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Combinatorics and Reasoning: Representing, Justifying and Building Isomorphisms is based on the accomplishments of a cohort group of learners from first grade through high school and beyond, concentrating on their work on a set of combinatorics tasks. By studying these students, the editors gain insight into the foundations of proof building, the tools and environments necessary to make connections, activities to extend and generalize combinatoric learning, and even explore implications of this learning on the undergraduate level. This volume underscores the power of attending to basic ideas in building arguments; it shows the importance of providing opportunities for the co-construction of knowledge by groups of learners; and it demonstrates the value of careful construction of appropriate tasks. Moreover, it documents how reasoning that takes the form of proof evolves with young children and discusses the conditions for supporting student reasoning.
This book may be used for research, graduate and undergraduate teacher education, and teacher development. It presents an integrated set of studies of a heterogeneously grouped class of twenty-one nine-year olds, engaged in exploring fraction ideas prior to classroom instruction under conditions that supported investigation, collaboration and argumentation. It demonstrates with text and video narrative how young children can reason about mathematics in surprisingly sophisticated ways when provided the opportunity to do so in the proper classroom environment. In this volume, fourth grade students’ reasoning about fraction concepts is described through careful analysis and accompanying video excerpts showcasing the variety and originality of their thinking. These children will serve as an inspiration for educators to encourage the development of reasoning and argumentation in their students as part of a mathematics curriculum designed to produce critical thinkers.
Lesson study is a professional development process that teachers engage in to systematically examine their practice, with the goal of becoming more effective. Originating in Japan, lesson study has gained significant momentum in the mathematics education community in recent years. As a process for professional development, lesson study became highly visible when it was proposed as a means of supporting the common practice of promoting better teaching by disseminating documents like standards, benchmarks and nationally validated curricula. While the body of knowledge about lesson study is growing, it remains somewhat elusive and composed of discrete research endeavors. As a new research area ...
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A 15-year-old planter's daughter commits the unpardonable social sin of marrying a man beneath her family's social station. But following her sudden death, the people of Murrell�s Inlet, South Carolina, began to see a despondent ghost who haunts the countryside even today.
This book examines the many reincarnations of Carroll’s texts, illuminating how the meaning of the original books has been re-negotiated through adaptations, appropriations, and transmediality. The volume is an edited collection of eighteen essays and is divided into three sections that examine the re-interpretations of Alice in Wonderland and Through the Looking-Glass in literature, film, and other media (including the branches of commerce, music videos, videogames, and madness studies). This collection is an addition to the existing work on Alice in Wonderland and its sequels, adaptations, and appropriations, and helps readers to have a more comprehensive view of the extent to which the Alice story world is vast and always growing.