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Mental calculations and estimations are basic, everyday skills that are essential for real-life arithmetic operations and number sense. This book presents a much needed overview and analysis of mental computation and estimation, drawing on contemporary research and empirical studies that were conducted on students, teachers and adults to cover all aspects of this complex field. Mental Computation and Estimation analyses the implications that are involved in the research, teaching and learning of mathematics and delivers effective practices that will enhance everyday learning for students. Focusing on a range of international research and studies from the School of Nature and Life Mathematics in Greece, it answers a number of important questions including: What mental calculations and estimations are, why they are important and what other mathematical concepts and cognitive behaviors are they related to? What strategies are used on mental additions, subtractions, multiplications and divisions and how are multiplication tables learned? What are the new trends in the teaching of mental calculation and estimation? An invaluable resource for all those involved in the practice and research of mathematics education, Mental Computation and Estimation will also be a useful tool for researchers, policy makers and developers of educational programs.
Mental calculations and estimations are basic, everyday skills that are essential for real-life arithmetic operations and number sense. This book presents a much needed overview and analysis of mental computation and estimation, drawing on contemporary research and empirical studies that were conducted on students, teachers and adults to cover all aspects of this complex field. Mental Computation and Estimation analyses the implications that are involved in the research, teaching and learning of mathematics and delivers effective practices that will enhance everyday learning for students. Focusing on a range of international research and studies from the School of Nature and Life Mathematics in Greece, it answers a number of important questions including: What mental calculations and estimations are, why they are important and what other mathematical concepts and cognitive behaviors are they related to? What strategies are used on mental additions, subtractions, multiplications and divisions and how are multiplication tables learned? What are the new trends in the teaching of mental calculation and estimation? An invaluable resource for all those involved in the practice and research of mathematics education, Mental Computation and Estimation will also be a useful tool for researchers, policy makers and developers of educational programs.
Did you know that it's easier to add and subtract from left to right, rather than the other way round? And that you can be taught to square a three-digit number in seconds? In Think Like A Maths Genius, two mathematicians offer tips and tricks for doing tricky maths the easy way. With their help, you can learn how to perform lightning calculations in your head, discover methods of incredible memorisation and other feats of mental agility. Learn maths secrets for the real world, from adding up your shopping and calculating a restaurant tip, to figuring out gambling odds (or how much you've won) and how to solve sudoku faster.
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.
An antidote to mathematical rigor mortis, teaching how to guess answers without needing a proof or an exact calculation. In problem solving, as in street fighting, rules are for fools: do whatever works—don't just stand there! Yet we often fear an unjustified leap even though it may land us on a correct result. Traditional mathematics teaching is largely about solving exactly stated problems exactly, yet life often hands us partly defined problems needing only moderately accurate solutions. This engaging book is an antidote to the rigor mortis brought on by too much mathematical rigor, teaching us how to guess answers without needing a proof or an exact calculation. In Street-Fighting Mathematics, Sanjoy Mahajan builds, sharpens, and demonstrates tools for educated guessing and down-and-dirty, opportunistic problem solving across diverse fields of knowledge—from mathematics to management. Mahajan describes six tools: dimensional analysis, easy cases, lumping, picture proofs, successive approximation, and reasoning by analogy. Illustrating each tool with numerous examples, he carefully separates the tool—the general principle—from the particular application so that the reader can most easily grasp the tool itself to use on problems of particular interest. Street-Fighting Mathematics grew out of a short course taught by the author at MIT for students ranging from first-year undergraduates to graduate students ready for careers in physics, mathematics, management, electrical engineering, computer science, and biology. They benefited from an approach that avoided rigor and taught them how to use mathematics to solve real problems. Street-Fighting Mathematics will appear in print and online under a Creative Commons Noncommercial Share Alike license.
"A multimedia professional learning resource"--Cover.
This volume focuses on two related questions that are central to both the psychology of mathematical thinking and learning and to the improvement of mathematics education: What is the nature of arithmetic expertise? How can instruction best promote it? Contributors from a variety of specialities, including cognitive, developmental, educational, and neurological psychology; mathematics education; and special education offer theoretical perspectives and much needed empirical evidence about these issues. As reported in this volume, both theory and research indicate that the nature of arithmetic expertise and how to best promote it are far more complex than conventional wisdom and many scholars, past and present, have suggested. The results of psychological, educational, and clinical studies using a wide range of arithmetic tasks and populations (including "normally" and atypically developing children, non-injured and brain-injured adults, and savants) all point to the same conclusion: The heart of arithmetic fluency, in general, and the flexible and creative use of strategies, in particular, is what is termed "adaptive expertise" (meaningful or conceptually based knowledge). The construction of adaptive expertise in mathematics is, for the first time, examined across various arithmetic topics and age groups. This book will be an invaluable resource for researchers and graduate students interested in mathematical cognition and learning (including mathematics educators, developmental and educational psychologists, and neuropsychologists), educators (including teachers, curriculum supervisors, and school administrators), and others interested in improving arithmetic instruction (including officials in national and local education departments, the media, and parents).