Children S Quantitative Sense Of Fractions
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Children S Quantitative Sense Of Fractions
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Author : Peter John Gould
language : en
Publisher:
Release Date : 2008
Children S Quantitative Sense Of Fractions written by Peter John Gould and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Fractions categories.
Learning the meaning of common fractions and how to operate with them is a traditionally difficult aspect of learning mathematics. The symbol system used to represent fractions, one whole number written above another whole number, is not transparent to the meaning of fractions. This difficulty of interpreting fractions contributes to traditional practice in teaching fractions emphasising the syntax of fractions over their semantics. Without a sense of the size of fractions students must rely solely on learning the fraction syntax, as there is no feasible way of checking the reasonableness of an answer. -- To investigate how well students had developed a sense of the size of fractions, a large cross-section of students from Years 4-8 (over 300 students in each grade) completed 37 tasks designed to draw upon a quantitative sense of fractions. The students' answers provided data for both a conceptual analysis and a related Rasch item analysis. The conceptual analysis found that although some studnets have a strong sense of the size of fractions, many students have developed pseudo fraction concepts. Rather than seeing fractions as relational numbers, more than 10% of the students responded as if fractions corresponded to a count of the number of parts in fraction representation. Questions involving the fraction notation increased the variety of incorrect interpretations of fractions. The Rasch analysis confirmed that the items related to the same trait and provided an ordering of the difficulty of the questions. The Rasch item map provided backing for a description of how students develop a sense of the size of fractions. -- The current methods of developing students' understanding of fractions have resulted in a large number of pseudo concepts being formed. The basis of making meaning from models used to introduce fractions, needs to be the focus of teaching fractions. As well as using counter-example to limit the number of unintended features of models students associate with fractions, comparison of length rather than area should be used to introduce fractions.
Children S Fractional Knowledge
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Author : Leslie P. Steffe
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-12-02
Children S Fractional Knowledge written by Leslie P. Steffe 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 2009-12-02 with Education categories.
Children’s Fractional Knowledge elegantly tracks the construction of knowledge, both by children learning new methods of reasoning and by the researchers studying their methods. The book challenges the widely held belief that children’s whole number knowledge is a distraction from their learning of fractions by positing that their fractional learning involves reorganizing—not simply using or building upon—their whole number knowledge. This hypothesis is explained in detail using examples of actual grade-schoolers approaching problems in fractions including the schemes they construct to relate parts to a whole, to produce a fraction as a multiple of a unit part, to transform a fraction into a commensurate fraction, or to combine two fractions multiplicatively or additively. These case studies provide a singular journey into children’s mathematics experience, which often varies greatly from that of adults. Moreover, the authors’ descriptive terms reflect children’s quantitative operations, as opposed to adult mathematical phrases rooted in concepts that do not reflect—and which in the classroom may even suppress—youngsters’ learning experiences. Highlights of the coverage: Toward a formulation of a mathematics of living instead of being Operations that produce numerical counting schemes Case studies: children’s part-whole, partitive, iterative, and other fraction schemes Using the generalized number sequence to produce fraction schemes Redefining school mathematics This fresh perspective is of immediate importance to researchers in mathematics education. With the up-close lens onto mathematical development found in Children’s Fractional Knowledge, readers can work toward creating more effective methods for improving young learners’ quantitative reasoning skills.
Extending Children S Mathematics
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Author : Susan B. Empson
language : en
Publisher: Heinemann Educational Books
Release Date : 2011
Extending Children S Mathematics written by Susan B. Empson and has been published by Heinemann Educational Books this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011 with Education categories.
"With the collaboration of a number of dedicated teachers and their students, Susan Empson and Linda Levi have produced a volume that is faithful to the basic principles of CGI while at the same time covering new ground with insight and innovation." -Thomas P. Carpenter This highly anticipated follow-up volume to the landmark Children's Mathematics: Cognitively Guided Instruction addresses the urgent need to help teachers understand and teach fraction concepts. Fractions remain one of the key stumbling blocks in math education, and here Empson and Levi lay a foundation for understanding fractions and decimals in ways that build conceptual learning. They show how the same kinds of intuitive knowledge and sense making that provides the basis for children's learning of whole number arithmetic can be extended to fractions and decimals. Just as they did in Children's Mathematics and Thinking Mathematically, Empson and Levi provide important insights into children's thinking and alternative approaches to solving problems. Three themes appear throughout the book: building meaning for fractions and decimals through discussing and solving word problems the progression of children's strategies for solving fraction word problems and equations from direct modeling through relational thinking designing instruction that capitalizes on students' relational thinking strategies to integrate algebra into teaching and learning fractions. With illuminating examples of student work, classroom vignettes, "Teacher Commentaries" from the field, sample problems and instructional guides provided in each chapter, you'll have all the tools you need to teach fractions and decimals with understanding and confidence.
Factors Contributing To Children S Understanding Of Fractions
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Author : Rossana Barros Baertl
language : en
Publisher:
Release Date : 2020
Factors Contributing To Children S Understanding Of Fractions written by Rossana Barros Baertl and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020 with categories.
Children S Reasoning While Building Fraction Ideas
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Author : Carolyn A. Maher
language : en
Publisher: Springer
Release Date : 2017-06-10
Children S Reasoning While Building Fraction Ideas written by Carolyn A. Maher and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-06-10 with Education categories.
This book may be used for research, graduate and undergraduate teacher education, and teacher development. It presents an integrated set of studies of a heterogeneously grouped class of twenty-one nine-year olds, engaged in exploring fraction ideas prior to classroom instruction under conditions that supported investigation, collaboration and argumentation. It demonstrates with text and video narrative how young children can reason about mathematics in surprisingly sophisticated ways when provided the opportunity to do so in the proper classroom environment. In this volume, fourth grade students’ reasoning about fraction concepts is described through careful analysis and accompanying video excerpts showcasing the variety and originality of their thinking. These children will serve as an inspiration for educators to encourage the development of reasoning and argumentation in their students as part of a mathematics curriculum designed to produce critical thinkers.
Providing A Foundation For Teaching Mathematics In The Middle Grades
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Author : Judith Sowder
language : en
Publisher: State University of New York Press
Release Date : 1995-08-03
Providing A Foundation For Teaching Mathematics In The Middle Grades written by Judith Sowder and has been published by State University of New York Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995-08-03 with Education categories.
This book is written primarily for middle grade teachers who are discovering that they now want to teach in ways that create positive mathematical learning environments and instigate rich classroom discourse. Many of these teachers are finding that their mathematical preparation did not address the complexities underlying the mathematics they now want to teach. In Part One, the authors provide a foundation for the mathematics of these grades, particularly the mathematics that grows out of concepts of number, quantity, and arithmetic operations. In Part Two, through three case studies, the authors demonstrate to teachers how a deeper understanding of the mathematics they teach can enhance classroom instruction. The book interweaves research and classroom practice. Mathematics teacher educators, researchers, curriculum developers, textbook authors, and supervisors of mathematics programs will find this book to be useful. Teachers, both prospective and practicing, will benefit most from this book when the chapters are used as catalysts for discussion in classes or professional development programs.
Using Research To Inform Practice
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Author : Sylvia Bulgar
language : en
Publisher:
Release Date : 2003
Using Research To Inform Practice written by Sylvia Bulgar and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with categories.
The purpose of this paper is to share the strategies that children invented to solve problems involving division of fractions in the absence of algorithmic instruction. The data come from two sources, the first being a teaching experiment and the second being the regular classroom practice of this teacher/researcher. It was found that when the conditions of the teaching experiment were replicated, the three methods that students constructed to solve the identical problems involving division of fractions were the same as those seen in the original group. The three methods involved reasoning concerning natural numbers, measurement and fraction knowledge, all of which relate to counting. (Contains 5 footnotes.) [For complete proceedings, see ED500859.].
Fostering Children S Mathematical Power
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Author : Arthur J. Baroody
language : en
Publisher: Routledge
Release Date : 1998-09-01
Fostering Children S Mathematical Power written by Arthur J. Baroody and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998-09-01 with Education categories.
Teachers have the responsibility of helping all of their students construct the disposition and knowledge needed to live successfully in a complex and rapidly changing world. To meet the challenges of the 21st century, students will especially need mathematical power: a positive disposition toward mathematics (curiosity and self confidence), facility with the processes of mathematical inquiry (problem solving, reasoning and communicating), and well connected mathematical knowledge (an understanding of mathematical concepts, procedures and formulas). This guide seeks to help teachers achieve the capability to foster children's mathematical power - the ability to excite them about mathematics, help them see that it makes sense, and enable them to harness its might for solving everyday and extraordinary problems. The investigative approach attempts to foster mathematical power by making mathematics instruction process-based, understandable or relevant to the everyday life of students. Past efforts to reform mathematics instruction have focused on only one or two of these aims, whereas the investigative approach accomplishes all three. By teaching content in a purposeful context, an inquiry-based fashion, and a meaningful manner, this approach promotes chilren's mathematical learning in an interesting, thought-provoking and comprehensible way. This teaching guide is designed to help teachers appreciate the need for the investigative approach and to provide practical advice on how to make this approach happen in the classroom. It not only dispenses information, but also serves as a catalyst for exploring, conjecturing about, discussing and contemplating the teaching and learning of mathematics.
Developing Number Knowledge
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Author : Robert J Wright
language : en
Publisher: SAGE
Release Date : 2011-11-04
Developing Number Knowledge written by Robert J Wright and has been published by SAGE this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-11-04 with Education categories.
Following the great success of the earlier books, this fourth book in the Mathematics Recovery series equips teachers with detailed pedagogical knowledge and resources for teaching number to 7 to 11-year olds. Drawing on extensive programs of research, curriculum development, and teacher development, the book offers a coherent, up-to-date approach emphasising computational fluency and the progressive development of students′ mathematical sophistication. The book is organized in key domains of number instruction, including structuring numbers 1 to 20, knowledge of number words and numerals, conceptual place value, mental computation, written computation methods, fractions, and early algebraic reasoning. Features include: fine-grained progressions of instruction within each domain; detailed descriptions of students′ strategies and difficulties; assessment tasks with notes on students′ responses; classroom-ready instructional activities; This book is designed for classroom and intervention teachers, special education teachers and classroom assistants. The book is an invaluable resource for mathematics advisors and coaches, learning support staff, numeracy consultants, curriculum developers, teacher educators and researchers.
Making Sense Of Fractions
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Author : Randy Palisoc
language : en
Publisher: CreateSpace
Release Date : 2014-08-06
Making Sense Of Fractions written by Randy Palisoc and has been published by CreateSpace this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-08-06 with categories.
Frustrated with fractions? They're easier than you think. Fractions have been given a bad rap. Understanding fractions is essential in math, yet too many students struggle to make sense of them. Even if students have performed well in math early in elementary school, they seem to hit a brick wall when it comes the "abstract" concepts involved with fractions. This is how Making Sense of Fractions helps. This unit challenges the long-held assumption that fractions are difficult because they're abstract. Fractions are actually more concrete and more logical than most people realize. Making Sense of Fractions helps students make these realizations, and it has a different philosophy from past approaches. This unit explains fractions in a more concrete way that makes logical sense to students (and to adults), making fractions easier to learn than before. Essential concepts include: * Simplifying Fractions * Adding Fractions * Subtracting Fractions * Multiplying Fractions * Dividing Fractions * Improper Fractions and Mixed Numbers * GCF (Greatest Common Factor) and LCM (Lowest Common Multiple)