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| at what age can humans show math abilities: The Everything Parent's Guide to Special Education Amanda Morin, 2014-04-18 Be your child's best advocate! Children with special needs who succeed in school have one thing in common--their parents are passionate and effective advocates. It's not an easy job, but with The Everything Parent's Guide to Special Education, you will learn how to evaluate, prepare, organize, and get quality services, no matter what your child's disability. This valuable handbook gives you the tools you need to navigate the complex world of special education and services, with information on: Assessment and evaluation Educational needs for different disabilities, including multiple disabilities Current law, including the Individuals with Disabilities Education Act (IDEA) Working within the school system to create an IEP The importance of keeping detailed records Dealing with parent-school conflict With worksheets, forms, and sample documents and letters, you can be assured that you'll have all you need to help your child thrive--in school and in life! |
| at what age can humans show math abilities: Transforming the Workforce for Children Birth Through Age 8 National Research Council, Institute of Medicine, Board on Children, Youth, and Families, Committee on the Science of Children Birth to Age 8: Deepening and Broadening the Foundation for Success, 2015-07-23 Children are already learning at birth, and they develop and learn at a rapid pace in their early years. This provides a critical foundation for lifelong progress, and the adults who provide for the care and the education of young children bear a great responsibility for their health, development, and learning. Despite the fact that they share the same objective - to nurture young children and secure their future success - the various practitioners who contribute to the care and the education of children from birth through age 8 are not acknowledged as a workforce unified by the common knowledge and competencies needed to do their jobs well. Transforming the Workforce for Children Birth Through Age 8 explores the science of child development, particularly looking at implications for the professionals who work with children. This report examines the current capacities and practices of the workforce, the settings in which they work, the policies and infrastructure that set qualifications and provide professional learning, and the government agencies and other funders who support and oversee these systems. This book then makes recommendations to improve the quality of professional practice and the practice environment for care and education professionals. These detailed recommendations create a blueprint for action that builds on a unifying foundation of child development and early learning, shared knowledge and competencies for care and education professionals, and principles for effective professional learning. Young children thrive and learn best when they have secure, positive relationships with adults who are knowledgeable about how to support their development and learning and are responsive to their individual progress. Transforming the Workforce for Children Birth Through Age 8 offers guidance on system changes to improve the quality of professional practice, specific actions to improve professional learning systems and workforce development, and research to continue to build the knowledge base in ways that will directly advance and inform future actions. The recommendations of this book provide an opportunity to improve the quality of the care and the education that children receive, and ultimately improve outcomes for children. |
| at what age can humans show math abilities: Helping Children Learn Mathematics National Research Council, Division of Behavioral and Social Sciences and Education, Center for Education, Mathematics Learning Study Committee, 2002-07-31 Results from national and international assessments indicate that school children in the United States are not learning mathematics well enough. Many students cannot correctly apply computational algorithms to solve problems. Their understanding and use of decimals and fractions are especially weak. Indeed, helping all children succeed in mathematics is an imperative national goal. However, for our youth to succeed, we need to change how we're teaching this discipline. Helping Children Learn Mathematics provides comprehensive and reliable information that will guide efforts to improve school mathematics from pre-kindergarten through eighth grade. The authors explain the five strands of mathematical proficiency and discuss the major changes that need to be made in mathematics instruction, instructional materials, assessments, teacher education, and the broader educational system and answers some of the frequently asked questions when it comes to mathematics instruction. The book concludes by providing recommended actions for parents and caregivers, teachers, administrators, and policy makers, stressing the importance that everyone work together to ensure a mathematically literate society. |
| at what age can humans show math abilities: Mathematics Form and Function Saunders MacLane, 2012-12-06 This book records my efforts over the past four years to capture in words a description of the form and function of Mathematics, as a background for the Philosophy of Mathematics. My efforts have been encouraged by lec tures that I have given at Heidelberg under the auspices of the Alexander von Humboldt Stiftung, at the University of Chicago, and at the University of Minnesota, the latter under the auspices of the Institute for Mathematics and Its Applications. Jean Benabou has carefully read the entire manuscript and has offered incisive comments. George Glauberman, Car los Kenig, Christopher Mulvey, R. Narasimhan, and Dieter Puppe have provided similar comments on chosen chapters. Fred Linton has pointed out places requiring a more exact choice of wording. Many conversations with George Mackey have given me important insights on the nature of Mathematics. I have had similar help from Alfred Aeppli, John Gray, Jay Goldman, Peter Johnstone, Bill Lawvere, and Roger Lyndon. Over the years, I have profited from discussions of general issues with my colleagues Felix Browder and Melvin Rothenberg. Ideas from Tammo Tom Dieck, Albrecht Dold, Richard Lashof, and Ib Madsen have assisted in my study of geometry. Jerry Bona and B.L. Foster have helped with my examina tion of mechanics. My observations about logic have been subject to con structive scrutiny by Gert Miiller, Marian Boykan Pour-El, Ted Slaman, R. Voreadou, Volker Weispfennig, and Hugh Woodin. |
| at what age can humans show math abilities: The Number Sense Stanislas Dehaene, 2011-04-29 Our understanding of how the human brain performs mathematical calculations is far from complete. In The Number Sense, Stanislas Dehaene offers readers an enlightening exploration of the mathematical mind. Using research showing that human infants have a rudimentary number sense, Dehaene suggests that this sense is as basic as our perception of color, and that it is wired into the brain. But how then did we leap from this basic number ability to trigonometry, calculus, and beyond? Dehaene shows that it was the invention of symbolic systems of numerals that started us on the climb to higher mathematics. Tracing the history of numbers, we learn that in early times, people indicated numbers by pointing to part of their bodies, and how Roman numerals were replaced by modern numbers. On the way, we also discover many fascinating facts: for example, because Chinese names for numbers are short, Chinese people can remember up to nine or ten digits at a time, while English-speaking people can only remember seven. A fascinating look at the crossroads where numbers and neurons intersect, The Number Sense offers an intriguing tour of how the structure of the brain shapes our mathematical abilities, and how math can open up a window on the human mind--Provided by publisher. |
| at what age can humans show math abilities: The Math Gene Keith Devlin, 2001-05-17 Why is math so hard? And why, despite this difficulty, are some people so good at it? If there's some inborn capacity for mathematical thinking—which there must be, otherwise no one could do it —why can't we all do it well? Keith Devlin has answers to all these difficult questions, and in giving them shows us how mathematical ability evolved, why it's a part of language ability, and how we can make better use of this innate talent.He also offers a breathtakingly new theory of language development—that language evolved in two stages, and its main purpose was not communication—to show that the ability to think mathematically arose out of the same symbol-manipulating ability that was so crucial to the emergence of true language. Why, then, can't we do math as well as we can speak? The answer, says Devlin, is that we can and do—we just don't recognize when we're using mathematical reasoning. |
| at what age can humans show math abilities: Math Right from the Start Jan Greenberg, 2008 New research shows that early mathematics knowledge is an important predictor of later school success. Yet maths is one of the most miss understood topics in early childhood. Many people think that maths is simply counting and recognizing numbers through school-based activities, but mathematics is so much more! When parents provide rich, everyday maths experiences at home, children gain a critical foundation for future learning - and an important connection is made between the home and school experience. This easy-to-read, beautifully illustrated booklet shows parents how they can help their children (birth to five years) gain the mathematical thinking and skills they need through incorporating the concepts of number, geometry, measurement, patterns, change, collecting and organising information into their everyday routines and conversation. |
| at what age can humans show math abilities: Heterogeneity of Function in Numerical Cognition Avishai Henik, Wim Fias, 2018-05-17 Heterogeneity of Function in Numerical Cognition presents the latest updates on ongoing research and discussions regarding numerical cognition. With great individual differences in the development or function of numerical cognition at neuroanatomical, neuropsychological, behavioral, and interactional levels, these issues are important for the achievement of a comprehensive understanding of numerical cognition, hence its brain basis, development, breakdown in brain-injured individuals, and failures to master mathematical skills. These functions are essential for the proper development of numerical cognition. - Provides an innovative reference on the emerging field of numerical cognition and the branches that converge on this diverse cognitive domain - Includes an overview of the multiple disciplines that comprise numerical cognition - Focuses on factors that influence numerical cognition, such as language, executive attention, memory and spatial processing - Features an innovative organization with each section providing a general overview, developmental research, and evidence from neurocognitive studies |
| at what age can humans show math abilities: Mathematics Learning in Early Childhood National Research Council, Division of Behavioral and Social Sciences and Education, Center for Education, Committee on Early Childhood Mathematics, 2009-11-13 Early childhood mathematics is vitally important for young children's present and future educational success. Research demonstrates that virtually all young children have the capability to learn and become competent in mathematics. Furthermore, young children enjoy their early informal experiences with mathematics. Unfortunately, many children's potential in mathematics is not fully realized, especially those children who are economically disadvantaged. This is due, in part, to a lack of opportunities to learn mathematics in early childhood settings or through everyday experiences in the home and in their communities. Improvements in early childhood mathematics education can provide young children with the foundation for school success. Relying on a comprehensive review of the research, Mathematics Learning in Early Childhood lays out the critical areas that should be the focus of young children's early mathematics education, explores the extent to which they are currently being incorporated in early childhood settings, and identifies the changes needed to improve the quality of mathematics experiences for young children. This book serves as a call to action to improve the state of early childhood mathematics. It will be especially useful for policy makers and practitioners-those who work directly with children and their families in shaping the policies that affect the education of young children. |
| at what age can humans show math abilities: On the Development of Space-Number Relations: Linguistic and Cognitive Determinants, Influences, and Associations Hans-Christoph Nuerk, Krzysztof Cipora, Frank Domahs, Maciej Haman, 2020-03-30 |
| at what age can humans show math abilities: What Counts Brian Butterworth, 1999 Though he admits to not being particularly good at math, Butterworth (cognitive neuropsychology, U. College, London), the founder of the Mathematical Cognition journal, contends that we all possess an inherent numerosity sense--developed to different degrees of course. The author bases his case on empirical research and historical speculation. Annotation copyrighted by Book News, Inc., Portland, OR |
| at what age can humans show math abilities: In the Light of Evolution National Academy of Sciences, 2007 The Arthur M. Sackler Colloquia of the National Academy of Sciences address scientific topics of broad and current interest, cutting across the boundaries of traditional disciplines. Each year, four or five such colloquia are scheduled, typically two days in length and international in scope. Colloquia are organized by a member of the Academy, often with the assistance of an organizing committee, and feature presentations by leading scientists in the field and discussions with a hundred or more researchers with an interest in the topic. Colloquia presentations are recorded and posted on the National Academy of Sciences Sackler colloquia website and published on CD-ROM. These Colloquia are made possible by a generous gift from Mrs. Jill Sackler, in memory of her husband, Arthur M. Sackler. |
| at what age can humans show math abilities: Primate Neuroethology Asif A. Ghazanfar, 2012-08-16 This edited volume is the first of its kind to bridge the epistemological gap between primate ethologists and primate neurobiologists. Leading experts in several fields review work ranging from primate foraging behavior to the neurophysiology of motor control, from vocal communication to the functions of the auditory cortex. |
| at what age can humans show math abilities: Brain Rules for Baby (Updated and Expanded) John Medina, 2014-04-22 What’s the single most important thing you can do during pregnancy? What does watching TV do to a child’s brain? What’s the best way to handle temper tantrums? Scientists know. In his New York Times bestseller Brain Rules, Dr. John Medina showed us how our brains really work—and why we ought to redesign our workplaces and schools. Now, in Brain Rules for Baby, he shares what the latest science says about how to raise smart and happy children from zero to five. This book is destined to revolutionize parenting. Just one of the surprises: The best way to get your children into the college of their choice? Teach them impulse control. Brain Rules for Baby bridges the gap between what scientists know and what parents practice. Through fascinating and funny stories, Medina, a developmental molecular biologist and dad, unravels how a child’s brain develops – and what you can do to optimize it. You will view your children—and how to raise them—in a whole new light. You’ll learn: Where nature ends and nurture begins Why men should do more household chores What you do when emotions run hot affects how your baby turns out, because babies need to feel safe above all TV is harmful for children under 2 Your child’s ability to relate to others predicts her future math performance Smart and happy are inseparable. Pursuing your child’s intellectual success at the expense of his happiness achieves neither Praising effort is better than praising intelligence The best predictor of academic performance is not IQ. It’s self-control What you do right now—before pregnancy, during pregnancy, and through the first five years—will affect your children for the rest of their lives. Brain Rules for Baby is an indispensable guide. |
| at what age can humans show math abilities: Satan, Cantor, And Infinity And Other Mind-bogglin Raymond M. Smullyan, 2012-05-30 More than two hundred new and challenging logic puzzles—the simplest brainteaser to the most complex paradoxes in contemporary mathematical thinking—from our topmost puzzlemaster (“the most entertaining logician who ever lived,” Martin Gardner has called him). Our guide to the puzzles is the Sorcerer, who resides on the Island of Knights and Knaves, where knights always tell the truth and knaves always lie, and he introduces us to the amazing magic—logic—that enables to discover which inhabitants are which. Then, in a picaresque adventure in logic, he takes us to the planet Og, to the Island of Partial Silence, and to a land where metallic robots wearing strings of capital letters are noisily duplicating and dismantling themselves and others. The reader’s job is to figure out how it all works. Finally, we accompany the Sorcerer on an alluring tour of Infinity which includes George Cantor’s amazing mathematical insights. The tour (and the book) ends with Satan devising a diabolical puzzle for one of Cantor’s prize students—who outwits him! In sum: a devilish magician’s cornucopia of puzzles—a delight for every age and level of ability. |
| at what age can humans show math abilities: The Handbook of Mathematical Cognition Jamie I.D. Campbell, 2005-08-15 How does the brain represent number and make mathematical calculations? What underlies the development of numerical and mathematical abilities? What factors affect the learning of numerical concepts and skills? What are the biological bases of number knowledge? Do humans and other animals share similar numerical representations and processes? What underlies numerical and mathematical disabilities and disorders, and what is the prognosis for rehabilitation? These questions are the domain of mathematical cognition, the field of research concerned with the cognitive and neurological processes that underlie numerical and mathematical abilities. TheHandbook of Mathematical Cognition is a collection of 27 essays by leading researchers that provides a comprehensive review of this important research field. |
| at what age can humans show math abilities: How to Think About Analysis Lara Alcock, 2014-09-25 Analysis (sometimes called Real Analysis or Advanced Calculus) is a core subject in most undergraduate mathematics degrees. It is elegant, clever and rewarding to learn, but it is hard. Even the best students find it challenging, and those who are unprepared often find it incomprehensible at first. This book aims to ensure that no student need be unprepared. It is not like other Analysis books. It is not a textbook containing standard content. Rather, it is designed to be read before arriving at university and/or before starting an Analysis course, or as a companion text once a course is begun. It provides a friendly and readable introduction to the subject by building on the student's existing understanding of six key topics: sequences, series, continuity, differentiability, integrability and the real numbers. It explains how mathematicians develop and use sophisticated formal versions of these ideas, and provides a detailed introduction to the central definitions, theorems and proofs, pointing out typical areas of difficulty and confusion and explaining how to overcome these. The book also provides study advice focused on the skills that students need if they are to build on this introduction and learn successfully in their own Analysis courses: it explains how to understand definitions, theorems and proofs by relating them to examples and diagrams, how to think productively about proofs, and how theories are taught in lectures and books on advanced mathematics. It also offers practical guidance on strategies for effective study planning. The advice throughout is research based and is presented in an engaging style that will be accessible to students who are new to advanced abstract mathematics. |
| at what age can humans show math abilities: Whither Opportunity? Greg J. Duncan, Richard J. Murnane, 2011-09-01 As the incomes of affluent and poor families have diverged over the past three decades, so too has the educational performance of their children. But how exactly do the forces of rising inequality affect the educational attainment and life chances of low-income children? In Whither Opportunity? a distinguished team of economists, sociologists, and experts in social and education policy examines the corrosive effects of unequal family resources, disadvantaged neighborhoods, insecure labor markets, and worsening school conditions on K-12 education. This groundbreaking book illuminates the ways rising inequality is undermining one of the most important goals of public education—the ability of schools to provide children with an equal chance at academic and economic success. The most ambitious study of educational inequality to date, Whither Opportunity? analyzes how social and economic conditions surrounding schools affect school performance and children’s educational achievement. The book shows that from earliest childhood, parental investments in children’s learning affect reading, math, and other attainments later in life. Contributor Meredith Phillip finds that between birth and age six, wealthier children will have spent as many as 1,300 more hours than poor children on child enrichment activities such as music lessons, travel, and summer camp. Greg Duncan, George Farkas, and Katherine Magnuson demonstrate that a child from a poor family is two to four times as likely as a child from an affluent family to have classmates with low skills and behavior problems – attributes which have a negative effect on the learning of their fellow students. As a result of such disparities, contributor Sean Reardon finds that the gap between rich and poor children’s math and reading achievement scores is now much larger than it was fifty years ago. And such income-based gaps persist across the school years, as Martha Bailey and Sue Dynarski document in their chapter on the growing income-based gap in college completion. Whither Opportunity? also reveals the profound impact of environmental factors on children’s educational progress and schools’ functioning. Elizabeth Ananat, Anna Gassman-Pines, and Christina Gibson-Davis show that local job losses such as those caused by plant closings can lower the test scores of students with low socioeconomic status, even students whose parents have not lost their jobs. They find that community-wide stress is most likely the culprit. Analyzing the math achievement of elementary school children, Stephen Raudenbush, Marshall Jean, and Emily Art find that students learn less if they attend schools with high student turnover during the school year – a common occurrence in poor schools. And David Kirk and Robert Sampson show that teacher commitment, parental involvement, and student achievement in schools in high-crime neighborhoods all tend to be low. For generations of Americans, public education provided the springboard to upward mobility. This pioneering volume casts a stark light on the ways rising inequality may now be compromising schools’ functioning, and with it the promise of equal opportunity in America. |
| at what age can humans show math abilities: The Doorbell Rang Pat Hutchins, 1989-10-26 Ma has made a dozen delicious cookies. It should be plenty for her two children. But then the doorbell rings -- and rings and rings.Each ring of the doorbell brings more friends to share the delicious cookies Ma has made.Refreshing, enjoyable and unpredictable. -- School Library Journal. Also available in a Spanish-language edition, Llaman a la puerta. |
| at what age can humans show math abilities: Numbers and the Making of Us Caleb Everett, 2017-03-13 “A fascinating book.” —James Ryerson, New York Times Book Review A Smithsonian Best Science Book of the Year Winner of the PROSE Award for Best Book in Language & Linguistics Carved into our past and woven into our present, numbers shape our perceptions of the world far more than we think. In this sweeping account of how the invention of numbers sparked a revolution in human thought and culture, Caleb Everett draws on new discoveries in psychology, anthropology, and linguistics to reveal the many things made possible by numbers, from the concept of time to writing, agriculture, and commerce. Numbers are a tool, like the wheel, developed and refined over millennia. They allow us to grasp quantities precisely, but recent research confirms that they are not innate—and without numbers, we could not fully grasp quantities greater than three. Everett considers the number systems that have developed in different societies as he shares insights from his fascinating work with indigenous Amazonians. “This is bold, heady stuff... The breadth of research Everett covers is impressive, and allows him to develop a narrative that is both global and compelling... Numbers is eye-opening, even eye-popping.” —New Scientist “A powerful and convincing case for Everett’s main thesis: that numbers are neither natural nor innate to humans.” —Wall Street Journal |
| at what age can humans show math abilities: Critical Pedagogy and the Everyday Classroom Tony Monchinski, 2008-06-28 Critical Pedagogy addresses the shortcomings of mainstream educational theory and practice and promotes the humanization of teacher and student. Where Critical Pedagogy is often treated as a discourse of academics in universities, this book explores the applications of Critical Pedagogy to actual classroom situations. Written in a straight-forward, concise, and lucid form by an American high school teacher, drawing examples from literature, film, and, above all, the everyday classroom, this book is meant to provoke thought in teachers, students and education activists as we transform our classrooms into democratic sites. From grading to testing, from content area disciplines to curriculum planning and instruction, from the social construction of knowledge to embodied cognition, this book takes the theories behind Critical Pedagogy and illustrates them at work in common classroom environments. |
| at what age can humans show math abilities: Astrology for Yourself Demetra George, Douglas Bloch, 2015-06-01 Astrology for Yourself is designed to introduce you to the language, art, and science of astrology through a series of self-directed, program-learning exercises that will literally enable you to write your own chart interpretation. Aside from providing you a wealth of knowledge about your birth chart, Astrology for Yourself promises to promote personal growth and change your life. |
| at what age can humans show math abilities: Principles to Actions National Council of Teachers of Mathematics, 2014-02 This text offers guidance to teachers, mathematics coaches, administrators, parents, and policymakers. This book: provides a research-based description of eight essential mathematics teaching practices ; describes the conditions, structures, and policies that must support the teaching practices ; builds on NCTM's Principles and Standards for School Mathematics and supports implementation of the Common Core State Standards for Mathematics to attain much higher levels of mathematics achievement for all students ; identifies obstacles, unproductive and productive beliefs, and key actions that must be understood, acknowledged, and addressed by all stakeholders ; encourages teachers of mathematics to engage students in mathematical thinking, reasoning, and sense making to significantly strengthen teaching and learning. |
| at what age can humans show math abilities: Developmental Dyscalculia Jörg-Tobias Kuhn, 2015-07-20 This volume aims to further our understanding of developmental dyscalculia and measures that might help to redress it. In addition to recent research findings highlighting the importance of working memory facets in developmental dyscalculia and investigating the IQ-achievement discrepancy criterion in defining the disorder, a meta-analysis on the effectiveness of interventions for children with mathematical difficulties provides new directions for how affected children can best be helped. |
| at what age can humans show math abilities: The Cambridge Handbook of Cognition and Education John Dunlosky, Katherine A. Rawson, 2019-02-07 This Handbook reviews a wealth of research in cognitive and educational psychology that investigates how to enhance learning and instruction to aid students struggling to learn and to advise teachers on how best to support student learning. The Handbook includes features that inform readers about how to improve instruction and student achievement based on scientific evidence across different domains, including science, mathematics, reading and writing. Each chapter supplies a description of the learning goal, a balanced presentation of the current evidence about the efficacy of various approaches to obtaining that learning goal, and a discussion of important future directions for research in this area. It is the ideal resource for researchers continuing their study of this field or for those only now beginning to explore how to improve student achievement. |
| at what age can humans show math abilities: Introduction to Abstract Algebra W. Keith Nicholson, 2012-03-20 Praise for the Third Edition . . . an expository masterpiece of the highest didactic value that has gained additional attractivity through the various improvements . . .—Zentralblatt MATH The Fourth Edition of Introduction to Abstract Algebra continues to provide an accessible approach to the basic structures of abstract algebra: groups, rings, and fields. The book's unique presentation helps readers advance to abstract theory by presenting concrete examples of induction, number theory, integers modulo n, and permutations before the abstract structures are defined. Readers can immediately begin to perform computations using abstract concepts that are developed in greater detail later in the text. The Fourth Edition features important concepts as well as specialized topics, including: The treatment of nilpotent groups, including the Frattini and Fitting subgroups Symmetric polynomials The proof of the fundamental theorem of algebra using symmetric polynomials The proof of Wedderburn's theorem on finite division rings The proof of the Wedderburn-Artin theorem Throughout the book, worked examples and real-world problems illustrate concepts and their applications, facilitating a complete understanding for readers regardless of their background in mathematics. A wealth of computational and theoretical exercises, ranging from basic to complex, allows readers to test their comprehension of the material. In addition, detailed historical notes and biographies of mathematicians provide context for and illuminate the discussion of key topics. A solutions manual is also available for readers who would like access to partial solutions to the book's exercises. Introduction to Abstract Algebra, Fourth Edition is an excellent book for courses on the topic at the upper-undergraduate and beginning-graduate levels. The book also serves as a valuable reference and self-study tool for practitioners in the fields of engineering, computer science, and applied mathematics. |
| at what age can humans show math abilities: What is the Name of this Book? Raymond M. Smullyan, 2011 A celebrated mathematician presents more than 200 increasingly complex problems that delve into Gödel's undecidability theorem and other examples of the deepest paradoxes of logic and set theory. Solutions. |
| at what age can humans show math abilities: Understanding the Brain Function and Emotions José Manuel Ferrández Vicente, José Ramón Álvarez-Sánchez, Félix de la Paz López, Javier Toledo Moreo, Hojjat Adeli, 2019-05-09 The two volume set LNCS 11486 and 11487 constitutes the proceedings of the International Work-Conference on the Interplay Between Natural and Artificial Computation, IWINAC 2019, held in Almería, Spain,, in June 2019. The total of 103 contributions was carefully reviewed and selected from 190 submissions during two rounds of reviewing and improvement. The papers are organized in two volumes, one on understanding the brain function and emotions, addressing topics such as new tools for analyzing neural data, or detection emotional states, or interfacing with physical systems. The second volume deals with bioinspired systems and biomedical applications to machine learning and contains papers related bioinspired programming strategies and all the contributions oriented to the computational solutions to engineering problems in different applications domains, as biomedical systems, or big data solutions. |
| at what age can humans show math abilities: Let's Play Math Denise Gaskins, 2012-09-04 |
| at what age can humans show math abilities: Count Down Steve Olson, 2004 Each summer six math whizzes selected from nearly a half-million American teens compete against the world's best problem solvers at the International Mathematical Olympiad.Steve Olson followed the six 2001 contestants from the intense tryouts to the Olympiad's nail-biting final rounds to discover not only what drives these extraordinary kids but what makes them both unique and typical.In the process he provides fascinating insights into the science of intelligence and learning and, finally, the nature of genius.Brilliant, but defying all the math-nerd stereotypes, these teens want to excel in whatever piques their curiosity, and they are curious about almost everything - music, games, politics, sports, literature.One team member is ardent about both water polo and creative writing. Another plays four musical instruments.For fun and entertainment during breaks, the Olympians invent games of mind-boggling difficulty.Though driven by the glory of winning this ultimate math contest, they are in many ways not so different from other teenagers, finding pure joy in indulging their personal passions. Beyond the the Olympiad, Olson sheds light on many questions, from why Americans feel so queasy about math, to why so few girls compete in the subject, to whether or not talent is innate.Inside the cavernous gym where the competition takes place, Count Down uncovers a fascinating subculture and its engaging, driven inhabitants. |
| at what age can humans show math abilities: Short Calculus Serge Lang, 2012-12-06 From the reviews This is a reprint of the original edition of Lang’s ‘A First Course in Calculus’, which was first published in 1964....The treatment is ‘as rigorous as any mathematician would wish it’....[The exercises] are refreshingly simply stated, without any extraneous verbiage, and at times quite challenging....There are answers to all the exercises set and some supplementary problems on each topic to tax even the most able. --Mathematical Gazette |
| at what age can humans show math abilities: The Mathematical Brain Across the Lifespan , 2016-06-20 The Mathematical Brain Across the Lifespan is the latest volume in the Progress in Brain Research series that focuses on new trends and developments. This established international series examines major areas of basic and clinical research within the neurosciences, as well as popular and emerging subfields. Provides a comprehensive review of the most recent progress in the mathematical brain across the lifespan Explores new trends and developments in the field Enhances the literature of neuroscience by further expanding the established, ongoing international series Progress in Brain Research |
| at what age can humans show math abilities: Mathematics Education in the Early Years Tamsin Meaney, Ola Helenius, Maria L. Johansson, Troels Lange, Anna Wernberg, 2016-01-22 This book presents chapters based on papers presented at the second POEM conference on early mathematics learning. These chapters broaden the discussion about mathematics education in early childhood, by exploring the debate about construction versus instruction. Specific sections investigate the teaching and learning of mathematical processes and mathematical content, early childhood teacher development, transitions for young children between home and preschool, between home and school and between preschool and school. The chapters use a range of innovative theoretical and methodological approaches which will form an interesting basis for future research in this area. |
| at what age can humans show math abilities: The Functional and Neural Mechanisms of Numerosity Processing: From Perception to Cognition Michele Fornaciai, Joonkoo Park, Roberto Arrighi, 2022-04-29 |
| at what age can humans show math abilities: Cognitive Foundations for Improving Mathematical Learning David C. Geary, Daniel B. Berch, Kathleen Mann Koepke, 2019-01-03 The fifth volume in the Mathematical Cognition and Learning series focuses on informal learning environments and other parental influences on numerical cognitive development and formal instructional interventions for improving mathematics learning and performance. The chapters cover the use of numerical play and games for improving foundational number knowledge as well as school math performance, the link between early math abilities and the approximate number system, and how families can help improve the early development of math skills. The book goes on to examine learning trajectories in early mathematics, the role of mathematical language in acquiring numeracy skills, evidence-based assessments of early math skills, approaches for intensifying early mathematics interventions, the use of analogies in mathematics instruction, schema-based diagrams for teaching ratios and proportions, the role of cognitive processes in treating mathematical learning difficulties, and addresses issues associated with intervention fadeout. - Identifies the relative influence of school and family on math learning - Discusses the efficacy of numerical play for improvement in math - Features learning trajectories in math - Examines the role of math language in numeracy skills - Includes assessments of math skills - Explores the role of cognition in treating math-based learning difficulties |
| at what age can humans show math abilities: Mathematics and Sex Clio Cresswell, 2003-09-01 Dabble in the beauty and wonder of mathematics as it contributes to a variety of fields including literature, biology, economics and of course psychology, where the mathematics of sex plays some unexpected roles. |
| at what age can humans show math abilities: Numeracy Across the Curriculum Merrilyn Goos, Vince Geiger, Shelley Dole, Helen Forgasz, Anne Bennison, 2020-07-16 Being numerate involves more than mastering basic mathematics. Numeracy connects the mathematics learned at school with out-of-school situations that require capabilities such as problem solving, critical judgment, and sense-making related to non-mathematical contexts. This book provides prospective and practising teachers with practical, research-based strategies for embedding numeracy across the primary and secondary school curriculum. Based on the authors' ten-year research program, the text explains what numeracy is and how numeracy has developed as an educational goal. It describes in detail the five dimensions of the authors' model: attention to real-life contexts; application of mathematical knowledge; use of physical, representational and digital tools; the promotion of positive dispositions towards the use of mathematics to solve problems encountered in day-to-day life; and a critical orientation to interpreting mathematical results and making evidence-based judgements. There is guidance on how to embed numeracy across all subjects within the curriculum, how to assess numeracy learning and how to deal with challenges and dilemmas including working with discipline boundaries and developing support resources. Featuring practical examples and case studies throughout, this book will build pre-service teacher confidence, demystify common misconceptions and grounds theory into practice in this vital area of student competency. 'The authors of this text are recognised authorities on numeracy. They have engaged heavily in numeracy research over many years and this text reflects the depth of their understanding and knowledge.' - Geoff Hilton, University of Queensland |
| at what age can humans show math abilities: Building the Foundation: Whole Numbers in the Primary Grades Maria G. Bartolini Bussi, Xu Hua Sun, 2018-03-29 This twenty-third ICMI Study addresses for the first time mathematics teaching and learning in the primary school (and pre-school) setting, while also taking international perspectives, socio-cultural diversity and institutional constraints into account. One of the main challenges of designing the first ICMI primary school study of this kind is the complex nature of mathematics at the early level. Accordingly, a focus area that is central to the discussion was chosen, together with a number of related questions. The broad area of Whole Number Arithmetic (WNA), including operations and relations and arithmetic word problems, forms the core content of all primary mathematics curricula. The study of this core content area is often regarded as foundational for later mathematics learning. However, the principles and main goals of instruction on the foundational concepts and skills in WNA are far from universally agreed upon, and practice varies substantially from country to country. As such, this study presents a meta-level analysis and synthesis of what is currently known about WNA, providing a useful base from which to gauge gaps and shortcomings, as well as an opportunity to learn from the practices of different countries and contexts. |
| at what age can humans show math abilities: Blood Meridian Cormac McCarthy, 2010-08-11 25th ANNIVERSARY EDITION • From the bestselling author of The Passenger and the Pulitzer Prize–winning novel The Road: an epic novel of the violence and depravity that attended America's westward expansion, brilliantly subverting the conventions of the Western novel and the mythology of the Wild West. Based on historical events that took place on the Texas-Mexico border in the 1850s, Blood Meridian traces the fortunes of the Kid, a fourteen-year-old Tennesseean who stumbles into the nightmarish world where Indians are being murdered and the market for their scalps is thriving. Look for Cormac McCarthy's latest bestselling novels, The Passenger and Stella Maris. |
| at what age can humans show math abilities: Why is Math So Hard for Some Children? Daniel B. Berch, Michèle M. M. Mazzocco, 2007 This landmark resource gives educational decision-makers and researchers theoretical and practical insight into mathematical learning difficulties and disabilities, combining diverse perspectives from fields such as special education, developmental |
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