Using Mathematics to Understand the World: How Culture Promotes Children's Mathematics offers fundamental insight into how mathematics permeates our lives as a way of representing and thinking about the world. Internationally renowned experts Terezinha Nunes and Peter Bryant examine research into children's mathematical development to show why it is important to distinguish between quantities, relations and numbers. Using Mathematics to Understand the World presents a theory about the development of children's quantitative reasoning and reveals why and how teaching about quantitative reasoning can be used to improve children's mathematical attainment in school. It describes how learning about the analytical meaning of numbers is established as part of mathematics at school but quantitative reasoning is emphasized less even though it is increasingly acclaimed as essential for thinking mathematically and for using mathematics to understand the world. This essential text is for all students of mathematics education, developmental psychology and cognitive psychology. By including activities for parents and professionals to try themselves, it may help you to recognize your own quantitative reasoning.

Using Mathematics to Understand the World: How Culture Promotes Children's Mathematics offers fundamental insight into how mathematics permeates our lives as a way of representing and thinking about the world. Internationally renowned experts Terezinha Nunes and Peter Bryant examine research into children's mathematical development to show why it is important to distinguish between quantities, relations and numbers. Using Mathematics to Understand the World presents a theory about the development of children's quantitative reasoning and reveals why and how teaching about quantitative reasoning can be used to improve children's mathematical attainment in school. It describes how learning about the analytical meaning of numbers is established as part of mathematics at school but quantitative reasoning is emphasized less even though it is increasingly acclaimed as essential for thinking mathematically and for using mathematics to understand the world. This essential text is for all students of mathematics education, developmental psychology and cognitive psychology. By including activities for parents and professionals to try themselves, it may help you to recognize your own quantitative reasoning.

With reports from several studies showing the benefits of teaching young children about morphemes, this book is essential reading for anyone concerned with helping children to read and write.

By breaking words down into chunks of meaning that can be analyzed as complete units rather than as strings of individual letters, children are better able to make sense of the often contradictory spelling and reading rules of English. As a result, their enjoyment of learning about words increases, and their literacy skills improve. Written by leading researchers for trainee teachers, practising teachers and interested parents, this highly accessible and innovative book provides sound, evidence-based advice and materials that can be used to help teach children about morphemes, and highlights the beneficial effects of this approach.

Words consist of units of meaning, called morphemes. These morphemes have a striking effect on spelling which has been largely neglected until now. For example, nouns that end in "-ian" are words which refer to people, and so when this ending is attached to "magic" we can tell that the resulting word means someone who produces magic. Knowledge of this rule, therefore, helps us with spelling: it tells us that this word is spelled as "magician" and not as "magicion."
This new book by Terezinha Nunes and Peter Bryant and their colleagues shows how important and necessary it is for children to find out about morphemes when they are learning to read and to spell. The book concentrates on how to teach children about the morphemic structure of words and on the beneficial effects of this teaching for children's spelling and for the breadth of their vocabulary. It reports the results of several studies in the laboratory and in school classrooms of the effects of teaching children about a wide variety of morphemes. These projects showed that school children enjoy learning about morphemes and that this learning improves their spelling and their vocabulary as well. The book, therefore, suggests new directions in the teaching of literacy. It should be read by everyone concerned with helping children to learn to read and to write.

PETER BRYANT & TEREZINHA NUNES The time that it takes children to learn to read varies greatly between different orthographies, as the chapter by Sprenger-Charolles clearly shows, and so do the difficulties that they encounter in learning about their own orthography. Nevertheless most people, who have the chance to learn to read, do in the end read well enough, even though a large number experience some significant difficulties on the way. Most of them eventually become reasonably efficient spellers too, even though they go on make spelling mistakes (at any rate if they are English speakers) for the rest of their lives. So, the majority of humans plainly does have intellectual resources that are needed for reading and writing, but it does not always find these resources easy to marshal. What are these resources? Do any of them have to be acquired? Do different orthographies make quite different demands on the intellect? Do people differ significantly from each other in the strength and accessibility of these resources? If they do, are these differences an important factor in determining children's success in learning to read and write? These are the main questions that the different chapters in this section on Basic Processes set out to answer.

Literacy research has continued to develop at a rapid pace in these last five years of the millennium. New ideas about how children learn to read have led to a better understanding of the causes of progress and failure in the mastery of literacy, with repercussions for children's assessment and teacher education. These new discoveries also allow teachers to transcend the old debates in reading instruction (phonics versus whole language) and offer the path to a synthesis. At the same time, research with teachers about their own implementation of methods and the development of their own knowledge about the teaching of literacy has produced a fresh analysis of the practice of literacy teaching. Inspired by these developments, teachers, teacher educators and researchers worked together to produce this volume, which promotes the integration of literacy research and practice.

Literacy research has continued to develop at a rapid pace in these last five years of the millennium. New ideas about how children learn to read have led to a better understanding of the causes of progress and failure in the mastery of literacy, with repercussions for children's assessment and teacher education. These new discoveries also allow teachers to transcend the old debates in reading instruction (phonics versus whole language) and offer the path to a synthesis. At the same time, research with teachers about their own implementation of methods and the development of their own knowledge about the teaching of literacy has produced a fresh analysis of the practice of literacy teaching. Inspired by these developments, teachers, teacher educators and researchers worked together to produce this volume, which promotes the integration of literacy research and practice.

The authors of this volume, which is newly available in paperback, all hold the view that mathematics is a form of intelligent problem solving which plays an important part in children's lives outside the classroom as well as in it. Learning and Teaching Mathematics provides an exciting account of recent and radically different research on teaching and learning mathematics which will have a far reaching effect on views about mathematical education.

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PETER BRYANT & TEREZINHA NUNES The time that it takes children to learn to read varies greatly between different orthographies, as the chapter by Sprenger-Charolles clearly shows, and so do the difficulties that they encounter in learning about their own orthography. Nevertheless most people, who have the chance to learn to read, do in the end read well enough, even though a large number experience some significant difficulties on the way. Most of them eventually become reasonably efficient spellers too, even though they go on make spelling mistakes (at any rate if they are English speakers) for the rest of their lives. So, the majority of humans plainly does have intellectual resources that are needed for reading and writing, but it does not always find these resources easy to marshal. What are these resources? Do any of them have to be acquired? Do different orthographies make quite different demands on the intellect? Do people differ significantly from each other in the strength and accessibility of these resources? If they do, are these differences an important factor in determining children's success in learning to read and write? These are the main questions that the different chapters in this section on Basic Processes set out to answer.

This book offers a theory for the analysis of how children learn and are taught about whole numbers. Two meanings of numbers are distinguished - the analytical meaning, defined by the number system, and the representational meaning, identified by the use of numbers as conventional signs that stand for quantities. This framework makes it possible to compare different approaches to making numbers meaningful in the classroom and contrast the outcomes of these diverse aspects of teaching. The book identifies themes and trends in empirical research on the teaching and learning of whole numbers since the launch of the major journals in mathematics education research in the 1970s. It documents a shift in focus in the teaching of arithmetic from research about teaching written algorithms to teaching arithmetic in ways that result in flexible approaches to calculation. The analysis of studies on quantitative reasoning reveals classifications of problem types that are related to different cognitive demands and rates of success in both additive and multiplicative reasoning. Three different approaches to quantitative reasoning education illustrate current thinking on teaching problem solving: teaching reasoning before arithmetic, schema-based instruction, and the use of pre-designed diagrams. The book also includes a summary of contemporary approaches to the description of the knowledge of numbers and arithmetic that teachers need to be effective teachers of these aspects of mathematics in primary school. The concluding section includes a brief summary of the major themes addressed and the challenges for the future. The new theoretical framework presented offers researchers in mathematics education novel insights into the differences between empirical studies in this domain. At the same time the description of the two meanings of numbers helps teachers distinguish between the different aims of teaching about numbers supported by diverse methods used in primary school. The framework is a valuable tool for comparing the different methods and identifying the various assumptions about teaching and learning.

In Hungarian the differences between short and long consonants are subtle due to various factors (e.g. debate whether length is a distinctive feature of the language, arbitrary lengthening of short consonants or abbreviating of long ones), thus it is difficult to distinguish between them. However, if distinguishing between the pronunciation of short and long consonantal sounds is difficult, their representations as single and double letters by means of spelling must be even more difficult for children. The present study aims to find out if and to what extent does knowledge of linguistic constraints aid Hungarian children's spelling by investigating whether they find it difficult to master the function between consonant length and their manifestations in spelling as singletons and doublets. By shedding light to these questions the study's purpose is to contribute to children's understanding of the functional relationship between long consonants and doublets.

People who learn to solve problems ‘on the job’ often have to do it differently from people who learn in theory. Practical knowledge and theoretical knowledge is different in some ways but similar in other ways - or else one would end up with wrong solutions to the problems. Mathematics is also like this. People who learn to calculate, for example, because they are involved in commerce frequently have a more practical way of doing mathematics than the way we are taught at school. This book is about the differences between what we call practical knowledge of mathematics - that is street mathematics - and mathematics learned in school, which is not learned in practice. The authors look at the differences between these two ways of solving mathematical problems and discuss their advantages and disadvantages. They also discuss ways of trying to put theory and practice together in mathematics teaching.