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Arguing with Numbers: The Intersections of Rhetoric and Mathematics (RSA Series in Transdisciplinary Rhetoric #16)
by James Wynn G. Mitchell ReyesAs discrete fields of inquiry, rhetoric and mathematics have long been considered antithetical to each other. That is, if mathematics explains or describes the phenomena it studies with certainty, persuasion is not needed. This volume calls into question the view that mathematics is free of rhetoric. Through nine studies of the intersections between these two disciplines, Arguing with Numbers shows that mathematics is in fact deeply rhetorical. Using rhetoric as a lens to analyze mathematically based arguments in public policy, political and economic theory, and even literature, the essays in this volume reveal how mathematics influences the values and beliefs with which we assess the world and make decisions and how our worldviews influence the kinds of mathematical instruments we construct and accept. In addition, contributors examine how concepts of rhetoric—such as analogy and visuality—have been employed in mathematical and scientific reasoning, including in the theorems of mathematical physicists and the geometrical diagramming of natural scientists. Challenging academic orthodoxy, these scholars reject a math-equals-truth reduction in favor of a more constructivist theory of mathematics as dynamic, evolving, and powerfully persuasive. By bringing these disparate lines of inquiry into conversation with one another, Arguing with Numbers provides inspiration to students, established scholars, and anyone inside or outside rhetorical studies who might be interested in exploring the intersections between the two disciplines.In addition to the editors, the contributors to this volume are Catherine Chaput, Crystal Broch Colombini, Nathan Crick, Michael Dreher, Jeanne Fahnestock, Andrew C. Jones, Joseph Little, and Edward Schiappa.
Arguing with Numbers: The Intersections of Rhetoric and Mathematics (RSA Series in Transdisciplinary Rhetoric)
by James Wynn G. Mitchell ReyesAs discrete fields of inquiry, rhetoric and mathematics have long been considered antithetical to each other. That is, if mathematics explains or describes the phenomena it studies with certainty, persuasion is not needed. This volume calls into question the view that mathematics is free of rhetoric. Through nine studies of the intersections between these two disciplines, Arguing with Numbers shows that mathematics is in fact deeply rhetorical. Using rhetoric as a lens to analyze mathematically based arguments in public policy, political and economic theory, and even literature, the essays in this volume reveal how mathematics influences the values and beliefs with which we assess the world and make decisions and how our worldviews influence the kinds of mathematical instruments we construct and accept. In addition, contributors examine how concepts of rhetoric—such as analogy and visuality—have been employed in mathematical and scientific reasoning, including in the theorems of mathematical physicists and the geometrical diagramming of natural scientists. Challenging academic orthodoxy, these scholars reject a math-equals-truth reduction in favor of a more constructivist theory of mathematics as dynamic, evolving, and powerfully persuasive. By bringing these disparate lines of inquiry into conversation with one another, Arguing with Numbers provides inspiration to students, established scholars, and anyone inside or outside rhetorical studies who might be interested in exploring the intersections between the two disciplines.In addition to the editors, the contributors to this volume are Catherine Chaput, Crystal Broch Colombini, Nathan Crick, Michael Dreher, Jeanne Fahnestock, Andrew C. Jones, Joseph Little, and Edward Schiappa.
The Argument of Mathematics
by Andrew Aberdein Ian J DoveWritten by experts in the field, this volume presents a comprehensive investigation into the relationship between argumentation theory and the philosophy of mathematical practice. Argumentation theory studies reasoning and argument, and especially those aspects not addressed, or not addressed well, by formal deduction. The philosophy of mathematical practice diverges from mainstream philosophy of mathematics in the emphasis it places on what the majority of working mathematicians actually do, rather than on mathematical foundations. The book begins by first challenging the assumption that there is no role for informal logic in mathematics. Next, it details the usefulness of argumentation theory in the understanding of mathematical practice, offering an impressively diverse set of examples, covering the history of mathematics, mathematics education and, perhaps surprisingly, formal proof verification. From there, the book demonstrates that mathematics also offers a valuable testbed for argumentation theory. Coverage concludes by defending attention to mathematical argumentation as the basis for new perspectives on the philosophy of mathematics.
Argumentieren in mathematischen Spielsituationen im Kindergarten: Eine Videostudie zu Interaktions- und Argumentationsprozessen bei arithmetischen Regelspielen
by Julia BöhringerEinhergehend mit der zunehmenden Bedeutung frühkindlicher Bildung rückte in der mathematikdidaktischen Forschung auch die frühe mathematische Bildung in den Fokus. Ein Schwerpunkt liegt auf der Erforschung spielbasierter mathematischer Förderung und dabei entstehender Lerngelegenheiten. Ein Schlüssel zur Wissenskonstruktion beim mathematischen Lernen sind verbale und nonverbale Interaktionen und damit einhergehend auch Argumentationen, die als spezifische Form der Interaktion gelten. An diesem Punkt setzt die Studie an, die als Teilprojekt des von der Internationalen Bodenseehochschule (IBH) geförderten Projekts „Spielintegrierte mathematische Frühförderung (spimaf)" durchgeführt wurde. Julia Böhringer untersucht, wie sich Interaktions- und Argumentationsprozesse in mathematischen Spielsituationen unter Kindergartenkindern gestalten. Übergeordnete Ziele der qualitativen Studie sind die Erfassung und Beschreibung von strukturellen und inhaltlichen Aspekten der Interaktionen sowie die Analyse deren Qualität in Form von Argumentationstiefen. Insgesamt lassen die Ergebnisse darauf schließen, dass sich speziell konzipierte, arithmetische Regelspiele zur Anregung und Förderung von mathematischen Interaktionen und Argumentationen eignen.
An Aristotelian Realist Philosophy of Mathematics
by James FranklinMathematics is as much a science of the real world as biology is. It is the science of the world's quantitative aspects (such as ratio) and structural or patterned aspects (such as symmetry). The book develops a complete philosophy of mathematics that contrasts with the usual Platonist and nominalist options.
Aristotle's Modal Syllogistic
by Marko MalinkAristotle was the founder not only of logic but also of modal logic. In the Prior Analytics he developed a complex system of modal syllogistic which, while influential, has been disputed since antiquity--and is today widely regarded as incoherent. In this meticulously argued new study, Marko Malink presents a major reinterpretation of Aristotle's modal syllogistic. Combining analytic rigor with keen sensitivity to historical context, he makes clear that the modal syllogistic forms a consistent, integrated system of logic, one that is closely related to other areas of Aristotle's philosophy. Aristotle's modal syllogistic differs significantly from modern modal logic. Malink considers the key to understanding the Aristotelian version to be the notion of predication discussed in the Topics--specifically, its theory of predicables (definition, genus, differentia, proprium, and accident) and the ten categories (substance, quantity, quality, and so on). The predicables introduce a distinction between essential and nonessential predication. In contrast, the categories distinguish between substantial and nonsubstantial predication. Malink builds on these insights in developing a semantics for Aristotle's modal propositions, one that verifies the ancient philosopher's claims of the validity and invalidity of modal inferences. Malink recognizes some limitations of this reconstruction, acknowledging that his proof of syllogistic consistency depends on introducing certain complexities that Aristotle could not have predicted. Nonetheless, Aristotle's Modal Syllogistic brims with bold ideas, richly supported by close readings of the Greek texts, and offers a fresh perspective on the origins of modal logic.
Arithmechicks Add Up: A Math Story (Arithmechicks)
by Ann Marie StephensThis exuberant picture book demonstrates key math concepts to children as ten math-loving chicks make a new friend.As the Arithmechicks slide down the slide, swing on the swings, and play hide-and-seek, they don't realize that a lonely mouse is copying them, longing to join in. However, when their basketball becomes stuck, the chicks discover that a two-inch-tall new friend is exactly what they need. In this heartwarming story, there are many ways to add up ten cheerful chicks--but a new friend is what makes them cheer. The book includes a helpful glossary that defines the eight arithmetic strategies the chicks use throughout the story, providing a playful introduction to essential math for young children and their caregivers.
Arithmechicks Explore More: A Math Story (Arithmechicks #5)
by Ann Marie StephensThe Arithmechicks prove that love is greater than disappointment in this heartwarming story about a hike, a lost stuffed animal, and the math concepts of greater than, less than, and equal to.Publishers Weekly described the Arithmechicks as an &“enjoyable resource for young ones stepping up their counting game."Join the Arithmechicks and Mouse as they head off to the wilderness! These chicks can&’t wait to hike up the ridge, find delicious berries, and, best of all, spend time with their duckling cousins! But the day is off to a bad start when one duckling accidentally leaves a beloved stuffed animal on the bus. How can these chicks (and Mouse) cheer up their cousin? Discover how an adventure with the Arithmechicks brings both humor and heart to the math they stumble across during their journey. Ann Marie Stephens draws upon thirty years of teaching experience to ensure that readers absorb math while having fun. The book also includes a helpful glossary that defines the modern arithmetic strategies the chicks use throughout the story.Join the Arithmechicks on all of their math adventures! Readers will explore addition in Arithmechicks Add Up, subtraction in Arithmechicks Take Away, fact families in Arithmechicks Take a Calculation Vacation, fractions in Arithmechicks Play Fair, greater than/less than/equal to in Arithmechicks Explore More, and ordinal numbers in Arithmechicks Find Their Place.
Arithmechicks Find Their Place: A Math Story (Arithmechicks #6)
by Ann Marie StephensJoin the Arithmechicks on a mathematical adventure in the big city! Help them solve a mystery in this playful picture book that demonstrates the concept of ordinal numbers in a clever story featuring ten math-loving chicks. Publishers Weekly described the Arithmechicks as an &“enjoyable resource for young ones stepping up their counting game."The Arithmechicks and Mouse are excited to be traveling to the city—even more so when they learn that Mama has planned a secret scavenger hunt, culminating in a mysterious 10th stop! But when one chick wants to be the best, he starts disrupting the plans. How can these frustrated chicks (and Mouse) show their sibling that it&’s better to work together? This adventure with the Arithmechicks is made up of math, a mystery, and, most of all, humor and heart. Ann Marie Stephens draws upon thirty years of teaching experience to ensure that readers absorb math while having fun. The book also includes a helpful glossary that defines the modern arithmetic strategies the chicks use throughout the story.Join the Arithmechicks on all of their math adventures! Readers will explore addition in Arithmechicks Add Up, subtraction in Arithmechicks Take Away, fact families in Arithmechicks Take a Calculation Vacation, greater than/less than/equal to in Arithmechicks Explore More, fractions in Arithmechicks Play Fair, and ordinal numbers in Arithmechicks Find Their Place.
Arithmechicks Play Fair: A Math Story (Arithmechicks)
by Ann Marie StephensThis playful picture book demonstrates the concept of fractions in a story featuring the Arithmechicks, 10 math-loving chicks.Join the Arithmechicks and Mouse as they head off to the fair! These chicks can&’t wait to enjoy the roller coaster, bumper cars, games, and delicious snacks; meanwhile Mouse is determined to sink the rooster at the dunk tank. As the Arithmechicks explore the fair, they find ways to show how fractions work in the world. But when one chick doesn&’t get to select an activity, the day doesn&’t go according to plan until the chicks decide they all need to play fair. This book includes a helpful glossary with further information about fractions, while the story provides an exuberant introduction to essential math for young children and their caregivers.
Arithmechicks Take a Calculation Vacation: A Math Story (Arithmechicks)
by Ann Marie StephensThis playful picture book demonstrates key math concepts to children in a merry story featuring the Arithmechicks, ten math-loving chicks. The Arithmechicks are headed to the beach! Their good friend Mouse is going to compete in a sandcastle contest. The chicks are excited to play all sorts of beach games—including volleyball and surfing—as they cheer on Mouse. Readers are invited to add and subtract as these math-loving chicks also explore fact families—and to watch as Mouse, along with their new friend Crab, create a magnificent sandcastle! Will they win a prize? This book includes a helpful glossary that defines fact families, providing a playful introduction to essential math for young children and their caregivers.
Arithmechicks Take Away: A Math Story (Arithmechicks)
by Ann Marie StephensThis playful picture book demonstrates key math concepts to children in a merry story featuring the Arithmechicks, ten math-loving chicks.The Arithmechicks have invited their new friend Mouse for a sleepover. When Mama says it's time for bed, the clever chicks decide it's time to prolong the fun instead! During the story, readers are invited to count and take away during everyone's favorite game of hide-and-seek—and to find Mouse, who hides in a different place in each illustration -- until all settle down for bed in the warm, cozy conclusion. The book is the perfect introduction to essential math for young children and their caregivers. It includes a helpful glossary that defines the eight arithmetic strategies the chicks use throughout the story.
Arithmetic
by Paul LockhartPaul Lockhart reveals arithmetic not as the rote manipulation of numbers but as a set of ideas that exhibit the surprising behaviors usually reserved for higher branches of mathematics. In this entertaining survey, he explores the nature of counting and different number systems—Western and non-Western—and weighs the pluses and minuses of each.
Arithmetic 4 Work-text
by Judy HoweThis colorful workbook reviews facts and concepts learned in previous grades before moving on to new material. Concepts covered in Grade 4 include: multiplying and dividing by two-digit numbers, estimation, square measures, writing decimals as fractions, and simple geometry. A major emphasis is working with proper and improper fractions-adding, subtracting, multiplying, and finding the least common denominator.
Arithmetic and Geometry
by Luis Dieulefait Gerd Faltings D. R. Heath-Brown Yu. V. Manin B. Z. Moroz Jean-Pierre WintenbergerThe 'Arithmetic and Geometry' trimester, held at the Hausdorff Research Institute for Mathematics in Bonn, focussed on recent work on Serre's conjecture and on rational points on algebraic varieties. The resulting proceedings volume provides a modern overview of the subject for graduate students in arithmetic geometry and Diophantine geometry. It is also essential reading for any researcher wishing to keep abreast of the latest developments in the field. Highlights include Tim Browning's survey on applications of the circle method to rational points on algebraic varieties and Per Salberger's chapter on rational points on cubic hypersurfaces.