Download or read book Math Misconceptions written by Honi Joyce Bamberger and published by Heinemann Educational Books. This book was released on 2010-01-01 with total page 186 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Mathematical Misconceptions written by Anne D Cockburn and published by SAGE. This book was released on 2008-11-19 with total page 178 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Student Misconceptions and Errors in Physics and Mathematics written by Teresa Neidorf and published by Springer Nature. This book was released on 2019-10-30 with total page 173 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Common Misconceptions in Mathematics written by Bobby Ojose and published by University Press of America. This book was released on 2015-05-01 with total page 151 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Mathematical Misconceptions written by Anne D Cockburn and published by SAGE. This book was released on 2008-11-19 with total page 177 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Mine the Gap for Mathematical Understanding Grades K 2 written by John SanGiovanni and published by Corwin Press. This book was released on 2016-10-31 with total page 385 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Interventions in Mathematics written by Tierney Kennedy and published by . This book was released on 2014-06-15 with total page 88 pages. Available in PDF, EPUB and Kindle. Book excerpt: Fractions is one concept that consistently proves difficult for students to understand. This intervention program has been designed as a targeted approach to catch kids up on multiple years of fraction concepts that ideally should have been developed in primary school, but which I have found are often missing for students in secondary school. Inside you will find diagnostic tasks to uncover misconceptions that are holding kids back from understanding fractions as well as lessons with unique confrontational questions to fix misconceptions for good. These lessons will show you how to lead kids to abandon their wrong ideas and figure out how fractions work for themselves so that they really understand them and don't forget what we are teaching.

Download or read book Mine the Gap for Mathematical Understanding Grades 3 5 written by John SanGiovanni and published by Corwin Press. This book was released on 2016-09-16 with total page 385 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Children s Errors in Mathematics written by Alice Hansen and published by Learning Matters. This book was released on 2014-06-23 with total page 305 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Children S Mathematics 4 15 Learning From Errors And Misconceptions written by Ryan, Julie and published by McGraw-Hill Education (UK). This book was released on 2007-04-01 with total page 262 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Becoming the Math Teacher You Wish You d Had written by Tracy Johnston Zager and published by Taylor & Francis. This book was released on 2023-10-10 with total page 393 pages. Available in PDF, EPUB and Kindle. Book excerpt: Ask mathematicians to describe mathematics and they' ll use words like playful, beautiful, and creative. Pose the same question to students and many will use words like boring, useless, and even humiliating. Becoming the Math Teacher You Wish You' d Had, author Tracy Zager helps teachers close this gap by making math class more like mathematics. Zager has spent years working with highly skilled math teachers in a diverse range of settings and grades and has compiled those' ideas from these vibrant classrooms into' this game-changing book. Inside you' ll find: ' How to Teach Student-Centered Mathematics:' Zager outlines a problem-solving approach to mathematics for elementary and middle school educators looking for new ways to inspire student learning Big Ideas, Practical Application:' This math book contains dozens of practical and accessible teaching techniques that focus on fundamental math concepts, including strategies that simulate connection of big ideas; rich tasks that encourage students to wonder, generalize, hypothesize, and persevere; and routines to teach students how to collaborate Key Topics for Elementary and Middle School Teachers:' Becoming the Math Teacher You Wish You' d Had' offers fresh perspectives on common challenges, from formative assessment to classroom management for elementary and middle school teachers No matter what level of math class you teach, Zager will coach you along chapter by chapter. All teachers can move towards increasingly authentic and delightful mathematics teaching and learning. This important book helps develop instructional techniques that will make the math classes we teach so much better than the math classes we took.

Download or read book Mine the Gap for Mathematical Understanding Grades 6 8 written by John SanGiovanni and published by Corwin Press. This book was released on 2017-09-12 with total page 409 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Issues in Mathematics Teaching written by Peter Gates and published by Routledge. This book was released on 2002-09-11 with total page 335 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the key debates that the mathematics teacher will need to understand, reflect on and engage in as part of their professional development. Issues in Mathematics Teaching is suitable for those at initial training level right through to practising mathematics teachers. Its accessible structure enables the reader to pursue the issues raised as each chapter includes suggestions for further reading and questions for reflection or debate.

Download or read book The Sourcebook for Teaching Science Grades 6 12 written by Norman Herr and published by John Wiley & Sons. This book was released on 2008-08-11 with total page 614 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Sourcebook for Teaching Science is a unique, comprehensive resource designed to give middle and high school science teachers a wealth of information that will enhance any science curriculum. Filled with innovative tools, dynamic activities, and practical lesson plans that are grounded in theory, research, and national standards, the book offers both new and experienced science teachers powerful strategies and original ideas that will enhance the teaching of physics, chemistry, biology, and the earth and space sciences.

Download or read book Strategies for Teaching Fractions written by David B. Spangler and published by Corwin Press. This book was released on 2011-08-17 with total page 249 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Analyzing student work for error patterns (such as on a diagnostic test) and then providing timely, specific, and meaningful intervention will decrease the probability that the errors will be repeated in the future. Taking into account academic research on how students learn, Spangler provides a practical intervention model and specific hands-on materials for teachers to use when working with the many students who struggle with fractions. The step-by-step intervention strategies illustrated in this book will result in improved student performance and improved student dispositions towards mathematics. It will contain the following elements: reproducibles for fully functional diagnostic tests practice pages for exercises keyed to the diagnostic tests and error patterns, and pages to practice alternative algorithms and estimation teacher resources for hands-on activities, game sheets and pieces, and more"--Provided by publisher.

Download or read book Uncovering Student Thinking in Mathematics written by Cheryl M. Rose and published by Corwin Press. This book was released on 2006-12-20 with total page 201 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Uncovering Student Thinking in Mathematics shows us ways to listen and observe children and their mathematical understandings so we can find better ways to help them take their next learning steps. This book is a gift to educators who ′seek to understand before being understood.′" —From the Foreword by Anne Davies "A fresh and unique resource for mathematics teachers who recognize the importance of carefully establishing the starting points of instruction in terms of what students already know. The collection of assessment probes is inventive, engaging for students, and invaluable for teachers." —Richard H. Audet, Associate Professor, Roger Williams University Use formative assessment probes to take the guesswork out of mathematics instruction and improve learning! Students learn at varying rates, and if a misconception in mathematics develops early, it may be carried from year to year and obstruct a student′s progress. To identify fallacies in students′ preconceived ideas, Uncovering Student Thinking in Mathematics offers educators a powerful diagnostic technique in the form of field-tested assessment probes—brief, easily administered activities to determine students′ thinking on core mathematical concepts. Designed to question students′ conceptual knowledge and reveal common understandings and misunderstandings, the probes generate targeted information for modifying mathematics instruction, allowing teachers to build on students′ existing knowledge and individually address their identified difficulties. Linked to National Council of Teachers of Mathematics standards, this invaluable handbook assists educators with: 25 ready-to-use mathematical probes Teacher guides for implementing each probe at any grade level Examples of typical obstacles and faulty thinking demonstrated by students This rich resource combines standards, educational research findings, and practical craft knowledge to help teachers deliver informed instruction that strengthens all students′ learning and achievement in mathematics.

Download or read book Math for the Frightened written by Colin Pask and published by . This book was released on 2011 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Introduces the reader to the main ideas of mathematics, and painlessly demonstrates how they are expressed in symbols while helping to overcome the fear of math and begin to appreciate the science that Einstein called the poetry of logical ideas.