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The Math Handbook for Students with Math Difficulties, Dyscalculia, Dyslexia or ADHD: (Grades 1-7)
by Helmy FaberThe Math Handbook has been developed for students with Dyscalculia and others who are struggling with mathematics. The book is based upon the Singapore Primary Mathematics curriculum, as well as the International Math curriculum. More than twenty topics are covered and explained step by step through visual representation to convey mathematical concepts. It has been specially developed for: • Students who have been diagnosed with Dyscalculia; other terms may include Mathematics Learning Disability, or Mathematics Disorder • Students who have been diagnosed with Dyslexia; as according to research more than fifty percent of those experience difficulties with mathematics. Some students may have Dyslexia and Dyscalculia as co-existing disorders • Students diagnosed with ADHD; as they may struggle with mathematics. Some students may have ADHD and Dyscalculia as co-existing disorders. • Students who have difficulties in learning Mathematics • Slow learners • Teens/Adults who have severe Math Difficulties or Dyscalculia. Students will gain more confidence in mathematics, become more independent and produce better results. This book will provide them with an opportunity to experience success and maintain a positive attitude towards math. It is suitable to be used in combination with Educational Therapy or remedial intervention in Math that students with dyscalculia or Math difficulties need. An assessment conducted by a psychologist is essential and early interventions are most effective. • Please note that the ePub edition of The Math Handbook for tablets and mobile devices may not appear as well organized since the material doesn't always appear together on a single page as in the print edition. Therefore, we recommend the print edition for students.
The Math Myth: And Other STEM Delusions
by Andrew HackerA New York Times–bestselling author looks at mathematics education in America—when it&’s worthwhile, and when it&’s not. Why do we inflict a full menu of mathematics—algebra, geometry, trigonometry, even calculus—on all young Americans, regardless of their interests or aptitudes? While Andrew Hacker has been a professor of mathematics himself, and extols the glories of the subject, he also questions some widely held assumptions in this thought-provoking and practical-minded book. Does advanced math really broaden our minds? Is mastery of azimuths and asymptotes needed for success in most jobs? Should the entire Common Core syllabus be required of every student? Hacker worries that our nation&’s current frenzied emphasis on STEM is diverting attention from other pursuits and even subverting the spirit of the country. Here, he shows how mandating math for everyone prevents other talents from being developed and acts as an irrational barrier to graduation and careers. He proposes alternatives, including teaching facility with figures, quantitative reasoning, and understanding statistics. Expanding upon the author&’s viral New York Times op-ed, The Math Myth is sure to spark a heated and needed national conversation—not just about mathematics but about the kind of people and society we want to be. &“Hacker&’s accessible arguments offer plenty to think about and should serve as a clarion call to students, parents, and educators who decry the one-size-fits-all approach to schooling.&” —Publishers Weekly, starred review
The Math Pact, Elementary: Achieving Instructional Coherence Within and Across Grades (Corwin Mathematics Series)
by Karen S. Karp Sarah B. Bush Barbara J. DoughertyA schoolwide solution for mathematics success! When &“rules&” seem to change from year to year, mathematics can seem like a disconnected mystery for students. Clear up the confusion with a Mathematics Whole-School Agreement! Expanded from the highly popular &“Rules that Expire&” series of NCTM articles, this essential guide leads educators through the collaborative step-by-step process of establishing a coherent and consistent learner-centered and equitable approach to mathematics instruction. You&’ll learn to avoid &“rules that expire&”—tricks that may seem to help students in one grade but hurt in the long run. Features include · Abundant grade-specific examples · Effective working plans for sustainability · Barrier-busting tips, to-dos, and try-it-outs · PLC prompts and discussion points
The Math Pact, Elementary: Achieving Instructional Coherence Within and Across Grades (Corwin Mathematics Series)
by Karen S. Karp Sarah B. Bush Barbara J. DoughertyA schoolwide solution for mathematics success! When &“rules&” seem to change from year to year, mathematics can seem like a disconnected mystery for students. Clear up the confusion with a Mathematics Whole-School Agreement! Expanded from the highly popular &“Rules that Expire&” series of NCTM articles, this essential guide leads educators through the collaborative step-by-step process of establishing a coherent and consistent learner-centered and equitable approach to mathematics instruction. You&’ll learn to avoid &“rules that expire&”—tricks that may seem to help students in one grade but hurt in the long run. Features include · Abundant grade-specific examples · Effective working plans for sustainability · Barrier-busting tips, to-dos, and try-it-outs · PLC prompts and discussion points
The Math Pact, High School: Achieving Instructional Coherence Within and Across Grades (Corwin Mathematics Series)
by Karen S. Karp Sarah B. Bush Barbara J. DoughertyA schoolwide solution for students’ mathematics success! Do you sometimes start to teach a mathematics concept and feel like you’re staring at a sea of bewildered faces? What happens when you discover students previously learned a calculation trick or a mnemonic that has muddied their long-term understanding? When "rules" seem to change from year to year, teacher to teacher, or school to school, mathematics can seem like a disconnected mystery for students. Clear up the confusion with a Mathematics Whole-School Agreement! Expanded from the highly popular "Rules that Expire" series of NCTM articles, this essential guide leads educators through the collaborative step-by-step process of establishing a coherent and consistent learner-centered and equitable approach to mathematics instruction. Through this work, you will identify, streamline, and become passionate about using clear and consistent mathematical language, notations, representations, rules, and generalizations within and across classrooms and grades. Importantly, you’ll learn to avoid "rules that expire"—tricks that may seem to help students in one grade but hurt in the long run. Features of this book include: • Abundant grade-specific examples • Effective working plans for sustainability • Barrier-busting tips, to-dos, and try-it-outs • Practical templates and checklists • PLC prompts and discussion points When teachers unite across grades, students hit the ground running every year. Take the next step together as a team and help all your students build on existing understanding to find new success and most importantly, love learning and doing mathematics!
The Math Pact, High School: Achieving Instructional Coherence Within and Across Grades (Corwin Mathematics Series)
by Karen S. Karp Sarah B. Bush Barbara J. DoughertyA schoolwide solution for students’ mathematics success! Do you sometimes start to teach a mathematics concept and feel like you’re staring at a sea of bewildered faces? What happens when you discover students previously learned a calculation trick or a mnemonic that has muddied their long-term understanding? When "rules" seem to change from year to year, teacher to teacher, or school to school, mathematics can seem like a disconnected mystery for students. Clear up the confusion with a Mathematics Whole-School Agreement! Expanded from the highly popular "Rules that Expire" series of NCTM articles, this essential guide leads educators through the collaborative step-by-step process of establishing a coherent and consistent learner-centered and equitable approach to mathematics instruction. Through this work, you will identify, streamline, and become passionate about using clear and consistent mathematical language, notations, representations, rules, and generalizations within and across classrooms and grades. Importantly, you’ll learn to avoid "rules that expire"—tricks that may seem to help students in one grade but hurt in the long run. Features of this book include: • Abundant grade-specific examples • Effective working plans for sustainability • Barrier-busting tips, to-dos, and try-it-outs • Practical templates and checklists • PLC prompts and discussion points When teachers unite across grades, students hit the ground running every year. Take the next step together as a team and help all your students build on existing understanding to find new success and most importantly, love learning and doing mathematics!
The Math Pact, Middle School: Achieving Instructional Coherence Within and Across Grades (Corwin Mathematics Series)
by Karen S. Karp Sarah B. Bush Barbara J. DoughertyA schoolwide solution for mathematics success! When &“rules&” seem to change from year to year, mathematics can seem like a disconnected mystery for students. Clear up the confusion with a Mathematics Whole-School Agreement! Expanded from the highly popular &“Rules that Expire&” series of NCTM articles, this essential guide leads educators through the collaborative step-by-step process of establishing a coherent and consistent learner-centered and equitable approach to mathematics instruction. You&’ll learn to avoid &“rules that expire&”—tricks that may seem to help students in one grade but hurt in the long run. Features include · Abundant grade-specific examples · Effective working plans for sustainability · Barrier-busting tips, to-dos, and try-it-outs · PLC prompts and discussion points
The Math Pact, Middle School: Achieving Instructional Coherence Within and Across Grades (Corwin Mathematics Series)
by Karen S. Karp Sarah B. Bush Barbara J. DoughertyA schoolwide solution for mathematics success! When &“rules&” seem to change from year to year, mathematics can seem like a disconnected mystery for students. Clear up the confusion with a Mathematics Whole-School Agreement! Expanded from the highly popular &“Rules that Expire&” series of NCTM articles, this essential guide leads educators through the collaborative step-by-step process of establishing a coherent and consistent learner-centered and equitable approach to mathematics instruction. You&’ll learn to avoid &“rules that expire&”—tricks that may seem to help students in one grade but hurt in the long run. Features include · Abundant grade-specific examples · Effective working plans for sustainability · Barrier-busting tips, to-dos, and try-it-outs · PLC prompts and discussion points
The Math Teacher's Toolbox: Hundreds of Practical Ideas to Support Your Students (The Teacher's Toolbox Series)
by Bobson Wong Larisa BukalovMath teachers will find the classroom-tested lessons and strategies in this book to be accessible and easily implemented in the classroom The Teacher’s Toolbox series is an innovative, research-based resource providing teachers with instructional strategies for students of all levels and abilities. Each book in the collection focuses on a specific content area. Clear, concise guidance enables teachers to quickly integrate low-prep, high-value lessons and strategies in their middle school and high school classrooms. Every strategy follows a practical, how-to format established by the series editors. The Math Teacher's Toolbox contains hundreds of student-friendly classroom lessons and teaching strategies. Clear and concise chapters, fully aligned to Common Core math standards, cover the underlying research, required technology, practical classroom use, and modification of each high-value lesson and strategy. This book employs a hands-on approach to help educators quickly learn and apply proven methods and techniques in their mathematics courses. Topics range from the planning of units, lessons, tests, and homework to conducting formative assessments, differentiating instruction, motivating students, dealing with “math anxiety,” and culturally responsive teaching. Easy-to-read content shows how and why math should be taught as a language and how to make connections across mathematical units. Designed to reduce instructor preparation time and increase student engagement and comprehension, this book: Explains the usefulness, application, and potential drawbacks of each instructional strategy Provides fresh activities for all classrooms Helps math teachers work with ELLs, advanced students, and students with learning differences Offers real-world guidance for working with parents, guardians, and co-teachers The Math Teacher's Toolbox: Hundreds of Practical ideas to Support Your Students is an invaluable source of real-world lessons, strategies, and techniques for general education teachers and math specialists, as well as resource specialists/special education teachers, elementary and secondary educators, and teacher educators.
The Math Teachers Know: Profound Understanding of Emergent Mathematics
by Brent Davis Moshe RenertWhat sorts of mathematics competencies must teachers have in order to teach the discipline well? This book offers a novel take on the question. Most research is focused on explicit knowledge–that is, on the sorts of insights that might be specified, catalogued, taught, and tested. In contrast, this book focuses on the tacit dimensions of teachers’ mathematics knowledge that precede and enable their competencies with formal mathematics. It highlights the complexity of this knowledge and offers strategies to uncover it, analyze it, and re-synthesize it in ways that will make it more available for teaching. Emerging from 10 years of collaborative inquiry with practicing teachers, it is simultaneously informed by the most recent research and anchored to the realities of teachers’ lives in classrooms.
The Math Tutor′s Handbook: Strategies and Tips for Success (Corwin Mathematics Series)
by Steven Leinwand Caroline WeltyBoost confidence, reduce anxiety, and spark those "aha" moments for students through effective math tutoring! Filled with research-backed guidance for tutors to ensure students develop the confidence and skills they need, The Math Tutor′s Handbook: Strategies and Tips for Success is the ultimate guide for effective math tutoring. As national data suggest that students are falling behind in mathematics performance, the role of the math tutor is more critical than ever before. The authors bring decades of wisdom and know-how to the tutoring table. Steve Leinwand—a renowned leader in math education—and Caroline Welty—a sought-after tutor who brings current insight into today’s learners—have blended their collective experience into a comprehensive handbook that offers clear guidance for effective tutoring in grades K-12 mathematics. With their conversational style, the authors provide hands-on resources to help diagnose individuals’ mathematical strengths and needs to make sure that each tutoring session carries the necessary impact.. Through a range of activities, checklists, examples, stories, and suggestions, this handbook Focuses on the importance of personalized instruction that no computer program can match Describes how to develop strong, supportive relationships between tutor and student Identifies common stumbling blocks around the big ideas in mathematics across grade levels and suggests how to overcome them Celebrates mistakes as valuable learning opportunities to foster a deeper comprehension of mathematical concepts rather than just getting the right answer Promotes skills needed for the future, such as problem-solving and critical thinking, which are beneficial not only in future math classes but also in various aspects of life and work Let The Math Tutor′s Handbook empower you to create a positive learning environment for your students and help them boost self-confidence, reduce math anxiety, and master essential skills. Whether you are a private tutor or parent, you work in a tutoring center, or you are an in-school K-12 math teacher, coach, or specialist, this is the resource you need for the math tutoring strategies and practices that are foundational to successful learning.
The Math Tutor′s Handbook: Strategies and Tips for Success (Corwin Mathematics Series)
by Steven Leinwand Caroline WeltyBoost confidence, reduce anxiety, and spark those "aha" moments for students through effective math tutoring! Filled with research-backed guidance for tutors to ensure students develop the confidence and skills they need, The Math Tutor′s Handbook: Strategies and Tips for Success is the ultimate guide for effective math tutoring. As national data suggest that students are falling behind in mathematics performance, the role of the math tutor is more critical than ever before. The authors bring decades of wisdom and know-how to the tutoring table. Steve Leinwand—a renowned leader in math education—and Caroline Welty—a sought-after tutor who brings current insight into today’s learners—have blended their collective experience into a comprehensive handbook that offers clear guidance for effective tutoring in grades K-12 mathematics. With their conversational style, the authors provide hands-on resources to help diagnose individuals’ mathematical strengths and needs to make sure that each tutoring session carries the necessary impact.. Through a range of activities, checklists, examples, stories, and suggestions, this handbook Focuses on the importance of personalized instruction that no computer program can match Describes how to develop strong, supportive relationships between tutor and student Identifies common stumbling blocks around the big ideas in mathematics across grade levels and suggests how to overcome them Celebrates mistakes as valuable learning opportunities to foster a deeper comprehension of mathematical concepts rather than just getting the right answer Promotes skills needed for the future, such as problem-solving and critical thinking, which are beneficial not only in future math classes but also in various aspects of life and work Let The Math Tutor′s Handbook empower you to create a positive learning environment for your students and help them boost self-confidence, reduce math anxiety, and master essential skills. Whether you are a private tutor or parent, you work in a tutoring center, or you are an in-school K-12 math teacher, coach, or specialist, this is the resource you need for the math tutoring strategies and practices that are foundational to successful learning.
The Math You Need: A Comprehensive Survey of Undergraduate Mathematics
by Thomas MackA comprehensive survey of undergraduate mathematics, compressing four years of study into one robust overview.In The Math You Need, Thomas Mack provides a singular, comprehensive survey of undergraduate mathematics, compressing four years of math curricula into one volume. Without sacrificing rigor, this book provides a go-to resource for the essentials that any academic or professional needs. Each chapter is followed by numerous exercises to provide the reader an opportunity to practice what they learned. The Math You Need is distinguished in its use of the Bourbaki style—the gold standard for concision and an approach that mathematicians will find of particular interest. As ambitious as it is compact, this text embraces mathematical abstraction throughout, avoiding ad hoc computations in favor of general results.Covering nine areas—group theory, commutative algebra, linear algebra, topology, real analysis, complex analysis, number theory, probability, and statistics—this thorough and highly effective overview of the undergraduate curriculum will prove to be invaluable to students and instructors alike.
The Math of Life and Death: 7 Mathematical Principles That Shape Our Lives
by Kit YatesA brilliant and entertaining mathematician illuminates seven mathematical principles that shape our lives. &“Kit Yates shows how our private and social lives are suffused by mathematics. Ignorance may bring tragedy or farce. This is an exquisitely interesting book. It&’s a deeply serious one too and, for those like me who have little math, it&’s delightfully readable.&” —Ian McEwan, author of Atonement &“Kit Yates is a natural storyteller. Through fascinating stories and examples, he shows how maths is the beating heart of so much of modern life. An exciting new voice in the world of science communication.&” —Marcus du Sautoy, author of The Music of the PrimesFrom birthdays to birth rates to how we perceive the passing of time, mathematical patterns shape our lives. But for those of us who left math behind in high school, the numbers and figures hurled at us as we go about our days can sometimes leave us scratching our heads and feeling as if we&’re fumbling through a mathematical minefield. In this eye-opening and extraordinarily accessible book, mathematician Kit Yates illuminates hidden principles that can help us understand and navigate the chaotic and often opaque surfaces of our world. In The Math of Life and Death, Yates takes us on a fascinating tour of everyday situations and grand-scale applications of mathematical concepts, including exponential growth and decay, optimization, statistics and probability, and number systems. Along the way he reveals the mathematical undersides of controversies over DNA testing, medical screening results, and historical events such as the Chernobyl disaster and the Amanda Knox trial. Readers will finish this book with an enlightened perspective on the news, the law, medicine, and history, and will be better equipped to make personal decisions and solve problems with math in mind, whether it&’s choosing the shortest checkout line at the grocery store or halting the spread of a deadly disease.
The Mathemagician and Pied Puzzler: A Collection in Tribute to Martin Gardner
by Tom Rodgers Elwyn BerlekampThis volume comprises an imaginative collection of pieces created in tribute to Martin Gardner. Perhaps best known for writing Scientific American's "Mathematical Games" column for years, Gardner used his personal exuberance and fascination with puzzles and magic to entice a wide range of readers into a world of mathematical discovery. This tribute
The Mathematical Artist: A Tribute To John Horton Conway (Emergence, Complexity and Computation #45)
by Sukanta Das Souvik Roy Kamalika BhattacharjeeThis book brings together the impact of Prof. John Horton Conway, the playful and legendary mathematician's wide range of contributions in science which includes research areas—Game of Life in cellular automata, theory of finite groups, knot theory, number theory, combinatorial game theory, and coding theory. It contains transcripts where some eminent scientists have shared their first-hand experience of interacting with Conway, as well as some invited research articles from the experts focusing on Game of Life, cellular automata, and the diverse research directions that started with Conway's Game of Life. The book paints a portrait of Conway's research life and philosophical direction in mathematics and is of interest to whoever wants to explore his contribution to the history and philosophy of mathematics and computer science. It is designed as a small tribute to Prof. Conway whom we lost on April 11, 2020.
The Mathematical Foundation of Multi-Space Learning Theory
by Tai Wang Mengsiying LiThis book explores the measurement of learning effectiveness and the optimization of knowledge retention by modeling the learning process and building the mathematical foundation of multi-space learning theory.Multi-space learning is defined in this book as a micro-process of human learning that can take place in more than one space, with the goal of effective learning and knowledge retention. This book models the learning process as a temporal sequence of concept learning, drawing on established principles and empirical evidence. It also introduces the matroid to strengthen the mathematical foundation of multi-space learning theory and applies the theory to vocabulary and mathematics learning, respectively. The results show that, for vocabulary learning, the method can be used to estimate the effectiveness of a single learning strategy, to detect the mutual interference that might exist between learning strategies, and to predict the optimal combination of strategies. In mathematical learning, it was found that timing is crucial in both first learning and second learning in scheduling optimization to maximize the intersection effective interval.The title will be of interest to researchers and students in a wide range of areas, including educational technology, learning sciences, mathematical applications, and mathematical psychology.
The Mathematical Heritage of Guido Weiss (Applied and Numerical Harmonic Analysis)
by Anita Tabacco Fernando Soria Fulvio Ricci Eugenio Hernández Marco Maria PelosoThis work is a tribute to the life and work of Guido Weiss, a mathematician whose profound contributions shaped the field of harmonic analysis over a span of more than six decades. His groundbreaking research, from pioneering real and complex analysis to his later work on wavelets, continues to influence generations of scholars. More than just a researcher, Guido was a mentor, collaborator, and friend to many, creating a global community of mathematicians. His charisma and generosity fostered lasting professional and personal connections across continents, touching lives far beyond academia. This volume features contributions of collaborators, students, and colleagues of Guido, who had a particularly intense relationship with him. From a heartfelt remembrance of Guido Weiss to advanced discussions on spectral synthesis and wavelet theory, this collection contains a diverse landscape of mathematical results. Readers will delve into topics such as the compactness of bilinear commutators, the intricacies of analytic families in extrapolation theory, and the intersections of time-frequency analysis with modern learning techniques. With contributions to Hardy spaces, Haar multipliers, and crystalline measures, this book serves both as a tribute to past achievements and a beacon for future exploration.
The Mathematical Imagination: On the Origins and Promise of Critical Theory
by Matthew HandelmanThis book offers an archeology of the undeveloped potential of mathematics for critical theory. As Max Horkheimer and Theodor W. Adorno first conceived of the critical project in the 1930s, critical theory steadfastly opposed the mathematization of thought. Mathematics flattened thought into a dangerous positivism that led reason to the barbarism of World War II. The Mathematical Imagination challenges this narrative, showing how for other German-Jewish thinkers, such as Gershom Scholem, Franz Rosenzweig, and Siegfried Kracauer, mathematics offered metaphors to negotiate the crises of modernity during the Weimar Republic. Influential theories of poetry, messianism, and cultural critique, Handelman shows, borrowed from the philosophy of mathematics, infinitesimal calculus, and geometry in order to refashion cultural and aesthetic discourse.Drawn to the austerity and muteness of mathematics, these friends and forerunners of the Frankfurt School found in mathematical approaches to negativity strategies to capture the marginalized experiences and perspectives of Jews in Germany. Their vocabulary, in which theory could be both mathematical and critical, is missing from the intellectual history of critical theory, whether in the work of second generation critical theorists such as Jürgen Habermas or in contemporary critiques of technology. The Mathematical Imagination shows how Scholem, Rosenzweig, and Kracauer’s engagement with mathematics uncovers a more capacious vision of the critical project, one with tools that can help us intervene in our digital and increasingly mathematical present.
The Mathematical Legacy of Leon Ehrenpreis
by Daniele C. Struppa Irene SabadiniLeon Ehrenpreis has been one of the leading mathematicians in the twentieth century. His contributions to the theory of partial differential equations were part of the golden era of PDEs, and led him to what is maybe his most important contribution, the Fundamental Principle, which he announced in 1960, and fully demonstrated in 1970. His most recent work, on the other hand, focused on a novel and far reaching understanding of the Radon transform, and offered new insights in integral geometry. Leon Ehrenpreis died in 2010, and this volume collects writings in his honor by a cadre of distinguished mathematicians, many of which were his collaborators.
The Mathematical Legacy of Srinivasa Ramanujan
by M. Ram Murty V. Kumar MurtySrinivasa Ramanujan was a mathematician brilliant beyond comparison who inspired many great mathematicians. There is extensive literature available on the work of Ramanujan. But what is missing in the literature is an analysis that would place his mathematics in context and interpret it in terms of modern developments. The 12 lectures by Hardy, delivered in 1936, served this purpose at the time they were given. This book presents Ramanujan's essential mathematical contributions and gives an informal account of some of the major developments that emanated from his work in the 20th and 21st centuries. It contends that his work still has an impact on many different fields of mathematical research. This book examines some of these themes in the landscape of 21st-century mathematics. These essays, based on the lectures given by the authors focus on a subset of Ramanujan's significant papers and show how these papers shaped the course of modern mathematics.
The Mathematical Mechanic
by Mark LeviEverybody knows that mathematics is indispensable to physics--imagine where we'd be today if Einstein and Newton didn't have the math to back up their ideas. But how many people realize that physics can be used to produce many astonishing and strikingly elegant solutions in mathematics? Mark Levi shows how in this delightful book, treating readers to a host of entertaining problems and mind-bending puzzlers that will amuse and inspire their inner physicist. Levi turns math and physics upside down, revealing how physics can simplify proofs and lead to quicker solutions and new theorems, and how physical solutions can illustrate why results are true in ways lengthy mathematical calculations never can. Did you know it's possible to derive the Pythagorean theorem by spinning a fish tank filled with water? Or that soap film holds the key to determining the cheapest container for a given volume? Or that the line of best fit for a data set can be found using a mechanical contraption made from a rod and springs? Levi demonstrates how to use physical intuition to solve these and other fascinating math problems. More than half the problems can be tackled by anyone with precalculus and basic geometry, while the more challenging problems require some calculus. This one-of-a-kind book explains physics and math concepts where needed, and includes an informative appendix of physical principles. The Mathematical Mechanic will appeal to anyone interested in the little-known connections between mathematics and physics and how both endeavors relate to the world around us.
The Mathematical Representation of Physical Reality (The Frontiers Collection)
by Shahen HacyanThis book deals with the rise of mathematics in physical sciences, beginning with Galileo and Newton and extending to the present day. The book is divided into two parts. The first part gives a brief history of how mathematics was introduced into physics—despite its "unreasonable effectiveness" as famously pointed out by a distinguished physicist—and the criticisms it received from earlier thinkers. The second part takes a more philosophical approach and is intended to shed some light on that mysterious effectiveness. For this purpose, the author reviews the debate between classical philosophers on the existence of innate ideas that allow us to understand the world and also the philosophically based arguments for and against the use of mathematics in physical sciences. In this context, Schopenhauer’s conceptions of causality and matter are very pertinent, and their validity is revisited in light of modern physics. The final question addressed is whether the effectiveness of mathematics can be explained by its “existence” in an independent platonic realm, as Gödel believed.The book aims at readers interested in the history and philosophy of physics. It is accessible to those with only a very basic (not professional) knowledge of physics.
The Mathematical Resilience Book: How Everyone Can Progress in Mathematics
by Sue Johnston-Wilder Clare LeeThis book is about mathematical resilience: what it is, why it is important, how learners can develop it and how teachers can teach in ways that help learners become mathematically resilient. Teaching for mathematical resilience helps mitigate mathematics anxiety, which is often hidden from view as poor behaviour, avoidance and underachievement and can have long-term implications especially for people’s employment opportunities and career progression.Written by a team of expert contributors that specialise in teaching every age of learner from primary school through to adult, the book shows that everyone can progress in mathematics if they have Mathematical Resilience and sets out practical strategies to support learners in developing this important attribute. Chapters cover: How to measure mathematics anxiety and resilience Tools for building mathematical resilience Building a resilient mathematical learning environment The power of coaching Working with groups, individuals and support staff Supporting parents and carers The world faces huge challenges that involve mathematical thinking, including climate change and economic injustice. This valuable text shows teachers how they can help learners to engage positively with mathematical learning and reach their full potential.
The Mathematical Sciences in 2025
by Committee on the Mathematical Sciences in 2025The mathematical sciences are part of nearly all aspects of everyday life--the discipline has underpinned such beneficial modern capabilities as Internet search, medical imaging, computer animation, numerical weather predictions, and all types of digital communications. The Mathematical Sciences in 2025 examines the current state of the mathematical sciences and explores the changes needed for the discipline to be in a strong position and able to maximize its contribution to the nation in 2025. It finds the vitality of the discipline excellent and that it contributes in expanding ways to most areas of science and engineering, as well as to the nation as a whole, and recommends that training for future generations of mathematical scientists should be re-assessed in light of the increasingly cross-disciplinary nature of the mathematical sciences. In addition, because of the valuable interplay between ideas and people from all parts of the mathematical sciences, the report emphasizes that universities and the government need to continue to invest in the full spectrum of the mathematical sciences in order for the whole enterprise to continue to flourish long-term.