Based on the author’s experience as a researcher and teacher of lower-track students, Beyond Formulas in Mathematics and Teaching illuminates the complex dynamics of the algebra classroom. From within this setting, Daniel Chazan thoughtfully explores topics that concern all dedicated educators, how to really know one’s students, how to find engaging material, and how to inspire meaningful classroom conversations. Throughout, he addresses the predicaments that are central to the lives of teachers who work in standard educational settings. By highlighting teaching dilemmas, Chazan prompts readers to consider what their own responses would be in similar situations. With an eye to ways of restructuring roles and relationships, Beyond Formulas in Mathematics and Teaching is essential reading for educators seeking to enhance their teaching practices and understanding of students who may be estranged from school.

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 book reviews the evaluation research literature that has accumulated around 19 K-12 mathematics curricula and breaks new ground in framing an ambitious and rigorous approach to curriculum evaluation that has relevance beyond mathematics. The committee that produced this book consisted of mathematicians, mathematics educators, and methodologists who began with the following charge: Evaluate the quality of the evaluations of the thirteen National Science Foundation (NSF)-supported and six commercially generated mathematics curriculum materials; Determine whether the available data are sufficient for evaluating the efficacy of these materials, and if not; Develop recommendations about the design of a project that could result in the generation of more reliable and valid data for evaluating such materials. The committee collected, reviewed, and classified almost 700 studies, solicited expert testimony during two workshops, developed an evaluation framework, established dimensions/criteria for three methodologies (content analyses, comparative studies, and case studies), drew conclusions on the corpus of studies, and made recommendations for future research.

From a critically acclaimed master of language, a look at the trends, phenomena, and battles on the front lines of modern American English. In You Need to Read This, language expert Ben Yagoda writes about the cuckoo things we have done to the English language. His witty, insightful, and wise observations and advice are gathered here together for the first time. From the phenomenon of curate, to the rise of the glottal stop, to the prevalence of starting sentences with so, to the story of an epithet of the moment (douchey), Yagoda chronicles the trends in our language. In the second part of You Need to Read This, he examines the issue of mistakes and “mistakes,” and the battles between prescriptivists, who nitpick grammar, and descriptivists, who defend new expressions and casual usage. Yagoda is on the front lines of the language wars, and you need to read this book to find out which side you’re on.

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.

This volume sheds a new light on Philosophical Investigations, Ludwig Wittgenstein’s master opus, by taking a new approach to its first stretch (sections §§1-88), with special emphasis on its atypical opening. The methodological conviction that subtends the volume is that the highly unconventional form assumed by the book is internal to its content and crucial to its reconception of the relation between logic and language. This disconcerting form is dictated by the new modes of criticism deployed by Wittgenstein as he engages the philosophical tradition in the new terms afforded by the revolutionary “method of language-games”. In the essays collected here, seven authors, including some of the most influential figures in the field, offer close and often unorthodox readings of pivotal passages from the beginning of the book. These readings are also shaped by the conviction that the Philosophical Investigations are hardly intelligible apart from an appreciation of the concerns that they inherit from Wittgenstein’s early work, the Tractatus Logico-Philosophicus. The authors contend that we need to consider the continuities between the early and the later works if we are to disclose the true discontinuities between them.