This paper takes the other papers in this issue as ‘data’—in other words, as a source of observat... more This paper takes the other papers in this issue as ‘data’—in other words, as a source of observation and comment—and then proceeds to further discussion, analysis and surmise. By focusing in substantial measure on the notions of authority, explanation, contention and register, ideas which occur both explicitly and tacitly in different articles here, and in conjunction with the different natures and uses to which language data are put, I attempt to explore aspects of contemporary work on language and communication and how to some varying degree a search for essence sits at its heart.
We began this book with a claim that induction represents a phase and not simply a program. In ar... more We began this book with a claim that induction represents a phase and not simply a program. In arguing for recognizing induction as a unique period, we are reminded of the lessons of Aries (1996) and others about childhood. That research demonstrated how ‘childhood’ came to be constructed as a category during the nineteenth century, created in part to go against a then-prevailing view of a child as simply a ‘little adult’. This was done in order to argue for a protected period in the life of the young human, where particular things both should and should not happen. Yet, nowadays, childhood has become a ‘natural’ category.
Throughout much of her work, Jill Adler’s abiding interest has lain in the political implications... more Throughout much of her work, Jill Adler’s abiding interest has lain in the political implications of language in practice in mathematics classrooms, not solely because of the cultural importance ascribed to success in mathematics, but also because of there being some specific interactions of significance to be found within mathematics–language, our equally weighted hybrid term coined to signal their unseparateness. In the closing chapter of her 2001 book, she offers a number of questions that remain relevant fifteen years later: “If the costs of obtaining meaningful mathematical communication are so high, can they possibly be made widely available? Or does meaningful mathematics conversation as a route to mathematical learning, become, however unintentionally, the preserve of the privileged few? Expressed in more political terms: in whose interests is the dominant construction of mathematically rich and meaningful communication?” In this chapter, we explore these questions. To do so, we critically review some key ideas in Adler’s work, notably the concepts of dilemma and resource in relation to language. Our review of these ideas is informed by and elaborated through a Bakhtinian theoretical perspective.
Advances in mobile and distance learning book series, 2015
TouchCounts is a novel iPad application, one which makes full use of its multi-touch affordance t... more TouchCounts is a novel iPad application, one which makes full use of its multi-touch affordance to engage young children in aspects of the cultures of counting and adding/subtracting, by means of engagement with the combined sensory modalities of the visible, the audible and the tangible. Drawing on various excerpts with children aged three to six working with this App in educational settings (both day-care and kindergarten), we investigate how this trio of senses is utilised in children's activity with TouchCounts. Our work focuses in considerable part on issues of ordinality, as well as highlighting the particular significance of tangibility in the context of young children coming to terms with counting and early arithmetic.
Teachers' practices and learners' experiences school mathematics textbooks, schemes and n... more Teachers' practices and learners' experiences school mathematics textbooks, schemes and national curricula reflections.
This chapter, based both on pre-ICME-13 conference documents as well as on the author’s actual pa... more This chapter, based both on pre-ICME-13 conference documents as well as on the author’s actual panel presentation made at TSG 31, covers a range of themes concerned with the issues of ‘language data’ in mathematics education. It also addresses several instances from its history, including word problems, classroom language and transcription, in addition to the mathematics register, its syntax, semantics and pragmatics.
... Understanding can arise from the creative use of language (particularly metaphor), and from i... more ... Understanding can arise from the creative use of language (particularly metaphor), and from images ... of senses of words and other symbols which have particular and (often) variant meanings. ... Why do we use the same word, 'multiplication', for quite different operations: between ...
A CIP Catalogue record for this book is available from the Library of Congress. ISBN 1-4020-1147-... more A CIP Catalogue record for this book is available from the Library of Congress. ISBN 1-4020-1147-4 (HB) ISBN 1-4020-1148-2 (PB) Published by Kluwer Academic Publishers, PO Box 17, 3300 AA Dordrecht, The Netherlands. Sold and distributed in North, Central and ...
Studies on the foundations of mathematics and mathematical method should make substantial room fo... more Studies on the foundations of mathematics and mathematical method should make substantial room for psychology, indeed even for the aesthetic. (Henri Lebesgue, 1941, p. 122) Woe betide him who relies solely on mathematics. (Wassily Kandinsky, 1931, p. 351) Aesthetic ...
This paper takes the other papers in this issue as ‘data’—in other words, as a source of observat... more This paper takes the other papers in this issue as ‘data’—in other words, as a source of observation and comment—and then proceeds to further discussion, analysis and surmise. By focusing in substantial measure on the notions of authority, explanation, contention and register, ideas which occur both explicitly and tacitly in different articles here, and in conjunction with the different natures and uses to which language data are put, I attempt to explore aspects of contemporary work on language and communication and how to some varying degree a search for essence sits at its heart.
We began this book with a claim that induction represents a phase and not simply a program. In ar... more We began this book with a claim that induction represents a phase and not simply a program. In arguing for recognizing induction as a unique period, we are reminded of the lessons of Aries (1996) and others about childhood. That research demonstrated how ‘childhood’ came to be constructed as a category during the nineteenth century, created in part to go against a then-prevailing view of a child as simply a ‘little adult’. This was done in order to argue for a protected period in the life of the young human, where particular things both should and should not happen. Yet, nowadays, childhood has become a ‘natural’ category.
Throughout much of her work, Jill Adler’s abiding interest has lain in the political implications... more Throughout much of her work, Jill Adler’s abiding interest has lain in the political implications of language in practice in mathematics classrooms, not solely because of the cultural importance ascribed to success in mathematics, but also because of there being some specific interactions of significance to be found within mathematics–language, our equally weighted hybrid term coined to signal their unseparateness. In the closing chapter of her 2001 book, she offers a number of questions that remain relevant fifteen years later: “If the costs of obtaining meaningful mathematical communication are so high, can they possibly be made widely available? Or does meaningful mathematics conversation as a route to mathematical learning, become, however unintentionally, the preserve of the privileged few? Expressed in more political terms: in whose interests is the dominant construction of mathematically rich and meaningful communication?” In this chapter, we explore these questions. To do so, we critically review some key ideas in Adler’s work, notably the concepts of dilemma and resource in relation to language. Our review of these ideas is informed by and elaborated through a Bakhtinian theoretical perspective.
Advances in mobile and distance learning book series, 2015
TouchCounts is a novel iPad application, one which makes full use of its multi-touch affordance t... more TouchCounts is a novel iPad application, one which makes full use of its multi-touch affordance to engage young children in aspects of the cultures of counting and adding/subtracting, by means of engagement with the combined sensory modalities of the visible, the audible and the tangible. Drawing on various excerpts with children aged three to six working with this App in educational settings (both day-care and kindergarten), we investigate how this trio of senses is utilised in children's activity with TouchCounts. Our work focuses in considerable part on issues of ordinality, as well as highlighting the particular significance of tangibility in the context of young children coming to terms with counting and early arithmetic.
Teachers' practices and learners' experiences school mathematics textbooks, schemes and n... more Teachers' practices and learners' experiences school mathematics textbooks, schemes and national curricula reflections.
This chapter, based both on pre-ICME-13 conference documents as well as on the author’s actual pa... more This chapter, based both on pre-ICME-13 conference documents as well as on the author’s actual panel presentation made at TSG 31, covers a range of themes concerned with the issues of ‘language data’ in mathematics education. It also addresses several instances from its history, including word problems, classroom language and transcription, in addition to the mathematics register, its syntax, semantics and pragmatics.
... Understanding can arise from the creative use of language (particularly metaphor), and from i... more ... Understanding can arise from the creative use of language (particularly metaphor), and from images ... of senses of words and other symbols which have particular and (often) variant meanings. ... Why do we use the same word, 'multiplication', for quite different operations: between ...
A CIP Catalogue record for this book is available from the Library of Congress. ISBN 1-4020-1147-... more A CIP Catalogue record for this book is available from the Library of Congress. ISBN 1-4020-1147-4 (HB) ISBN 1-4020-1148-2 (PB) Published by Kluwer Academic Publishers, PO Box 17, 3300 AA Dordrecht, The Netherlands. Sold and distributed in North, Central and ...
Studies on the foundations of mathematics and mathematical method should make substantial room fo... more Studies on the foundations of mathematics and mathematical method should make substantial room for psychology, indeed even for the aesthetic. (Henri Lebesgue, 1941, p. 122) Woe betide him who relies solely on mathematics. (Wassily Kandinsky, 1931, p. 351) Aesthetic ...
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