chapter builds a rationale for looking to developmental psychology for guidance in constructing models of reconstructing new forms of mathematical instruction. Another highlights the relevance to mathematics teacher development of research-based knowledge about how children construct mathematical ideas. Other chapters explore the relationships between the various contexts of schooling and instructional change. Included also are chapters that describe and analyze major reform efforts designed to assist teachers in modifying their instructional practices (Cognitively Guided Instruction, Math-Cubed, Project Impact, Mathematics in Context, and the Case-Based Project). Finally, the current state of knowledge about encouraging teachers to modify their instruction is discussed, the implications of major research and implementation findings are suggested, and some of the major questions that need to be addressed are identified, such as what we have learned about teacher change.
This open access book, inspired by the ICME 13 Thematic Afternoon on “European Didactic Traditions”, takes readers on a journey with mathematics education researchers, developers and educators in eighteen countries, who reflect on their experiences with Realistic Mathematics Education (RME), the domain-specific instruction theory for mathematics education developed in the Netherlands since the late 1960s. Authors from outside the Netherlands discuss what aspects of RME appeal to them, their criticisms of RME and their past and current RME-based projects. It is clear that a particular approach to mathematics education cannot simply be transplanted to another country. As such, in eighteen chapters the authors describe how they have adapted RME to their individual circumstances and view on mathematics education, and tell their personal stories about how RME has influenced their thinking on mathematics education.
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.
In Dutch "WISKOBAS" stands for a particular kind of mathematics in the elementary school (ages 6-12). In tum Wiskobas was one of the depart ments in the IOWO, the Institute for the Development of Mathematics Education. This institute was concerned with the development of material for mathematics education as well as the related research on the possibility of change from the then existing arithmetic instruction to the future mathematics education. The present publication Three Dimensions has three aims: to give a picture of the goals Wiskobas set for future mathematics education, at the same time to show how such goals can be described, and to show the theoretical framework of the Wiskobas curriculum. The problem at hand is not at all simple. What is more, Wiskobas' ideas about mathematics education cannot literally be translated into strings of words. So how can we face the accusation that our objectives are unattain able and the goal itself irrational? In order to avoid this vagueness as much as possible and for the sake of clarity, this book makes continuous use of illustrations of mathematics education. In these examples both the subject-matter and the methods of description of the goals are illustrated as explicitly as possible, while at the same time creating the opportunity to read between the lines. The reader is urged to follow carefully the mathe matical material at the start of each chapter. This advice applies both to the more general education oriented, and to the more mathematical! didactical reader.
This volume emphasizes students' inferred mathematical experiences as the starting point in the theory-building process. The book addresses conceptual constructions, including multiplicative notions, fractions, algebra, and the fundamental theorem of calculus, and theoretical constructs such as the crucial role of language and symbols, and the importance of dynamic imagery.
Learning potential assessment, which has lately been receiving a great deal of attention, consists of test procedures for measuring children's learning potential procedures that be regarded as an extension of current intelligence testing.