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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 Algebraic Geometry: A Mathematical Tribute to Yuri Manin (Simons Symposia)
by Yuri TschinkelThis book is a tribute to the memory of Yuri Ivanovich Manin, who passed away on January 7, 2023. Manin was one of the giants of modern mathematics. His work covered a wide range of fields, including logic, number theory, geometry, mathematical physics, theoretical computer science, and linguistics. The contributions collected here are on topics close to his life-long passion: arithmetic and algebraic geometry.
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.
Arithmetic and Geometry of K3 Surfaces and Calabi–Yau Threefolds (Fields Institute Communications #67)
by Matthias Schütt Radu Laza Noriko YuiIn recent years, research in K3 surfaces and Calabi-Yau varieties has seen spectacular progress from both arithmetic and geometric points of view, which in turn continues to have a huge influence and impact in theoretical physics--in particular, in string theory. The workshop on Arithmetic and Geometry of K3 surfaces and Calabi-Yau threefolds, held at the Fields Institute (August 16-25, 2011), aimed to give a state-of-the-art survey of these new developments. This proceedings volume includes a representative sampling of the broad range of topics covered by the workshop. While the subjects range from arithmetic geometry through algebraic geometry and differential geometry to mathematical physics, the papers are naturally related by the common theme of Calabi-Yau varieties. With the big variety of branches of mathematics and mathematical physics touched upon, this area reveals many deep connections between subjects previously considered unrelated. Unlike most other conferences, the 2011 Calabi-Yau workshop started with 3 days of introductory lectures. A selection of 4 of these lectures is included in this volume. These lectures can be used as a starting point for the graduate students and other junior researchers, or as a guide to the subject.
Arithmetic and Geometry over Local Fields: VIASM 2018 (Lecture Notes in Mathematics #2275)
by Bruno Anglès Tuan Ngo DacThis volume introduces some recent developments in Arithmetic Geometry over local fields. Its seven chapters are centered around two common themes: the study of Drinfeld modules and non-Archimedean analytic geometry. The notes grew out of lectures held during the research program "Arithmetic and geometry of local and global fields" which took place at the Vietnam Institute of Advanced Study in Mathematics (VIASM) from June to August 2018. The authors, leading experts in the field, have put great effort into making the text as self-contained as possible, introducing the basic tools of the subject. The numerous concrete examples and suggested research problems will enable graduate students and young researchers to quickly reach the frontiers of this fascinating branch of mathematics.
Arithmetic Geometry of Logarithmic Pairs and Hyperbolicity of Moduli Spaces: Hyperbolicity in Montréal (CRM Short Courses)
by Marc-Hubert NicoleThis textbook introduces exciting new developments and cutting-edge results on the theme of hyperbolicity. Written by leading experts in their respective fields, the chapters stem from mini-courses given alongside three workshops that took place in Montréal between 2018 and 2019. Each chapter is self-contained, including an overview of preliminaries for each respective topic. This approach captures the spirit of the original lectures, which prepared graduate students and those new to the field for the technical talks in the program. The four chapters turn the spotlight on the following pivotal themes:The basic notions of o-minimal geometry, which build to the proof of the Ax–Schanuel conjecture for variations of Hodge structures;A broad introduction to the theory of orbifold pairs and Campana's conjectures, with a special emphasis on the arithmetic perspective;A systematic presentation and comparison between different notions of hyperbolicity, as an introduction to the Lang–Vojta conjectures in the projective case;An exploration of hyperbolicity and the Lang–Vojta conjectures in the general case of quasi-projective varieties.Arithmetic Geometry of Logarithmic Pairs and Hyperbolicity of Moduli Spaces is an ideal resource for graduate students and researchers in number theory, complex algebraic geometry, and arithmetic geometry. A basic course in algebraic geometry is assumed, along with some familiarity with the vocabulary of algebraic number theory.
The Arithmetic of Elliptic Curves
by Joseph H. SilvermanThe theory of elliptic curves is distinguished by its long history and by the diversity of the methods that have been used in its study. This book treats the arithmetic approach in its modern formulation, through the use of basic algebraic number theory and algebraic geometry. Following a brief discussion of the necessary algebro-geometric results, the book proceeds with an exposition of the geometry and the formal group of elliptic curves, elliptic curves over finite fields, the complex numbers, local fields, and global fields. Final chapters deal with integral and rational points, including Siegels theorem and explicit computations for the curve Y = X + DX, while three appendices conclude the whole: Elliptic Curves in Characteristics 2 and 3, Group Cohomology, and an overview of more advanced topics.
Arithmetic of Finite Fields: 5th International Workshop, WAIFI 2014, Gebze, Turkey, September 27-28, 2014. Revised Selected Papers (Lecture Notes in Computer Science #9061)
by Çetin Kaya Koç Sihem Mesnager Erkay SavaşThis book constitutes the refereed proceedings of the 5th International Workshop on the Arithmetic of Finite Field, WAIFI 2014, held in Gebze, Turkey, in September 2014. The 9 revised full papers and 43 invited talks presented were carefully reviewed and selected from 27 submissions. This workshop is a forum of mathematicians, computer scientists, engineers and physicists performing research on finite field arithmetic, interested in communicating the advances in the theory, applications, and implementations of finite fields. The workshop will help to bridge the gap between the mathematical theory of finite fields and their hardware/software implementations and technical applications.
Arithmetic of Quadratic Forms (Springer Monographs in Mathematics #109)
by Goro ShimuraThis book is divided into two parts. The first part is preliminary and consists of algebraic number theory and the theory of semisimple algebras. There are two principal topics: classification of quadratic forms and quadratic Diophantine equations. The second topic is a new framework which contains the investigation of Gauss on the sums of three squares as a special case. To make the book concise, the author proves some basic theorems in number theory only in some special cases. However, the book is self-contained when the base field is the rational number field, and the main theorems are stated with an arbitrary number field as the base field. So the reader familiar with class field theory will be able to learn the arithmetic theory of quadratic forms with no further references.
Arithmetic Optimization Techniques for Hardware and Software Design
by Ryan Kastner Anup Hosangadi Farzan FallahObtain better system performance, lower energy consumption, and avoid hand-coding arithmetic functions with this concise guide to automated optimization techniques for hardware and software design. High-level compiler optimizations and high-speed architectures for implementing FIR filters are covered, which can improve performance in communications, signal processing, computer graphics, and cryptography. Clearly explained algorithms and illustrative examples throughout make it easy to understand the techniques and write software for their implementation. Background information on the synthesis of arithmetic expressions and computer arithmetic is also included, making the book ideal for new-comers to the subject. This is an invaluable resource for researchers, professionals, and graduate students working in system level design and automation, compilers, and VLSI CAD.
Arithmetic Refresher (Dover Books on Mathematics)
by A. A. KlafThe farther we get from our grade school days, the easier it is to forget those operations and nuances of arithmetical computation that keep recurring in our daily lives: interest and discount problems, time-payment calculations, tax problems, and so on.This handy book is designed to streamline your methods and resharpen your calculation skills for a variety of situations. Starting with the most elementary operations, the book goes on to cover all basic topics and processes of arithmetic: addition, subtraction, multiplication, division, fractions, percentage, interest, ratio and proportion, denominate numbers, averages, etc. The text continues into other useful matters, such as powers and roots, logarithms, positive and negative numbers, harmonic progression, and introductory concepts of algebra.Entirely practical in approach and using an easy-to-follow question and answer style, this book covers a wide range of common knotty areas: filling and emptying receptacles, scales for models and maps, business and financial calculations (partial payment problems, compound interest, bank and sales discount, profit and loss problems, etc.), angle measurement, mixtures and solutions, graph and chart problems, and the like.The discussion contains numerous alternate and short-cut methods, such as quick ways to figure compound interest; to square a number from 1 to 100; to divide by 5, 25, 125, 99, etc.; to multiply two 2-digit numbers having the same figure in the tens place; and many more. These valuable tips, together with the huge fund of exercise problems (a total of 809, half of them answered in an appendix), help you to increase your computational proficiency and speed, and make this an extremely useful volume to have on your shelf at home or at work. Anyone who has to do any figuring at all -- housewife, merchant, student -- will profit from this refresher. Parents will find it an excellent source of material for helping children in school work.
Arithmetic Tales: Advanced Edition (Universitext)
by Olivier BordellèsThis textbook covers a wide array of topics in analytic and multiplicative number theory, suitable for graduate level courses.Extensively revised and extended, this Advanced Edition takes a deeper dive into the subject, with the elementary topics of the previous edition making way for a fuller treatment of more advanced topics. The core themes of the distribution of prime numbers, arithmetic functions, lattice points, exponential sums and number fields now contain many more details and additional topics. In addition to covering a range of classical and standard results, some recent work on a variety of topics is discussed in the book, including arithmetic functions of several variables, bounded gaps between prime numbers à la Yitang Zhang, Mordell's method for exponential sums over finite fields, the resonance method for the Riemann zeta function, the Hooley divisor function, and many others. Throughout the book, the emphasis is on explicit results.Assuming only familiarity with elementary number theory and analysis at an undergraduate level, this textbook provides an accessible gateway to a rich and active area of number theory. With an abundance of new topics and 50% more exercises, all with solutions, it is now an even better guide for independent study.
Arithmetic Tales (Universitext)
by Olivier Bordellès Véronique BordellèsNumber theory was once famously labeled the queen of mathematics by Gauss. The multiplicative structure of the integers in particular deals with many fascinating problems some of which are easy to understand but very difficult to solve. In the past, a variety of very different techniques has been applied to further its understanding. Classical methods in analytic theory such as Mertens' theorem and Chebyshev's inequalities and the celebrated Prime Number Theorem give estimates for the distribution of prime numbers. Later on, multiplicative structure of integers leads to multiplicative arithmetical functions for which there are many important examples in number theory. Their theory involves the Dirichlet convolution product which arises with the inclusion of several summation techniques and a survey of classical results such as Hall and Tenenbaum's theorem and the Möbius Inversion Formula. Another topic is the counting integer points close to smooth curves and its relation to the distribution of squarefree numbers, which is rarely covered in existing texts. Final chapters focus on exponential sums and algebraic number fields. A number of exercises at varying levels are also included. Topics in Multiplicative Number Theory introduces offers a comprehensive introduction into these topics with an emphasis on analytic number theory. Since it requires very little technical expertise it will appeal to a wide target group including upper level undergraduates, doctoral and masters level students.
Arithmetic Work-text 5
by Judy HoweArithmetic 5 contains a variety of exercises involving new/review material in each lesson. The workbook includes 169 lessons (excluding tests). Supplementary Exercises and Homework Exercises. The handbook at the end of the book contains facts, rules, and measures which are given throughout the workbook. Although all new material is presented at top of a workbook page, the workbook is not designed to be used without a teacher. Arithmetic 5 Curriculum/Lesson Plans, available separately or as part of the Grade 5 Curriculum, and the Teacher Edition provide complete daily plans for teaching, reviewing, and testing. The Teacher Edition also includes solutions to all exercises in the text. Student Quizzes, Tests, and Speed Drills are correlated with the work-text.
Arithmetical Properties of Commutative Rings and Monoids (Lecture Notes in Pure and Applied Mathematics)
by Scott T. ChapmanThe study of nonunique factorizations of elements into irreducible elements in commutative rings and monoids has emerged as an independent area of research only over the last 30 years and has enjoyed a recent flurry of activity and advancement. This book presents the proceedings of two recent meetings that gathered key researchers from around the w