Mathematics With Understanding

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Understanding In Mathematics

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Author : Anna Sierpinska
language : en
Publisher: Psychology Press
Release Date : 1996

Understanding In Mathematics written by Anna Sierpinska and has been published by Psychology Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996 with Education categories.

The concept of understanding in mathematics with regard to mathematics education is considered in this volume. The main problem for mathematics teachers being how to facilitate their students' understanding of the mathematics being taught. In combining elements of maths, philosophy, logic, linguistics and the psychology of maths education from her own and European research, Dr Sierpinska considers the contributions of the social and cultural contexts to understanding. The outcome is an insight into both mathematics and understanding.

Mathematics Explained For Primary Teachers

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Author : Derek Haylock
language : en
Publisher: SAGE
Release Date : 2018-11-19

Mathematics Explained For Primary Teachers written by Derek Haylock and has been published by SAGE this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-11-19 with Education categories.

‘This user-friendly interactive book makes concepts simple and gives you the confidence and knowledge to learn and teach mathematics to primary children. You can conveniently access easily digestible content to build and test your knowledge. It’s a must have on any teachers book shelf!’ SAGE Primary Mathematics Student Panel LESSON PLANS AND WORKSHEETS: Save time with ideas and resources for planning your lessons. PROBLEM SOLVED! VIDEOS: Visualise how to solve a question by watching a quick animated demonstration. LEARNING AND TEACHING POINTS: Feel confident in the classroom with these key points to remember when planning and teaching. QUESTIONS AND QUIZZES: Achieve a firm grasp of concepts and a clear understanding with self-assessment questions and quizzes. FREE INTERACTIVE EBOOK: Study anywhere with your portable and convenient eBook! USE ME WITH... Student Workbook Mathematics Explained for Primary Teachers 6th Edition 9781526424686

Teaching For Mathematical Understanding

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Author : Tony Cotton
language : en
Publisher: Routledge
Release Date : 2016-06-17

Teaching For Mathematical Understanding written by Tony Cotton and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-06-17 with Education categories.

Teaching for Mathematical Understanding develops the subject knowledge support and practical ideas from Tony Cotton’s Understanding and Teaching Primary Mathematics into resources for full lessons. With an emphasis on developing outstanding lessons using a problem-solving approach, this highly practical guide is packed with activities that all trainee and practising teachers can use in the primary classroom. Covering each area of mathematics, every activity offers helpful step-by-step guidance, including teaching and learning objectives; resources; lesson outlines; ideas for differentiation; assessment for learning and key probing questions. Also featured in this text are call-outs to the information contained in the book’s companion website, a shared site with a range of relevant resources to support and consolidate your learning. Teaching for Mathematical Understanding is an essential text for all trainee and practising teachers looking for inspiration and guidance towards outstanding mathematics teaching. Companion website features include: Video clips in which primary school teachers demonstrate concepts covered in the book through teaching to a real class PowerPoint presentations which provide support for those using the book as part of a teacher training course updated weblinks to external sites with useful teaching information and resources.

Learning Mathematics

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Author : Paul Cobb
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09

Learning Mathematics written by Paul Cobb and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-09 with Education categories.

This volume emphasizes students' inferred mathematical experiences as the starting point in the theory-building process. The book addresses conceptual constructions, including multiplicative notions, fractions, algebra, and the fundamental theorem of calculus, and theoretical constructs such as the crucial role of language and symbols, and the importance of dynamic imagery.

Primary Mathematics Knowledge And Understanding

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Author : Claire Mooney
language : en
Publisher: Learning Matters
Release Date : 2018-02-24

Primary Mathematics Knowledge And Understanding written by Claire Mooney and has been published by Learning Matters this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-02-24 with Education categories.

Secure subject knowledge and understanding is the foundation of confident, creative and effective teaching. To help your students master this, the 8th edition of this established text now comes with a range of online resources: Interactive Maths subject knowledge audit: to assess your students′ overall performance and ensure they have an accurate picture of their ability. Reflective self-assessment questions: to help consolidate students’ understanding of each chapter topic and monitor their learning as they work through the book. Glossary: building students′ knowledge of tricky terminology. Covering the whole primary curriculum, this edition also includes updated interactive activities throughout the book to engage students in their learning and enable discussion. Using this book in conjunction with the free online resources really makes this the complete package for developing Mathematics subject knowledge.

Basic Insights In Vector Calculus With A Supplement On Mathematical Understanding

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Author : Terrance J Quinn
language : en
Publisher: World Scientific
Release Date : 2020-07-24

Basic Insights In Vector Calculus With A Supplement On Mathematical Understanding written by Terrance J Quinn and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-07-24 with Mathematics categories.

Basic Insights in Vector Calculus provides an introduction to three famous theorems of vector calculus, Green's theorem, Stokes' theorem and the divergence theorem (also known as Gauss's theorem). Material is presented so that results emerge in a natural way. As in classical physics, we begin with descriptions of flows.The book will be helpful for undergraduates in Science, Technology, Engineering and Mathematics, in programs that require vector calculus. At the same time, it also provides some of the mathematical background essential for more advanced contexts which include, for instance, the physics and engineering of continuous media and fields, axiomatically rigorous vector analysis, and the mathematical theory of differential forms.There is a Supplement on mathematical understanding. The approach invites one to advert to one's own experience in mathematics and, that way, identify elements of understanding that emerge in all levels of learning and teaching.Prerequisites are competence in single-variable calculus. Some familiarity with partial derivatives and the multi-variable chain rule would be helpful. But for the convenience of the reader we review essentials of single- and multi-variable calculus needed for the three main theorems of vector calculus.Carefully developed Problems and Exercises are included, for many of which guidance or hints are provided.

Mine The Gap For Mathematical Understanding Grades 3 5

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Author : John SanGiovanni
language : en
Publisher: Corwin Press
Release Date : 2016-09-16

Mine The Gap For Mathematical Understanding Grades 3 5 written by John SanGiovanni and has been published by Corwin Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-09-16 with Education categories.

Being an effective math educator is one part based on the quality of the tasks we give, one part how we diagnose what we see, and one part what we do with what we find. Yet with so many students and big concepts to cover, it can be hard to slow down enough to look for those moments when students’ responses tell us what we need to know about next best steps. In this remarkable book, John SanGiovanni helps us value our students’ misconceptions and incomplete understandings as much as their correct ones—because it’s the gap in their understanding today that holds the secrets to planning tomorrow’s best teaching. SanGiovanni lays out 180 high-quality tasks aligned to the standards and big ideas of Grades 3-5 mathematics, including addition and subtraction of multi-digit whole numbers, multiplication and division of single and multi-digit whole numbers, foundational fraction concepts, foundational decimal concepts, and operations with fractions and decimals. The tasks are all downloadable so you can use or modify them for instruction and assessment. Each big idea offers a starting task followed by: what makes it a high-quality task what you might anticipate before students work with the task 4 student examples of the completed task showcasing a distinct "gap" commentary on what precisely counts for mathematical understanding and the next instructional steps commentary on the misconception or incomplete understanding so you learn why the student veered off course three additional tasks aligned to the mathematics topic and ideas about what students might do with these additional tasks. It’s time to break our habit of rushing into re-teaching for correctness and instead get curious about the space between right and wrong answers. Mine the Gap for Mathematical Understanding is a book you will return to again and again to get better at selecting tasks that will uncover students’ reasoning—better at discerning the quality and clarity of students’ understanding—and better at planning teaching based on the gaps you see.

Mine The Gap For Mathematical Understanding Grades 6 8

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Author : John SanGiovanni
language : en
Publisher: Corwin Press
Release Date : 2017-09-12

Mine The Gap For Mathematical Understanding Grades 6 8 written by John SanGiovanni and has been published by Corwin Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-09-12 with Education categories.

Being an effective math educator is one part based on the quality of the tasks we give, one part how we diagnose what we see, and one part what we do with what we find. Yet with so many students and big concepts to cover, it can be hard to slow down enough to look for those moments when students’ responses tell us what we need to know about next best steps. In this remarkable book, John SanGiovanni and Jennifer Rose Novak help us value our students’ misconceptions and incomplete understandings as much as their correct ones—because it’s the gap in their understanding today that holds the secrets to planning tomorrow’s best teaching. The authors lay out 180 high-quality tasks aligned to the standards and big ideas of Grades 6–8 mathematics, including number systems, integers, ratio and proportion, equations and expressions, geometry, and statistics and probability. The tasks are all downloadable so you can use or modify them for instruction and assessment. Each big idea offers a starting task followed by: what makes it a high-quality task what you might anticipate before students work with the task four student examples of the completed task showcasing a distinct "gap" commentary on what precisely counts for mathematical understanding and the next instructional steps commentary on the misconception or incomplete understanding so you learn why the student veered off course three additional tasks aligned to the mathematics topic and ideas about what students might do with these additional tasks It’s time to break our habit of rushing into re-teaching for correctness and instead get curious about the space between right and wrong answers. Mine the Gap for Mathematical Understanding is a book you will return to again and again to get better at selecting tasks that will uncover students’ reasoning, better at discerning the quality and clarity of students’ understanding, and better at planning teaching based on the gaps you see.

Mathematics Explained For Healthcare Practitioners

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Author : Derek Haylock
language : en
Publisher: SAGE
Release Date : 2013-01-11

Mathematics Explained For Healthcare Practitioners written by Derek Haylock and has been published by SAGE this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-01-11 with Medical categories.

If you find mathematics a struggle, or if mathematics makes you panic - whether you′re a student preparing for a calculations test, or a qualified healthcare professional - this is the book for you. Its focus is first and foremost on helping you develop a proper and lasting understanding of mathematical concepts and processes in a healthcare context, with an emphasis on developing mental strategies to reinforce your feeling for number and numerical relationships. Clear, accessible chapters take you step-by-step through specific sets of objectives, and once you feel you have fully mastered a particular mathematical process, you′re encouraged to practise your skills through a range of practical examples. Each chapter also contains a ′Spot the Errors′ feature designed to reflect the busy, pressurised healthcare environment. Written by Derek Haylock, a best-selling mathematics educator, and Paul Warburton, co-ordinator of the Non-Medical Prescribing programme at Edge Hill University, the book is directly linked to the NMC′s competencies and will give you the confidence to perform the safe, error-free calculations required of all healthcare professionals.

Psychology And Mathematics Education

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Author : Gila Hanna
language : en
Publisher: Frontiers Media SA
Release Date : 2023-09-05

Psychology And Mathematics Education written by Gila Hanna and has been published by Frontiers Media SA this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-09-05 with Science categories.

Modern Mathematics is constructed rigorously through proofs, based on truths, which are either axioms or previously proven theorems. Thus, it is par excellence a model of rational inquiry. Links between Cognitive Psychology and Mathematics Education have been particularly strong during the last decades. Indeed, the Enlightenment view of the rational human mind that reasons, makes decisions and solves problems based on logic and probabilities, was shaken during the second half of the twentieth century. Cognitive psychologists discovered that humans' thoughts and actions often deviate from rules imposed by strict normative theories of inference. Yet, these deviations should not be called "errors": as Cognitive Psychologists have demonstrated, these deviations may be either valid heuristics that succeed in the environments in which humans have evolved, or biases that are caused by a lack of adaptation to abstract information formats. Humans, as the cognitive psychologist and economist Herbert Simon claimed, do not usually optimize, but rather satisfice, even when solving problem. This Research Topic aims at demonstrating that these insights have had a decisive impact on Mathematics Education. We want to stress that we are concerned with the view of bounded rationality that is different from the one espoused by the heuristics-and-biases program. In Simon’s bounded rationality and its direct descendant ecological rationality, rationality is understood in terms of cognitive success in the world (correspondence) rather than in terms of conformity to content-free norms of coherence (e.g., transitivity).