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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.
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