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The book aims at showing the state-of-the-art in the field of modeling and applications in mathematics education. This is the first volume to do this. The book deals with the question of how key competencies of applications and modeling at the heart of mathematical literacy may be developed; with the roles that applications and modeling may play in mathematics teaching, making mathematics more relevant for students.
This volume presents a novel, theoretical, micro-analytical model – the 3A Methodology – for assessing the quality of school education. Drawing on philosophers as well as theoretical and pedagogical traditions from European and American contexts, the authors construct a model that is relevant to teachers, researchers, and teacher educators regardless of cultural setting. The chapters explain the 3A Methodology as a specific research tool developed to study classroom situations in the form of case studies, revealing findings that demonstrate prototypical failures (didactic formalism) that threaten to compromise the quality of learning as well as prototypical didactic virtues that verifiably support students’ learning. Ultimately building on the distinction of three modes of existence of educational content (the intersubjective, the subjective, and the objective modes), the book helps rediscover didactics as a transdisciplinary theory of content transformation and contributes to the improvement of teaching and learning in the classroom long term. This volume will be of interest to scholars, researchers, and postgraduate students working in school education, educational psychology, and didactics more broadly. Teacher educators and school administrators may also find the book of interest. Chapters 1, 3, and 6 of this book is freely available as a downloadable Open Access PDF at http://www.taylorfrancis.com under a Creative Commons Attribution-Non Commercial-No Derivatives (CC-BY-NC-ND) 4.0 license.
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.
The diversity of research domains and theories in the field of mathematics education has been a permanent subject of discussions from the origins of the discipline up to the present. On the one hand the diversity is regarded as a resource for rich scientific development on the other hand it gives rise to the often repeated criticism of the discipline’s lack of focus and identity. As one way of focusing on core issues of the discipline the book seeks to open up a discussion about fundamental ideas in the field of mathematics education that permeate different research domains and perspectives. The book addresses transformation as one fundamental idea in mathematics education and examines it from different perspectives. Transformations are related to knowledge, related to signs and representations of mathematics, related to concepts and ideas, and related to instruments for the learning of mathematics. The book seeks to answer the following questions: What do we know about transformations in the different domains? What kinds of transformations are crucial? How is transformation in each case conceptualized?
This book presents the main research veins developed within the framework of the Anthropological Theory of the Didactic (ATD), a paradigm that originated in French didactics of mathematics. While a great number of publications on ATD are available in French and Spanish, Working with the Anthropological Theory of the Didactic in Mathematics Education is the first directed at English-speaking international audiences. Written and edited by leading researchers in ATD, the book covers all aspects of ATD theory and practice, including teaching applications. The chapters feature the most relevant and recent investigations presented at the 6th international conference on the ATD, offering a unique opportunity for an international audience interested in the study of mathematics teaching and learning to keep in touch with advances in educational research. The book is divided into four sections and the contributions explore key topics such as: The core concept of ‘praxeology’, including its development and functionalities The need for new teaching praxeologies in the paradigm of questioning the world The impact of ATD on the teaching profession and the education of teachers This is the second volume in the New Perspectives on Research in Mathematics Education. This comprehensive casebook is an indispensable resource for researchers, teachers and graduate students around the world.
The notion of otherness, often misused, requires important conceptualization work in order for it to be considered in all of its forms, and not simply reduced to the account of others. Although otherness certainly questions the link to the other (relation), it also questions the link to the self (reflexivity) and the link to knowledge (epistemology). Being tridimensional, the process of otherness is a paradox, the meaning of which can only be drawn thanks to ethics, psychoanalytical orientation and the history of philosophical ideas. This book, which relates to philosophy of education, seeks to explain the problematic notion of otherness, the desire for which is specific to humankind. It examines how otherness questions the limits of knowledge, transmission and language, and argues that it is in fact a value, a tool and practice for all the actors involved in the relationship between education, knowledge and care.
This book comprises the full selected Regular Lectures from the Proceedings of the 12th International Congress on Mathematical Education (ICME-12), which was held at COEX in Seoul, Korea, from July 8th to 15th, 2012. ICME-12 brought together 4700 experts from 100 countries, working to understand all of the intellectual and attitudinal challenges in the subject of mathematics education as a multidisciplinary research and practice. These selected Regular Lectures present the work of fifty-one prominent mathematics educators from all over the globe. The Lectures cover a wide spectrum of topics, themes and issues and aim to give direction to future research towards educational improvement in the teaching and learning of mathematics education. This book is of particular interest to researchers, teachers and curriculum developers in mathematics education.
This edited volume will help educators better analyze methodological and practical tools designed to aid classroom instruction. It features papers that explore the need to create a system in order to fully meet the uncertainties and developments of modern educational phenomena. These have emerged due to the abundance of digital resources and new forms of collective work. The collected papers offer new perspectives to a rising field of research known as the Documentational Approach to Didactics. This framework was first created by the editors of this book. It seeks to develop a deeper understanding of mathematics teaching expertise. Readers will gain insight into how to meet the theoretical questions brought about by digitalization. These include: how to analyze teachers’ work when they prepare for their teaching, how to conceptualize the relationships between individual and collective work, and how to follow the related processes over the long term. The contributors also provide a comparative view in terms of contrasting selected phenomena across different educational cultures and education systems. For instance, they consider how differences in curriculum resources are available to teachers and how teachers make use of them to shape instruction. Coverage also considers the extent to which teachers make use of additional material, particularly those available through the global marketplace on the Internet. This book builds on works from the Re(s)sources 2018 Conference, Understanding teachers’ work through their interactions with resources for teaching, held in Lyon, France.
The book contains the Proceedings of the 2010 Conference of the Italian Systems Society. Papers deal with the interdisciplinary study of processes of changing related to a wide variety of specific disciplinary aspects. Classical attempts to deal with them, based on generalising approaches used to study the movement of bodies and environmental influence, have included ineffective reductionistic simplifications. Indeed changing also relates, for instance, to processes of acquisition and varying properties such as for software; growing and aging biological systems; learning/cognitive systems; and socio-economic systems growing and developing through innovations. Some approaches to modelling such processes are based on considering changes in structure, e.g., phase-transitions. Other approaches are based on considering (1) periodic changes in structure as for processes of self-organisation; (2) non-periodic but coherent changes in structure, as for processes of emergence; (3) the quantum level of description. Papers in the book study the problem considering its transdisciplinary nature, i.e., systemic properties studied per se and not within specific disciplinary contexts. The aim of these studies is to outline a transdisciplinary theory of change in systemic properties. Such a theory should have simultaneous, corresponding and eventually hierarchical disciplinary aspects as expected for a general theory of emergence. Within this transdisciplinary context, specific disciplinary research activities and results are assumed to be mutually represented as within a philosophical and conceptual framework based on the theoretical centrality of the observer and conceptual non-separability of context and observer, related to logically open systems and Quantum Entanglement. Contributions deal with such issues in interdisciplinary ways considering theoretical aspects and applications from Physics, Cognitive Science, Biology, Artificial Intelligence, Economics, Architecture, Philosophy, Music and Social Systems.
Teachers' knowledge of the subjects they teach has been of enduring interest to governments, the profession and the wider society. In this book, Viv Ellis traces the development of three beginning teachers thinking about their subject knowledge in the context of Standards-based teacher education and the practice of auditing student teachers' subject knowledge. Ellis puts forward a theory of subject knowledge development that moves on from the objectivist and individualistic epistemologies associated with Standards and the practices of auditing to more a contextualist and sociocultural understanding of teachers' cognition and learning. An important implication of this study is that if teacher education wishes to have greater impact on the development of beginning teachers, teacher educators need to pay greater attention to the schools and subject department settings in which these beginning teachers learn.