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Monkey has gathered a huge pile of tasty coconuts. Before he can enjoy them he must count them. He discovers counting in sets is the fastest way to complete the task.
This unique volume presents an ecocultural and embodied perspective on understanding numbers and their history in indigenous communities. The book focuses on research carried out in Papua New Guinea and Oceania, and will help educators understand humanity's use of numbers, and their development and change. The authors focus on indigenous mathematics education in the early years and shine light on the unique processes and number systems of non-European styled cultural classrooms. This new perspective for mathematics education challenges educators who have not heard about the history of number outside of Western traditions, and can help them develop a rich cultural competence in their own practice and a new vision of foundational number concepts such as large numbers, groups, and systems. Featured in this invaluable resource are some data and analyses that chief researcher Glendon Angove Lean collected while living in Papua New Guinea before his death in 1995. Among the topics covered: The diversity of counting system cycles, where they were established, and how they may have developed. A detailed exploration of number systems other than base 10 systems including: 2-cycle, 5-cycle, 4- and 6-cycle systems, and body-part tally systems. Research collected from major studies such as Geoff Smith's and Sue Holzknecht’s studies of Morobe Province's multiple counting systems, Charly Muke's study of counting in the Wahgi Valley in the Jiwaka Province, and Patricia Paraide's documentation of the number and measurement knowledge of her Tolai community. The implications of viewing early numeracy in the light of this book’s research, and ways of catering to diversity in mathematics education. In this volume Kay Owens draws on recent research from diverse fields such as linguistics and archaeology to present their exegesis on the history of number reaching back ten thousand years ago. Researchers and educators interested in the history of mathematical sciences will find History of Number: Evidence from Papua New Guinea and Oceania to be an invaluable resource.
“A fascinating book.” —James Ryerson, New York Times Book Review A Smithsonian Best Science Book of the Year Winner of the PROSE Award for Best Book in Language & Linguistics Carved into our past and woven into our present, numbers shape our perceptions of the world far more than we think. In this sweeping account of how the invention of numbers sparked a revolution in human thought and culture, Caleb Everett draws on new discoveries in psychology, anthropology, and linguistics to reveal the many things made possible by numbers, from the concept of time to writing, agriculture, and commerce. Numbers are a tool, like the wheel, developed and refined over millennia. They allow us to grasp quantities precisely, but recent research confirms that they are not innate—and without numbers, we could not fully grasp quantities greater than three. Everett considers the number systems that have developed in different societies as he shares insights from his fascinating work with indigenous Amazonians. “This is bold, heady stuff... The breadth of research Everett covers is impressive, and allows him to develop a narrative that is both global and compelling... Numbers is eye-opening, even eye-popping.” —New Scientist “A powerful and convincing case for Everett’s main thesis: that numbers are neither natural nor innate to humans.” —Wall Street Journal
This monograph presents Azzouni’s new approach to the rule-following paradox. His solution leaves intact an isolated individual’s capacity to follow rules, and it simultaneously avoids replacing the truth conditions for meaning-talk with mere assertability conditions for that talk. Kripke’s influential version of Wittgenstein’s rule-following paradox—and Wittgenstein’s views more generally—on the contrary, make rule-following practices and assertions about those practices subject to community norms without which they lose their cogency. Azzouni summarizes and develops Kripke’s original version of Wittgenstein’s rule-following paradox to make salient the linchpin assumptions of the paradox. By doing so, Azzouni reveals how compelling Kripke’s earlier work on the paradox was. Objections raised over the years by Fodor, Forbes Ginsborg, Goldfarb, Tait, Wright, and many others, are all shown to fail. No straight solution (a solution that denies an assumption of the paradox) can be made to work. Azzouni illustrates this in detail by showing that a popular family of straight solutions due to Lewis and refined by Williams, “reference magnetism,” fail as well. And yet an overlooked sceptical solution is still available in logical space. Azzouni describes a series of “disposition-meaning” private languages that he shows can be successfully used by a population of speakers to communicate with one another despite their ideolectical character. The same sorts of languages enable solitary “Robinson Crusoes” to survive and flourish in their island habitats. These languages—sufficiently refined—have the same properties normal human languages have; and this is the key to solving the rule-following paradox without sacrificing the individual’s authority over her self-imposed rules or her ability to follow those rules. Azzouni concludes this unusual monograph by uncovering a striking resemblance between the rule-following paradox and Hume’s problem of induction: he shows the rule-following paradox to be a corollary of Hume’s problem that arises when the problem of induction is applied to an individual’s own abilities to follow rules. “The book is clearly and engagingly written, and the conclusions are well-argued-for. (Depressingly well-argued-for in the case of Chapter 3, as I've always been partial to Lewisian responses to Putnam's model-theoretic argument--I'm rethinking that now.) And the proposed solution to the rule-following paradox really is novel.” Joshua Brown - Gustavus Adolphus College
Achieve lasting health—without cutting calories or following dieting “rules”! Instead of obsessing about the quantity of food you eat, shift your focus to the quality, say Noelle Tarr and Stefani Ruper. The popular hosts of the Well-Fed Women podcast want you to make sure you’re getting enough food so that your body has the fuel and nourishment it needs to support a healthy, long, and energetic life. Noelle and Stefani know firsthand about the ups and downs of dieting. Like many people, they have struggled with confusing and frustrating health issues such as anxiety, infertility, and hormonal imbalance—but when they discovered that the secret to improving wellness was actually more food, they ditched the calorie counters and gave their bodies the nourishment they needed to heal. In the Coconuts and Kettlebells program, you’ll eat at least 2,000 calories a day—setting a minimum intake of fat, protein, and carbohydrates to ensure that your diet is full of nutrients. Noelle and Stefani identify the Big Four foods that cause the most health problems—grains, dairy, vegetable oils, and refined sugar. While many diets require you to eliminate these foods entirely, Coconuts and Kettlebells provides an easy-to-follow step-by-step system to test these foods and determine which you need to cut back on to feel better—and which you can eat without restrictions. To help you discover how your body responds to the Big Four, you’ll choose from two simple 4-week meal plans: one for Butter Lovers, people who tend to feel more satisfied eating higher ratios of fats, and one for Bread Lovers, people who tend to feel more satisfied eating higher ratios of carbs. Each meal plan comes with weekly shopping lists and instructions on how to batch cook, meal prep, and stock the pantry. In addition, you get more than 75 simple and delicious real food recipes, including: • Kale and Bacon Breakfast Skillet • Raspberry-Coconut Smoothie Bowl • Thai Coconut Curry Shrimp • Apple-Chicken Skillet • Moroccan Lamb Meatballs • Grilled Balsamic Flank Steak • Chocolate-Cherry Energy Bites • Lemon-Raspberry Mini Cheesecakes To go along with the meal plans, you’ll find three 4-week fitness plans tailored to beginner, intermediate, and advanced experience levels. Best of all, the workouts can be done anywhere—at your home or on the road—and take no more than 30 minutes each. A comprehensive whole-body program, Coconuts and Kettlebells provides the knowledge and tools you need to be healthy inside and out.
Insights from the history of numerical notation suggest that how humans write numbers is an active choice involving cognitive and social factors. Over the past 5,000 years, more than 100 methods of numerical notation--distinct ways of writing numbers--have been developed and used by specific communities. Most of these are barely known today; where they are known, they are often derided as cognitively cumbersome and outdated. In Reckonings, Stephen Chrisomalis considers how humans past and present use numerals, reinterpreting historical and archaeological representations of numerical notation and exploring the implications of why we write numbers with figures rather than words.
The Solomon Islands has a rich linguistic heritage of over 60 languages, many of which have not been described in detail. This first dictionary of Owa, a South East Solomonic Language, contains over 3900 entries, which are typically illustrated with examples of natural language. An overview of the phonology, morphology, and syntax is supplemented by notes on discourse features.
Whether used for thematic story times, program and curriculum planning, readers' advisory, or collection development, this updated edition of the well-known companion makes finding the right picture books for your library a breeze. Generations of savvy librarians and educators have relied on this detailed subject guide to children's picture books for all aspects of children's services, and this new edition does not disappoint. Covering more than 18,000 books published through 2017, it empowers users to identify current and classic titles on topics ranging from apples to zebras. Organized simply, with a subject guide that categorizes subjects by theme and topic and subject headings arranged alphabetically, this reference applies more than 1,200 intuitive (as opposed to formal catalog) subject terms to children's picture books, making it both a comprehensive and user-friendly resource that is accessible to parents and teachers as well as librarians. It can be used to identify titles to fill in gaps in library collections, to find books on particular topics for young readers, to help teachers locate titles to support lessons, or to design thematic programs and story times. Title and illustrator indexes, in addition to a bibliographic guide arranged alphabetically by author name, further extend access to titles.