- Table View
- List View
Math Warm-Ups: Developing Fluency in Math (Grade 2) (Math Warm-ups Ser.)
by Sheri DisbrowThese success-proven exercises provide daily practice in various areas of math. There are 10 problems per page that reinforce and facilitate conceptual understanding in number sense, math reasoning, computation, time, money, measurement, geometry, probability, graphing, fractions, and decimals. The exercises systematically provide students opportunities to get practice in the most important math objectives each week and provide the teacher with immediate, easy-to-administer feedback on students' mastery.This workbook can be used as a warm-up, homework, or as a diagnostic tool for the teacher, parent, or administrator. The individual pages can be used to diagnose weak areas and provide opportunities to facilitate the students' full understanding of concepts. Students are challenged and consistently exposed to a variety of concepts in all objective areas. Each book spirals in level of difficulty and continues to encourage students to think about math in real-life situations.For math proficiency activities at more advanced levels, see Math Warm-Ups Grade 3 and Math Warm-Ups Grade 4.This series meets NCTM standards and builds test-taking proficiency.Grade 2
Math Warm-Ups: Developing Fluency in Math (Grade 3) (Math Warm-ups Ser.)
by Sheri DisbrowThese success-proven exercises provide daily practice in various areas of math. There are 10 problems per page that reinforce and facilitate conceptual understanding in number sense, math reasoning, computation, time, money, measurement, geometry, probability, graphing, fractions, and decimals. The exercises systematically provide students opportunities to get practice in the most important math objectives each week and provide the teacher with immediate, easy-to-administer feedback on students' mastery.This workbook can be used as a warm-up, homework, or as a diagnostic tool for the teacher, parent, or administrator. The individual pages can be used to diagnose weak areas and provide opportunities to facilitate the students' full understanding of concepts. Students are challenged and consistently exposed to a variety of concepts in all objective areas. Each book spirals in level of difficulty and continues to encourage students to think about math in real-life situations.For math proficiency activities at alternative levels, see Math Warm-Ups Grade 2 and Math Warm-Ups Grade 4.This series meets NCTM standards and builds test-taking proficiency.Grade 3
Math Warm-Ups: Developing Fluency in Math (Grade 4) (Math Warm-ups Ser.)
by Sheri DisbrowThese success-proven exercises provide daily practice in various areas of math. There are 10 problems per page that reinforce and facilitate conceptual understanding in number sense, math reasoning, computation, time, money, measurement, geometry, probability, graphing, fractions, and decimals. The exercises systematically provide students opportunities to get practice in the most important math objectives each week and provide the teacher with immediate, easy-to-administer feedback on students' mastery.This workbook can be used as a warm-up, homework, or as a diagnostic tool for the teacher, parent, or administrator. The individual pages can be used to diagnose weak areas and provide opportunities to facilitate the students' full understanding of concepts. Students are challenged and consistently exposed to a variety of concepts in all objective areas. Each book spirals in level of difficulty and continues to encourage students to think about math in real-life situations.For math proficiency activities at lower levels, see Math Warm-Ups Grade 2 and Math Warm-Ups Grade 3.This series meets NCTM standards and builds test-taking proficiency.Grade 4
Math Wise! Over 100 Hands-On Activities that Promote Real Math Understanding, Grades K-8
by Laurie Kincheloe James L. OverholtA fun, easy-to-implement collection of activities that give elementary and middle-school students a real understanding of key math conceptsMath is a difficult and abstract subject for many students, yet teachers need to make sure their students comprehend basic math concepts. This engaging activity book is a resource teachers can use to give students concrete understanding of the math behind the questions on most standardized tests, and includes information that will give students a firm grounding to work with more advanced math concepts.Contains over 100 activities that address topics like number sense, geometry, computation, problem solving, and logical thinking.Includes projects and activities that are correlated to National Math Education StandardsActivities are presented in order of difficulty and address different learning styles Math Wise! is a key resource for teachers who want to teach their students the fundamentals that drive math problems.
Math Work Stations: Independent Learning You Can Count on K-2
by Debbie DillerIf you've ever questioned how to make math stations work, you'll find this photo-filled, idea-packed resource invaluable. This book extends Debbie Diller's best-selling work on literacy work stations and classroom design to the field of mathematics. In Math Work Stations you'll find ideas to help children develop conceptual understanding and skills, use math vocabulary as they talk about their mathematical thinking, and connect big ideas to meaningful independent exploration and practice. This book details how to set up, manage, and keep math stations going throughout the year. There's even a chapter devoted solely to organizing and using math manipulatives. Each chapter includes: key concepts based on NCTM and state math standards; math vocabulary resources and literature links; suggested materials to include at each station for the corresponding math content strand; ideas for modeling, troubleshooting, differentiating, and assessment; and reflection questions for professional development. Charts, reproducible forms, and math work stations icons are included to provide everything you'll need to get started with stations in your classroom right away.
Math Work Stations: Independent Learning You Can Count On, K-2
by Debbie DillerIf you' ve ever questioned how to make math stations work, you' ll find this photo-filled, idea-packed resource invaluable. This book extends Debbie Diller' s best-selling work on literacy work stations and classroom design to the field of mathematics. In Math Work Stations you' ll find ideas to help children develop conceptual understanding and skills, use math vocabulary as they talk about their mathematical thinking, and connect big ideas to meaningful independent exploration and practice. This book details how to set up, manage, and keep math stations going throughout the year. There' s even a chapter devoted solely to organizing and using math manipulatives. Each chapter includes: key concepts based on NCTM and state math standards; math vocabulary resources and literature links; suggested materials to include at each station for the corresponding math content strand; ideas for modeling, troubleshooting, differentiating, and assessment; and reflection questions for professional development.Throughout the book, Debbie has included hundreds of color photos showing math work stations in action from a variety of classrooms in which she has worked. Charts, reproducible forms, and math work stations icons are included to provide everything you' ll need to get started with stations in your classroom right away.
Math Workout for the GED Test
by Princeton ReviewGet the extra practice you need for the excellent GED Mathematical Reasoning section score you want! <P><P>The Math portion of the GED test is often considered the hardest part of the whole exam--and with the lowest average student scores and pass rates, this section can be tough to overcome! <P><P>Fortunately, The Princeton Review has developed Math Workout for the GED Test, a brand-new workbook designed to help students master the skills and content needed to ace the Mathematical Reasoning portion of the GED test. It has the tools and help you need to feel confident about doing well on test day.This eBook edition has been specially formatted for on-screen viewing with cross-linked questions, answers, and explanations. <P><P>Practice Your Way to Excellence. <br>* Drills for all GED Mathematical Reasoning question types and test topics <br>* Clear, step-by-step explanations for all questions <br>* Extra help to hone the Mathematical Reasoning skills learned in Cracking the GED Test or other math classes <P><P>Everything You Need to Know to Help Achieve a High Score. <br>* Essential strategies to help you work smarter, not harder <br>* Helpful tips to avoid tricks and traps <br>* An introduction to the computer-based question formats ]
Math Workout for the GMAT, 5th Edition
by Princeton ReviewAce the Quantitative section of the GMAT with help from The Princeton Review.Are difficulties with data sufficiency or problem-solving dragging your GMAT score down? If so, this is the workbook for you. Designed for students specifically looking to sharpen their math skills, this 5th edition of The Princeton Review's Math Workout for the GMAT provides the review and practice needed for Quantitative mastery.Techniques That Actually Work.* Tried-and-true tactics to help you avoid traps and beat the Quantitative section* Tips for pacing yourself and guessing logically* Essential strategies to help you work smarter, not harderEverything You Need to Know to Help Achieve a High Quantitative Score.* A comprehensive review of key algebra, geometry, data sufficiency, and integrated reasoning concepts* Expert review of all Quantitative question types on the test* Updated Integrated Reasoning section with guidance on tackling table analysis, graphics interpretation, and morePractice Your Way to Perfection.* 220+ practice problems, including a practice GMAT Quantitative section and drills/practice questions throughout each chapter* Step-by-step walk-throughs of key math problems, plus detailed answer explanations for the practice Quantitative sectionThis eBook edition has been specially formatted for on-screen viewing with cross-linked questions, answers, and explanations.
Math Workout for the GRE, 3rd Edition
by Princeton ReviewTHE PRINCETON REVIEW GETS RESULTS. The Princeton Review's Math Workout for the GRE gives you everything you need to practice your way to perfection on the quantitative portions of the GRE exam. Inside, you'll find useful reviews of key test topics, strategies for tackling tough questions, and all the practice you need to get the score you want.This eBook edition has been optimized for digital viewing with cross-linked questions, answers, and explanations. Inside the Book: All the Practice & Strategies You Need · 200+ practice questions with detailed answers and explanations · Step-by-step strategies to master every type of math question on the GRE, including tricky Quantitative Comparison, All-That-Apply, and Numeric Entry questions · Helpful review of the math basics, algebra, and geometry you'll need on the Math section of the GRE · Glossary of common terms to brush up on your math vocabulary · Summary of important triggers to maximize your test-taking time
Math Workout for the GRE, 4th Edition: 275+ Practice Questions with Detailed Answers and Explanations
by Princeton ReviewThis eBook edition has been specially formatted for on-screen viewing with cross-linked questions, answers, and explanations.THE PRINCETON REVIEW GETS RESULTS. The Princeton Review's Math Workout for the GRE is your one-stop guide to conquering the quantitative portions of the GRE exam—even if your math knowledge is a bit rusty. Inside, you'll find useful reviews of key test topics, strategies for tackling tough questions, and all the practice you need to get the score you want.Inside the Book: All the Practice & Strategies You Need· 275+ practice questions with detailed answers and explanations· Strategies for mastering tricky Quantitative Comparison, All-That-Apply, and Numeric Entry questions· Helpful review of the math basics, and in-depth coverage of the algebra and geometry you'll need on the Math section of the GRE· Glossary of common terms to brush up on your math vocabulary· Two sample GRE math sections to hone your skills
Math Workout for the New GMAT, 4th Edition
by Princeton ReviewIf you need to know it for the new, next-generation GMAT, it's in this book. Math Workout for the New GMAT, 4th Edition has been optimized for e-readers, with all questions, answers, and explanations cross-linked for easy on-screen viewing. It includes: * More than 220 practice questions with full answer explanations to show you exactly what to expect on the Quantitative section of the new GMAT, covering data sufficiency, statistics, algebra, geometry, and more * A thorough introduction to the brand-new Integrated Reasoning section and question types: table analysis, graphics interpretation, multi-source reasoning, and two-part analysis * Proven strategies for acing tricky data sufficiency problems * Tips and tricks to help you effectively manage your time on geometry and algebra questions
Math Workout for the New GRE, 2nd Edition
by Princeton ReviewIf it's on the math section of the GRE, it's in this book! Math Workout for the GRE, 2nd Edition is completely updated for the August 2011 changes to the GRE. Comprehensive and engaging, it includes: * More than 200 practice questions * Step-by-step strategies for cracking tricky Quantitative Comparison and Data Analysis questions * Complete coverage of the changes to the Quantitative Reasoning section * Detailed, comprehensive explanations for every question * Key stategies and techniques for mastering the math portion of the exam
Math Workout for the SAT, 4th Edition: Extra Practice to Help Achieve an Excellent SAT Math Score
by Princeton ReviewEXTRA PRACTICE TO HELP ACHIEVE AN EXCELLENT SAT MATH SCORE. Get the help you need for the score you want with this targeted SAT math workbook from The Princeton Review, packed with review content, specific strategies, and 260+ practice questions and explanations.This eBook edition has been specially formatted for on-screen viewing with cross-linked questions, answers, and explanations.Techniques That Actually Work.• Tried-and-true tactics to help you avoid traps and master the Math section of the exam• Tips for tackling tricky questions with elimination techniques• Essential strategies to help you maximize your efficiencyEverything You Need to Know to Help Achieve a High Score. • Expert review of core math concepts for all problems on the SAT Math section• Comprehensive content coverage, from algebra essentials to advanced math• Up-to-date information on the SATPractice Your Way to Excellence.• Quick quizzes throughout each chapter to help assess understanding• Step-by-step walk-throughs that demonstrate tips for each type of question, from Grid-Ins to those in the Calculator section• Detailed answer explanations that showcase each skill and strategy
Math Workout for the SAT, 5th Edition: Extra Practice for an Excellent Score (College Test Preparation)
by The Princeton ReviewSUCCEED ON THE SAT WITH THE PRINCETON REVIEW. Get targeted help for the Math section of the SAT with this top-rated guidebook. Includes reviews for exam topics, section-specific strategy help, and practice tests and drills. Designed for students specifically looking for extra help on the SAT quantitative section, this 5th edition of The Princeton Review's Math Workout for the SAT provides the review and practice needed for subject mastery.Everything You Need to Know to Help Achieve a High Score.• Expert review of core math concepts for all problems on the SAT• A comprehensive review of everything on the Math section, from algebra to statistics• Step-by-step walk-throughs that demonstrate tips for each type of question, including Grid-InsTechniques That Actually Work• Tried-and-true tactics to help you avoid traps and master both the No Calculator and Calculator portions of the exam• Tips for tackling tricky questions with elimination techniques• Essential strategies to help you maximize your efficiencyPractice Your Way to Excellence.• 310+ total practice questions with complete answer explanations• 28 quick quizzes throughout the content chapters to help assess understanding• 19 problem sets to help focus on strengths and weaknesses, including an online challenge section to really put you to the test• Detailed answer explanations that showcase each skill and strategy
Math Workshop in Action: Strategies for Grades K-5
by Nicki NewtonFind out how Math Workshops engage students and increase learning. This practical book from bestselling author Dr. Nicki Newton explains why Math Workshops are effective and gives you step-by-step instructions for implementing and managing your own workshop. You’ll find out how to... create a math-rich environment; use anchor charts effectively; manage the workshop; begin a workshop with activities; lead whole-group mini-lessons; make workstations meaningful and engaging; create guided math groups; implement "the Share" effectively; and ensure balanced assessments. Each chapter offers a variety of charts and tools that you can use in the classroom immediately, as well as reflection questions and key points. The book also features a handy Quick-Start Guide to help you as you implement your own workshop.
Math Workstations in Action: Powerful Possibilities for Engaged Learning in Grades 3–5
by Nicki NewtonLearn how to incorporate math workstations into your elementary math classes. Math workstations allow students to engage in meaningful, independent math practice through student-driven games and activities, and can be implemented as part of a math workshop or in a traditional math class. In this book, bestselling author and consultant Nicki Newton shows you how to set up and manage math workstations for topics such as fluency, word problems, math vocabulary, and more. You’ll also learn how to differentiate the activities for all ability levels and promote rigorous instruction, enabling your students to get the most out of this fun and engaging instructional method. Topics include: Teaching fractions, decimals, measurement, geometry, and more with a variety of tools and hands-on activities; Developing word problems and games to help students gain understanding of difficult mathematical concepts; Using precise mathematical language to encourage clear communication and logical thinking; Evaluating student competency and development with pre-assessments, anecdotals, checklists, and self-reflections; Implementing new technologies to think through, explain, and present mathematical concepts. Each chapter includes a variety of charts, tools, and practice problems that you can use in the classroom immediately, and the strategies can be easily adapted for students at all levels of math fluency across grades 3–5.
Mathability: Math in the Real World (Grades 5-8)
by Michael CainMathability gives students the experience and ability to analyze and solve real-life mathematical problems, and explain their methods for arriving at the solution. Mathability is an excellent resource for preparing students for the performance tasks of standards-based tests. The six units in this book each have 10 problems that deal with a variety of real-life situations, such as those at a construction site, on vacation, in a business, and at home. The open-ended problems let students hone their skills in geometry, probability, percentages, use of charts, algebra, number relations/operations, money, and decimals. Open-ended performance tasks have become a mainstay of standards-based testing. It is one of the tasks that most students perform at below proficiency level. Much of this low performance is due to a student's lack of experience with writing explanations of the mathematics that made it possible to solve the problem. Mathabilty presents a systematic approach that will lead students to proficiency.Within each unit, this book provides four different levels of problems. The Step-by-Step Level leads a student through the problem and provides a format for presenting their answers. The Prompted Level provides the format for presenting the solution and hints on how to solve the problem. The Independent Level allows students to solve and explain their answers on their own, and the Challenge Level problems present a venue for gifted and talented students to push their skills to a higher level.Grades 5-8
MathArts: Exploring Math Through Art for 3 to 6 Year Olds (Bright Ideas for Learning)
by MaryAnn F. Kohl Cindy GainerGet ready to create and count in this exciting introduction to math! MathArts is an innovative approach that uses creative art projects to introduce preschoolers to early math concepts. Each of the 200 hands-on projects is designed to help children discover essential math skills through a creative process unique to every individual. Math concepts include: One-to-one correspondence; matching; sorting; grouping; classifying; opposites; number recognition; number values, and counting. This well-organized book provides both teachers and parents with a diverse range of activities for making math both fun and fascinating. The possibilities are endless!
Mathe ist noch mehr: Aufgaben und Lösungen der Fürther Mathematik-Olympiade 2012–2017
by Paul Jainta Lutz Andrews Alfred Faulhaber Bertram Hell Eike Rinsdorf Christine StreibDer vorliegende Band enthält alle Probleme der 21. bis 25. Fürther Mathematik-Olympiade, getrennt nach Jahrgangsstufen und Lösungsstrategien. Die Aufgaben belegen, dass sich Problemlösen vermitteln und erlernen lässt. Zum erfolgreichen Lösen von Aufgaben gehört gar nicht so viel: Zuversicht, Konzentration und Mut. Zielloses Probieren und strenges Vorgehen sind ebenso legitime Maßnahmen. Als Zugewinn winkt ein Mix aus Strategien und taktischen Tricks. Das hat nicht selten den erfreulichen Nebeneffekt, dass Skeptiker („Wie bringe ich da Mathematik hinein?“) zu ihrer eigenen Verblüffung in manchen Alltagssituationen mathematische Zusammenhänge erkennen. Problemlösen kann durch viel Übung und Tun erlernt werden. Daher soll das Buch neugierig machen auf Knobeln, auf verschiedene Zugänge zu den Problemen – und auf Mathematik! Es richtet sich an eine breite Leserschaft, angefangen bei Schülern ab Klasse 5 bis 8, die wissbegierig sind und Neues lernen wollen, an Lehrkräfte, Eltern sowie an alle Liebhaber der Mathematik. Die Aufgaben sind erfolgreich einsetzbar in der mathematischen Förderung begabter SchülerInnen in Arbeitsgemeinschaften oder Pluskursen, können eine willkommene Abwechslung im Unterricht sein und eignen sich zum Selbststudium. Die zahlreichen Aufgaben stellen reichhaltiges Übungsmaterial für weiterführende Wettbewerbe bereit. Die Aufgabenstellungen sind in der Regel kurz und griffig wie eine Werbebotschaft, um vor allem auch jüngere SchülerInnen anzulocken.
Mathe ist noch viel mehr: Aufgaben und Lösungen der Fürther Mathematik-Olympiade 1992-1999
by Paul Jainta Lutz AndrewsMathe ist noch viel mehrDer vorliegende Band enthält alle Aufgaben und Lösungen aus den sieben Anfangsjahren 1992–1999 der Fürther Mathematik-Olympiade, getrennt nach Jahrgangsstufen und Lösungsstrategien. Die Fürther Mathematik-Olympiade ist ein zweistufiger Hausaufgabenwettbewerb. Ziel des Wettbewerbs ist, Schülerinnen und Schüler möglichst früh für Mathematik zu begeistern.Im Gründungsjahr boten wir Aufgaben für die Jahrgänge 7/8 und 9/10 an, ein Jahr später bereits für 5/6 bis 9/10 und schließlich kam noch die Jahrgangsstufe 11 hinzu. Die Olympiade Junger Mathematiker in der ehemaligen DDR war hierfür eine Blaupause.Wir empfehlen ausdrücklich, mit dem Buch zu arbeiten, etwa in Arbeitsgemeinschaften, Pluskursen, Zirkeln, zur Lockerungsübung im Unterricht zwischendurch oder in der Vertretungsstunde. Die Fragestellungen aus dem Buch eignen sich auch als Anregung für besondere Übungsaufgaben und zum Selbststudium in Anlehnung an die Worte von Seneca: „Wahre Freude ist eine ernste Sache“.Teilnehmer schätzen mathematische Aktivitäten oft als sportliche Betätigungen. Der Reiz liegt darin, Schwieriges mit schöpferischer Energie und Ausdauer und nicht selten dem gewissen Quäntchen Glück zu bewältigen und auch darin, dass man sich in Konkurrenz mit Wettkämpfern aus anderen Schulen messen kann. Es hat sich gezeigt, dass gerade der spielerische Charakter der Aufgaben sehr viele Jüngere anlockt.
Mathe ist wirklich noch viel mehr: Aufgaben und Lösungen der Fürther Mathematik-Olympiade 1999–2006
by Paul Jainta Lutz AndrewsDer vorliegende Band ist der dritte in der Reihe mit Aufgaben und Lösungen der Fürther Mathematik-Olympiade (FüMO). Das Buch umfasst den Zeitraum von 1999 bis 2006 und enthält alle Fragestellungen der 8. bis 14. FüMO. Mathe in der Schule ist schon schlimm genug und dann noch freiwillig mehr Tüfteln zu Hause? So werden sicher viele Schüler denken, wenn sie von der Fürther Mathematik-Olympiade hören.Wenn es an kreativen Ideen fehlt, wenn unkonventionelle Aufgaben schwer fallen, dann kann die Fürther Mathematik-Olympiade (FüMO) helfen: raus aus eingefahrenen Gleisen, hin zu Selbstständigkeit und Einfallsreichtum. Und mit FüMO hört es ja nicht auf: Es folgen Landeswettbewerbe, die deutschlandweite Mathematik-Olympiade, der Bundeswettbewerb Mathematik oder es winkt eine Einladung zum Projekt Jugend trainiert Mathematik (JuMa).Jede Wettbewerbsrunde FüMO bringt Neues zum Tüfteln: Logisches, Geometrisches, Alltägliches, Kombinatorik, Zahlentheorie, Winkel und Flächenberechnungen etc., mit ausführlichen Lösungen – nach Strategien oder Verfahren geordnet – und alles auf durchaus hohem Niveau: Mathematik-Olympiade eben! Bei der Fürther Mathematik-Olympiade finden besonders begabte Lernende ein Umfeld, in dem sie sich über dem schulischen Leistungsniveau bewegen können. Mathematik ist eben manchmal wie Bergsteigen: Man muss sich quälen, bis der Gipfel erreicht ist, aber das Gefühl etwas geschafft zu haben, ist herrlich. Und man wird belohnt: Der Ausblick auf (mathematische) Erhebungen und der Blick in tiefe Täler lässt alle Beschwernisse vergessen.
Mathematica: A Secret World of Intuition and Curiosity
by David BessisA fascinating look into how the transformative joys of mathematical experience are available to everyone, not just specialists Math has a reputation for being inaccessible. People think that it requires a special gift or that comprehension is a matter of genes. Yet the greatest mathematicians throughout history, from René Descartes to Alexander Grothendieck, have insisted that this is not the case. Like Albert Einstein, who famously claimed to have &“no special talent,&” they said that they had accomplished what they did using ordinary human doubts, weaknesses, curiosity, and imagination. David Bessis guides us on an illuminating path toward deeper mathematical comprehension, reconnecting us with the mental plasticity we experienced as children. With simple, concrete examples, Bessis shows how mathematical comprehension is integral to the great learning milestones of life, such as learning to see, to speak, to walk, and to eat with a spoon. Focusing on the deeply human roots of mathematics, Bessis dispels the myths of mathematical genius. He offers an engaging initiation into the experience of math not as a series of discouragingly incomprehensible logic problems but as a physical activity akin to yoga, meditation, or a martial art. This perspective will change the way you think not only about math but also about intelligence, intuition, and everything that goes on inside your head.
Mathematical and Analogical Reasoning of Young Learners (Studies in Mathematical Thinking and Learning Series)
by Lyn D. EnglishMathematical and Analogical Reasoning of Young Learners provides foundational knowledge of the nature, development, and assessment of mathematical and analogical reasoning in young children. Reasoning is fundamental to understanding mathematics and is identified as one of the 10 key standards for school mathematics for the new millennium. The book draws on longitudinal and cross-cultural studies, conducted in the United States and Australia, of children's reasoning development as they progressed from preschool through the end of second grade. The multifaceted analysis of young children's development of mathematical and analogical reasoning focuses on individual learners, their learning environments, and the interaction between the two. The multidisciplinary team of authors present multiple perspectives and multiple methodologies, and provide valuable information on organizing and sustaining interdisciplinary and cross-cultural inquiry. Key issues addressed include: *the relationship between mathematical and analogical reasoning; *how changes in children's reasoning relate to the implicit instruction they receive in their classrooms; *analyses of the participating teachers' knowledge, beliefs, and practices with respect to mathematical and analogical reasoning of young learners; and *ways in which we might promote development of mathematical and analogical reasoning in young children. This volume is highly relevant for mathematics educators, researchers in mathematics education, educational psychologists, early childhood teachers, and others interested in mathematical development of young children, in particular, the development of their reasoning processes.
Mathematical and Computational Modeling of Tonality
by Elaine ChewFrom the Preface: Blending ideas from operations research, music psychology, music theory, and cognitive science, this book aims to tell a coherent story of how tonality pervades our experience, and hence our models, of music. The story is told through the developmental stages of the Spiral Array model for tonality, a geometric model designed to incorporate and represent principles of tonal cognition, thereby lending itself to practical applications of tonal recognition, segmentation, and visualization. Mathematically speaking, the coils that make up the Spiral Array model are in effect helices, a spiral referring to a curve emanating from a central point. The use of "spiral" here is inspired by spiral staircases, intertwined spiral staircases: nested double helices within an outer spiral. The book serves as a compilation of knowledge about the Spiral Array model and its applications, and is written for a broad audience, ranging from the layperson interested in music, mathematics, and computing to the music scientist-engineer interested in computational approaches to music representation and analysis, from the music-mathematical and computational sciences student interested in learning about tonality from a formal modeling standpoint to the computer musician interested in applying these technologies in interactive composition and performance. Some chapters assume no musical or technical knowledge, and some are more musically or computationally involved.
MATHEMATICAL AND SCIENTIFIC DEVELOPMENT IN EARLY CHILDHOOD: A Workshop Summary
by National Research Council of the National AcademiesA report on the Mathematical and Scientific Development in Early Childhood