David Pimm - Academia.edu (original) (raw)
Papers by David Pimm
Commentary on Part II of Mathematical Challenges For All: Making Mathematics Difficult? What Could Make a Mathematical Challenge Challenging?
Springer eBooks, 2023
International Journal of Science and Mathematics Education, Sep 21, 2007
This opening article of the Special Issue makes an argument for parallel definitions of scientifi... more This opening article of the Special Issue makes an argument for parallel definitions of scientific literacy and mathematical literacy that have shared features: importance of general cognitive and metacognitive abilities and reasoning/thinking and discipline-specific language, habits-of-mind/emotional dispositions, and information communication technology strategies to prepare people for adult life and democratic citizenship. These frameworks provide potential insights into research and pedagogy. Furthermore, they provide guidelines for second-generation standards, curriculum development and assessment so as not to overlook or underemphasize the fundamental literacy component of mathematical and scientific literacy for all students, which can result in fuller participation in the public debate about science, mathematics, technology, society, and environment issues.
Authority, explanation, contention and register: language data and the surface search for essence
Zdm – Mathematics Education, Oct 17, 2014
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.
Some features of the mathematical writing system
Another Psychology of Mathematics Education
Taylor & Francis eBooks, Feb 16, 2010
Digital experiences in mathematics education, May 8, 2020
The development of touchscreen technology is providing alternative ways for learners to conceptua... more The development of touchscreen technology is providing alternative ways for learners to conceptualise, visualise, experiment with and communicate about mathematical ideas and relationships. While the multi-touch affordances of touchscreens enable children to produce and transform 'screen objects' with their fingers (by means of varied forms of pressure and propulsion), they also invoke an intricate interrelationship between the user's fingers and the surface of the device itself. Drawing on a half-hour video recording of two primary school children using the TouchTimes iPad app (about multiplication) for the first time, we examine how mutually interactive the children's fingers were, both with each other and with this particular touchscreen technology, not least their combining in ways which challenge the seemingly clear distinction between digital and physical tools, when viewed as discrete and disjoint entities. We also explore fingers being used as objects in themselves, while examining ways of doing multiplication digitally with fingers, with a particular focus on the singular role of fingers as physical intermediaries. Our aim is to consider possible ways to develop well-educated fingers in relation to engaging with mathematics. Keywords iPad technology. Elementary. Touch. Fingers. Multiplication. Tactile. Manipulative. Digits. TouchTimes. Chirality Put your Finger into every Bottle, to feel whether it be full, which is the surest Way, for feeling hath no fellow. (Swift 1745, p. 32) Digital Experiences in Mathematics Education
Springer eBooks, 2007
, except for brief excerpts in connection with reviews or scholarly analysis. Use in connection w... more , except for brief excerpts in connection with reviews or scholarly analysis. Use in connection with any form of information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed is forbidden. The use in this publication of trade names, trademarks, service marks, and similar terms, even if they are not identified as such, is not to be taken as an expression of opinion as to whether or not they are subject to proprietary rights.
Audience, Style and Criticism
Princeton University Press eBooks, Dec 31, 2011
In this paper, we explore a richer sense of finger gnosis (finger knowledge) with respect to thre... more In this paper, we explore a richer sense of finger gnosis (finger knowledge) with respect to three-and four-year-olds' interactions with a novel iPad application (TouchCounts), focusing on their responses to an "inverse subitising" task. The direct and tactile nature of their engagement with TouchCounts leads to a striking shift from incrementing using the index finger to deployment of several fingers all-at-once (in a cardinal touch gesture) to achieve a given target number that is then spoken by the iPad. This form of finger representation differs from the more ordinally-based differentiation of fingers that is discussed in the psychology literature.
Making Sense of Induction: Looking across International Cases
Springer eBooks, 2003
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.
Bakhtin and Some Dilemmas of Mathematics–Language
Springer eBooks, 2016
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.
Whatever Be Their Number
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.
Teaching and learning school mathematics : a reader
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.
New ICMI studies series, 2018
Routledge Revivals: Speaking Mathematically (1987): Communication in Mathematics Clasrooms
Sixty Years (or so) of Language Data in Mathematics Education
ICME-13 monographs, 2018
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.
Interchange, Dec 1, 1993
This paper is a rejoinder to John Wilson's piece "Power, Paranoia, and Education" which appeared ... more This paper is a rejoinder to John Wilson's piece "Power, Paranoia, and Education" which appeared in Interchange in 1991. Following a brief summary of Wilson's piece, I criticize his article under two major headings: some reactions to his psychological claims and terminology, and Wilson's style and form of argument. I conclude by offering some alternative work and observations in the same area, but from quite a different standpoint.
Symbols and Meanings in School Mathematics
Routledge eBooks, Nov 1, 2002
... 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 ...
Comprehensive Teacher Induction
Springer eBooks, 2003
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 ...
Introduction and Acknowledgements
International Journal of Science and Mathematics Education, Aug 25, 2007
Commentary on Part II of Mathematical Challenges For All: Making Mathematics Difficult? What Could Make a Mathematical Challenge Challenging?
Springer eBooks, 2023
International Journal of Science and Mathematics Education, Sep 21, 2007
This opening article of the Special Issue makes an argument for parallel definitions of scientifi... more This opening article of the Special Issue makes an argument for parallel definitions of scientific literacy and mathematical literacy that have shared features: importance of general cognitive and metacognitive abilities and reasoning/thinking and discipline-specific language, habits-of-mind/emotional dispositions, and information communication technology strategies to prepare people for adult life and democratic citizenship. These frameworks provide potential insights into research and pedagogy. Furthermore, they provide guidelines for second-generation standards, curriculum development and assessment so as not to overlook or underemphasize the fundamental literacy component of mathematical and scientific literacy for all students, which can result in fuller participation in the public debate about science, mathematics, technology, society, and environment issues.
Authority, explanation, contention and register: language data and the surface search for essence
Zdm – Mathematics Education, Oct 17, 2014
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.
Some features of the mathematical writing system
Another Psychology of Mathematics Education
Taylor & Francis eBooks, Feb 16, 2010
Digital experiences in mathematics education, May 8, 2020
The development of touchscreen technology is providing alternative ways for learners to conceptua... more The development of touchscreen technology is providing alternative ways for learners to conceptualise, visualise, experiment with and communicate about mathematical ideas and relationships. While the multi-touch affordances of touchscreens enable children to produce and transform 'screen objects' with their fingers (by means of varied forms of pressure and propulsion), they also invoke an intricate interrelationship between the user's fingers and the surface of the device itself. Drawing on a half-hour video recording of two primary school children using the TouchTimes iPad app (about multiplication) for the first time, we examine how mutually interactive the children's fingers were, both with each other and with this particular touchscreen technology, not least their combining in ways which challenge the seemingly clear distinction between digital and physical tools, when viewed as discrete and disjoint entities. We also explore fingers being used as objects in themselves, while examining ways of doing multiplication digitally with fingers, with a particular focus on the singular role of fingers as physical intermediaries. Our aim is to consider possible ways to develop well-educated fingers in relation to engaging with mathematics. Keywords iPad technology. Elementary. Touch. Fingers. Multiplication. Tactile. Manipulative. Digits. TouchTimes. Chirality Put your Finger into every Bottle, to feel whether it be full, which is the surest Way, for feeling hath no fellow. (Swift 1745, p. 32) Digital Experiences in Mathematics Education
Springer eBooks, 2007
, except for brief excerpts in connection with reviews or scholarly analysis. Use in connection w... more , except for brief excerpts in connection with reviews or scholarly analysis. Use in connection with any form of information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed is forbidden. The use in this publication of trade names, trademarks, service marks, and similar terms, even if they are not identified as such, is not to be taken as an expression of opinion as to whether or not they are subject to proprietary rights.
Audience, Style and Criticism
Princeton University Press eBooks, Dec 31, 2011
In this paper, we explore a richer sense of finger gnosis (finger knowledge) with respect to thre... more In this paper, we explore a richer sense of finger gnosis (finger knowledge) with respect to three-and four-year-olds' interactions with a novel iPad application (TouchCounts), focusing on their responses to an "inverse subitising" task. The direct and tactile nature of their engagement with TouchCounts leads to a striking shift from incrementing using the index finger to deployment of several fingers all-at-once (in a cardinal touch gesture) to achieve a given target number that is then spoken by the iPad. This form of finger representation differs from the more ordinally-based differentiation of fingers that is discussed in the psychology literature.
Making Sense of Induction: Looking across International Cases
Springer eBooks, 2003
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.
Bakhtin and Some Dilemmas of Mathematics–Language
Springer eBooks, 2016
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.
Whatever Be Their Number
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.
Teaching and learning school mathematics : a reader
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.
New ICMI studies series, 2018
Routledge Revivals: Speaking Mathematically (1987): Communication in Mathematics Clasrooms
Sixty Years (or so) of Language Data in Mathematics Education
ICME-13 monographs, 2018
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.
Interchange, Dec 1, 1993
This paper is a rejoinder to John Wilson's piece "Power, Paranoia, and Education" which appeared ... more This paper is a rejoinder to John Wilson's piece "Power, Paranoia, and Education" which appeared in Interchange in 1991. Following a brief summary of Wilson's piece, I criticize his article under two major headings: some reactions to his psychological claims and terminology, and Wilson's style and form of argument. I conclude by offering some alternative work and observations in the same area, but from quite a different standpoint.
Symbols and Meanings in School Mathematics
Routledge eBooks, Nov 1, 2002
... 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 ...
Comprehensive Teacher Induction
Springer eBooks, 2003
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 ...
Introduction and Acknowledgements
International Journal of Science and Mathematics Education, Aug 25, 2007