Mathematical Misconceptions

Author : Anne D Cockburn,Graham Littler
Publisher : SAGE
Page : 176 pages
File Size : 43,8 Mb
Release : 2008-11-19
Category : Education
ISBN : 9781446243992

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Mathematical Misconceptions by Anne D Cockburn,Graham Littler Pdf

How do children relate to numbers and mathematics? How can they be helped to understand and make sense of them? People are rarely ambivalent towards mathematics, having either a love or hate relationship with the subject, and our approach to it is influenced by a variety of factors. How we are taught mathematics as children plays a big role in our feelings towards it. Numbers play a large part in our lives, and it is therefore beneficial to inspire a positive attitude towards them at a young age. With contributors comprised of teachers, teacher educators, mathematicians and psychologists, Mathematical Misconceptions brings together information about pupils' work from four different countries, and looks at how children, from the ages of 3 - 11, think about numbers and use them. It explores the reasons for their successes, misunderstandings and misconceptions, while also broadening the reader's own mathematical knowledge. Chapters explore: - the seemingly paradoxical number zero - the concept of equality - children's perceptions and misconceptions of adding, subtracting, multiplying and dividing - the learning process - the ways in which children acquire number concepts. This unique book will transform the way in which primary school teachers think about mathematics. Fascinating reading for anyone working with children of this age, it will be of particular interest to teachers, trainee teachers and teaching assistants. It will show them how to engage children in the mysteries and delights of numbers.

Author : Ryan, Julie,Williams, Julian
Publisher : McGraw-Hill Education (UK)
Page : 262 pages
File Size : 49,9 Mb
Release : 2007-04-01
Category : Education
ISBN : 9780335220427

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Children'S Mathematics 4-15: Learning From Errors And Misconceptions by Ryan, Julie,Williams, Julian Pdf

This work uses data from the authors' own research on children's performance, errors and misconceptions across the mathematics curriculum. It develops concepts for teachers to use in organising their understanding and knowledge of children's mathematics, and concludes with theoretical accounts of learning and teaching.

Author : Honi Joyce Bamberger,Christine Oberdorf,Karren Schultz-Ferrell
Publisher : Heinemann Educational Books
Page : 186 pages
File Size : 52,8 Mb
Release : 2010-01-01
Category : Education
ISBN : 0325026130

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Math Misconceptions by Honi Joyce Bamberger,Christine Oberdorf,Karren Schultz-Ferrell Pdf

Children enter school filled with all kinds of ideas about numbers, shapes, measuring tools, time, and money--ideas formed from the expressions they hear ... the things they see on television ... the computer screen ... in children's books ... all around them. It's no wonder some children develop very interesting and perhaps incorrect ideas about mathematical concepts. "How can we connect the informal knowledge that students bring to our classrooms with the mathematics program adopted by our school system? Just as important, how do we ensure that the mathematics we are introducing and reinforcing is accurate and will not need to be re-taught in later years?" Math Misconceptions answers these questions by: identifying the most common errors relative to the five NCTM content strands (number and operations, algebra, geometry, measurement, and data analysis and probability); investigating the source of these misunderstandings; proposing ways to avoid as well as "undo" misconceptions. Using classroom vignettes that highlight common misconceptions in each content area, followed by applicable research about the root causes of the confusion, the authors offer numerous instructional ideas and interventions designed to prevent or correct the misconception. --Publisher's description.

Author : Teresa Neidorf,Alka Arora,Ebru Erberber,Yemurai Tsokodayi,Thanh Mai
Publisher : Springer Nature
Page : 173 pages
File Size : 45,6 Mb
Release : 2019-10-30
Category : Education
ISBN : 9783030301880

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Student Misconceptions and Errors in Physics and Mathematics by Teresa Neidorf,Alka Arora,Ebru Erberber,Yemurai Tsokodayi,Thanh Mai Pdf

This open access report explores the nature and extent of students’ misconceptions and misunderstandings related to core concepts in physics and mathematics and physics across grades four, eight and 12. Twenty years of data from the IEA’s Trends in International Mathematics and Science Study (TIMSS) and TIMSS Advanced assessments are analyzed, specifically for five countries (Italy, Norway, Russian Federation, Slovenia, and the United States) who participated in all or almost all TIMSS and TIMSS Advanced assessments between 1995 and 2015. The report focuses on students’ understandings related to gravitational force in physics and linear equations in mathematics. It identifies some specific misconceptions, errors, and misunderstandings demonstrated by the TIMSS Advanced grade 12 students for these core concepts, and shows how these can be traced back to poor foundational development of these concepts in earlier grades. Patterns in misconceptions and misunderstandings are reported by grade, country, and gender. In addition, specific misconceptions and misunderstandings are tracked over time, using trend items administered in multiple assessment cycles. The study and associated methodology may enable education systems to help identify specific needs in the curriculum, improve inform instruction across grades and also raise possibilities for future TIMSS assessment design and reporting that may provide more diagnostic outcomes.

Author : Anne D Cockburn,Graham Littler
Publisher : SAGE
Page : 177 pages
File Size : 46,8 Mb
Release : 2008-11-19
Category : Education
ISBN : 9780857029478

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Mathematical Misconceptions by Anne D Cockburn,Graham Littler Pdf

How do children relate to numbers and mathematics? How can they be helped to understand and make sense of them? People are rarely ambivalent towards mathematics, having either a love or hate relationship with the subject, and our approach to it is influenced by a variety of factors. How we are taught mathematics as children plays a big role in our feelings towards it. Numbers play a large part in our lives, and it is therefore beneficial to inspire a positive attitude towards them at a young age. With contributors comprised of teachers, teacher educators, mathematicians and psychologists, Mathematical Misconceptions brings together information about pupils′ work from four different countries, and looks at how children, from the ages of 3 - 11, think about numbers and use them. It explores the reasons for their successes, misunderstandings and misconceptions, while also broadening the reader′s own mathematical knowledge. Chapters explore: - the seemingly paradoxical number zero - the concept of equality - children′s perceptions and misconceptions of adding, subtracting, multiplying and dividing - the learning process - the ways in which children acquire number concepts. This unique book will transform the way in which primary school teachers think about mathematics. Fascinating reading for anyone working with children of this age, it will be of particular interest to teachers, trainee teachers and teaching assistants. It will show them how to engage children in the mysteries and delights of numbers.

Author : Bobby Ojose
Publisher : University Press of America
Page : 151 pages
File Size : 46,7 Mb
Release : 2015-05-01
Category : Mathematics
ISBN : 9780761858867

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Common Misconceptions in Mathematics by Bobby Ojose Pdf

This book should be a handy tool for teachers of mathematics as they develop plans to confront the problem of misconceptions, which are common with students that often have their own notion of certain mathematical concepts, right or not. The onus is on the teacher to detect those misconceptions and help students remedy them. This book is written for that purpose. Teachers could emulate the presented strategies that the book has elucidated. Teachers may also devise their own strategies based on the source of the misconception as presented in the book. The research segment of each identified misconception will be helpful if teachers want to apprise themselves with what the literature says about the concept. In general, the book is meant for teachers who want to help students engage in mathematics that emphasize conceptual understanding.

Author : Kieran Mackle
Publisher : Routledge
Page : 249 pages
File Size : 48,7 Mb
Release : 2016-10-04
Category : Education
ISBN : 9781317443353

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Tackling Misconceptions in Primary Mathematics by Kieran Mackle Pdf

Did you know that a circle has more than one side? Are you aware of the difference between 1:2 and 1⁄2? Could you spot when a 2D shape is actually 3D? Tackling Misconceptions in Primary Mathematics is a practical guide based on the principles that sound subject knowledge is key to fostering understanding, and addressing misconceptions is central to pupil progress. With an emphasis on preventing as well as unpicking misconceptions in the classroom, it offers trainee and practising teachers clear explanations, practical strategies, and examples of the classroom language and dialogue that will help pupils successfully navigate tricky topics. The book demonstrates the importance of preventing misconceptions through what is said, done and presented to children, giving a variety of examples of common misconceptions and exploring how they can be addressed in a classroom environment. Proper intervention at the point of misconception is regarded as a key skill for any outstanding classroom practitioner and the author stresses the value in understanding how the pupil got there and explaining that it’s okay to make mistakes. Misconceptions are only one step away from correctly formed concepts if harnessed with care and skill. This comprehensive text is designed to be read as either a short course introduction, or dipped into as a guide to assist teaching. It is essential reading for trainee primary school teachers on all routes to QTS, as well as mathematics subject leaders and practising teachers looking to inspire the next generation of confident and inquisitive mathematicians.

Author : Mike Spooner
Publisher : Routledge
Page : 61 pages
File Size : 47,5 Mb
Release : 2012-07-26
Category : Education
ISBN : 9781136611292

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Errors and Misconceptions in Maths at Key Stage 2 by Mike Spooner Pdf

The activities in this book are designed both to help children to learn and to understand math concepts, and also to prepare them for taking SATS papers at KS2. There is plenty of research evidence to suggest that children are helped in their understanding of math problems if teachers focus on common misconceptions, and if children are given opportunities for discussion and explanation of their own understanding. Children can also feel stigmatized by being made to focus on their own errors. Mike Spooner has developed activities that present already completed work which children then assess, correct and discuss - in this way they can analyze mistakes without damage to their own self-esteem. The activities are presented in the same format as the SATS papers, to give children practice in coping with that format. The book also contains writing frames that children can use to structure their discussions of math problems.

Author : Doreen Drews,John Dudgeon,Alice Hansen,Fiona Lawton,Liz Surtees
Publisher : SAGE
Page : 181 pages
File Size : 45,6 Mb
Release : 2005-07-07
Category : Education
ISBN : 9781844454303

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Children′s Errors in Mathematics by Doreen Drews,John Dudgeon,Alice Hansen,Fiona Lawton,Liz Surtees Pdf

This practical guide to children′s common errors and misconceptions in mathematics is ideal for anyone training to teach 4-11 year old children and keen to gain a deeper understanding of the difficulties children encounter during their mathematical development. The book is structured around National Curriculum Attainment Targets, and deals with individual misconceptions, in each case providing a description of the error, and an explanation of why the error happens.

Author : Alice Hansen,Doreen Drews,John Dudgeon,Fiona Lawton,Liz Surtees
Publisher : Learning Matters
Page : 321 pages
File Size : 54,7 Mb
Release : 2014-06-23
Category : Education
ISBN : 9781473905535

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Children's Errors in Mathematics by Alice Hansen,Doreen Drews,John Dudgeon,Fiona Lawton,Liz Surtees Pdf

This practical guide to children’s common errors and misconceptions in mathematics is a popular planning tool for primary trainees. It supports a deeper understanding of the difficulties encountered in mathematical development. This third edition has been updated to link to the new National Curriculum. New for this edition is a chapter on addressing errors misconceptions which explores how errors can best be identified and countered. The text examines misconceptions individually and in each case provides a description of the error alongside an explanation of why the error happens. The text also considers the role of the teacher in understanding and addressing children’s common mathematical misconceptions.

Author : Peter Gates
Publisher : Psychology Press
Page : 344 pages
File Size : 47,7 Mb
Release : 2001
Category : Education
ISBN : 0415238641

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Issues in Mathematics Teaching by Peter Gates Pdf

Containing a range of issues relating to the teaching of mathematics, this text builds on knowledge already gained on ITT and PGCE courses and encourages teachers to consider and reflect on the issues that affect their teaching skills.

Author : Anthony Barcellos
Publisher : Unknown
Page : 314 pages
File Size : 46,5 Mb
Release : 2005
Category : Electronic
ISBN : UCAL:X70635

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Mathematical Misconceptions of College-age Algebra Students by Anthony Barcellos Pdf

Author : Andreas M. Hinz,Sandi Klavžar,Uroš Milutinović,Ciril Petr
Publisher : Springer Science & Business Media
Page : 340 pages
File Size : 51,7 Mb
Release : 2013-01-31
Category : Mathematics
ISBN : 9783034802376

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The Tower of Hanoi – Myths and Maths by Andreas M. Hinz,Sandi Klavžar,Uroš Milutinović,Ciril Petr Pdf

This is the first comprehensive monograph on the mathematical theory of the solitaire game “The Tower of Hanoi” which was invented in the 19th century by the French number theorist Édouard Lucas. The book comprises a survey of the historical development from the game’s predecessors up to recent research in mathematics and applications in computer science and psychology. Apart from long-standing myths it contains a thorough, largely self-contained presentation of the essential mathematical facts with complete proofs, including also unpublished material. The main objects of research today are the so-called Hanoi graphs and the related Sierpiński graphs. Acknowledging the great popularity of the topic in computer science, algorithms and their correctness proofs form an essential part of the book. In view of the most important practical applications of the Tower of Hanoi and its variants, namely in physics, network theory, and cognitive (neuro)psychology, other related structures and puzzles like, e.g., the “Tower of London”, are addressed. Numerous captivating integer sequences arise along the way, but also many open questions impose themselves. Central among these is the famed Frame-Stewart conjecture. Despite many attempts to decide it and large-scale numerical experiments supporting its truth, it remains unsettled after more than 70 years and thus demonstrates the timeliness of the topic. Enriched with elaborate illustrations, connections to other puzzles and challenges for the reader in the form of (solved) exercises as well as problems for further exploration, this book is enjoyable reading for students, educators, game enthusiasts and researchers alike.

Author : Diane Pedrotty Bryant
Publisher : Guilford Publications
Page : 226 pages
File Size : 53,9 Mb
Release : 2021-07-05
Category : Education
ISBN : 9781462546190

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Intensifying Mathematics Interventions for Struggling Students by Diane Pedrotty Bryant Pdf

"This book, Intensive Mathematics Interventions, provides a thorough background knowledge about mathematics difficulties across the grade span. Even more valuable to educators-this book provides user friendly guidance on how to address all of the elements of mathematics difficulties from preschool to secondary grades. Each topic provides clear guidance to support decision making about intensive instruction including examples, ideas, practices, and suggestions. You will learn about the characteristics of students with math difficulties, how to use date to progress monitor them, how to intensify interventions, specific evidence-based practices for addressing early numeracy, time and money, whole numbers, rational numbers, word problem solving strategies, algebra and even technology"--

Author : John SanGiovanni
Publisher : Corwin Press
Page : 384 pages
File Size : 49,8 Mb
Release : 2016-11-15
Category : Education
ISBN : 9781506382296

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Mine the Gap for Mathematical Understanding, Grades K-2 by John SanGiovanni Pdf

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 young learners’ 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 160 high-quality tasks aligned to the standards and big ideas of grades K-2 mathematics, including counting and representing numbers, number relationships and comparison, addition and subtraction within 100 and 1000, money and time, and multiplication and division. 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 taskwhat 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.